Unless otherwise specified, all talks are held starting at 1.15pm in the Theory Library on the 4th floor of Physics East.

Everyone is encouraged to ask questions during the talk. You are welcome to leave when you need to, otherwise the talk will usually wrap up by 2.30pm, at which point there will be biscuits.

Thursday 25th April 2024: Martin Speight (University of Leeds)

Soliton crystals

Topological solitons are smooth spatially localized lump-like solutions of nonlinear field theories that can move around and interact in a particle-like manner. Examples are superconducting vortices, magnetic monopoles, domain walls and skyrmions. In condensed matter contexts they are usually observed in the laboratory in the form of spatially periodic arrays, analogous to crystals. The Abrikosov vortex lattice in type II superconductors is a prominent and influential example. Theoretical studies of soliton crystals almost always impose some plausible period lattice geometry (cubic, square or triangular) a priori, and optimize only over the size of the unit cell. I will argue that this assumption is, in general, ill-founded and that one should really optimize the system over the space of fields _and_ period lattices. The latter variation has an elegant reformulation in terms of the stress tensor of the field theory. When implemented numerically, one finds that much more exotic period lattices are possible than those conventionally imposed. The ideas will be illustrated by concentrating on skyrmion crystals in 2 and 3 spatial dimensions.

Joint work with Derek Harland and Paul Leask (also at Leeds).

Thursday 2nd May 2024: Alexander Mietke (University of Oxford)

How constraints and chirality guide self-organisation in living systems

Living matter has the fascinating ability to autonomously organise itself in space and time. Self-organisation refers typically to the fact that local interactions among microscopic agents enable an emerging dynamic that is seemingly coordinated on macroscopic length scales much larger than the agents. Classical examples are the interactions of actin and actin-binding molecules within the eukaryotic cell cortex, of cells within tissues or of entire organisms interacting within populations. While details of each self-organisation phenomenon will depend on the concrete biological system, mechanistic insights can still be developed by identifying generic features that are shared among systems – an abstraction that physics approaches provide many useful tools for. Two such generic features this talk focuses on are mechanical constraints and broken chiral symmetry, which are both ubiquitous in biological systems. Specifically, we will discuss the impact of mechanical constraints in guiding tissue morphogenesis in the flour beetle, the role of chirality in guiding the emergent properties of living crystals made of starfish embryos, as well as a mechanism to robustly establish a left-right body axis during nematode development when both, mechanical constraints and chirality, act in concert.

Thursday 9th May 2024: Orazio Scarlatella (University of Cambridge)

Strongly-coupled atomic arrays: a dynamical mean-field theory study

Subwavelength arrays of quantum emitters have emerged as an interesting platform displaying prominent collective effects. In this talk I will discuss the steady-states of such arrays under coherent driving, realizing an open quantum many-body problem with long range interactions and dissipation. I will discuss a Dynamical Mean Field Theory approach to the problem, for which few theoretical methods are available. I will show that the combination of dipolar interactions and regular geometry have a dramatic effect on the spectrum of emitted light in the strong-drive regime: the famous Mollow triplet characterizing the emission of a single atom develops a structured broadening with flat sidebands, distinguishing the emission of atomic arrays from that of disordered atomic clouds or of non-interacting emitters. For moderate drive strengths instead, I will show that the steady-state is influenced by the existence of guided modes in the single-particle regime that are completely decoupled from dissipation. 

Thursday 25th July 2024: Bryce Gadway (Penn State)

NB unusual time of 11am!

Synthetic dimensions in Rydberg atom arrays

Arrays of dipolar-interacting spins – magnetic atoms, polar molecules, and Rydberg atoms – represent powerful and versatile platforms for analog quantum simulation experiments. The internal state dynamics in such dipolar arrays provide a natural setting to explore problems of equilibrium and non-equilibrium quantum magnetism. The presence of many different internal states of the atoms and molecules in such experiments enables studies of large-spin magnetism, but also holds promise for more general quantum simulation studies. Here we describe how the simple addition of multi-frequency microwave fields to Rydberg arrays enables highly controllable studies of few- and many-body dynamics along an internal-state “synthetic” dimension. I’ll discuss several early studies in the Rydberg synthetic dimension platform, touching on interaction-driven phenomena relevant to topology, artificial gauge fields, and disorder-induced localization. Looking forward, such microwave manipulation opens up several new directions for exploring complex, driven quantum matter in dipolar arrays.

Wednesday 21st August 2024: Richard Brierley (Nature Physics) — Physics East Seminar Room 217

NB unusual time of 11am and unusual venue!

Inside Nature Physics

For nearly twenty years Nature Physics has aimed to publish high-quality research, reviews and commentary that are accessible and of interest to the whole physics community. I will give an introduction to the journal, its editors and how it fits into the wider Nature portfolio. I’ll also try to give insight into the editorial process and how we make our decisions.

Thursday 26th September 2024: Laura Messio (Sorbonne University)

Overview of the possibilities of high temperature series expansions

In the search for exotic properties of spin lattices, many numerical methods focus on the ground state and on the low-energy excitations of a model. Here, we use the opposite approach, with high temperature series expansions. The coefficients of the free energy, the specific heat or the magnetic susceptibility series are obtained up to beta^20 (depending on the model complexity). But the convergence radius limits the range of temperature where information can been obtained by simple summation. Thus, alternative methods are required. One of them is the entropy method, that uses some hypothesis on the nature of the ground state to reconstruct thermodynamic quantities over the whole temperature range. This method has been used on several compounds to propose exchange parameter values. When a finite temperature phase transition occurs, a singularity forbids to use the entropy method, but then, informations on the critical exponents and on the critical temperature can be extracted. A review of these methods and their limitations, together with some applications, will be presented.

Thursday 3rd October 2024: Nick Manton (Cambridge)

NB unusual time of 1.30pm!

Skyrme’s Original Skyrmions

Tony Skyrme (1922-87) spent the the majority of his career at Birmingham. His main interest was nuclear physics, which at that time was close to elementary particle physics. He proposed a model for the interaction of nucleons (protons and neutrons) inside larger nuclei; this is the “Skyrme force”, still regularly used by nuclear theorists. But his most bold and original idea was the Skyrmion, a model for an individual nucleon created out of a topologically twisted configuration of a nonlinear pion field. When a Skyrmion’s rotational motion is quantised, the lowest-energy states are naturally identified with spin-half states of protons or neutrons. There has been much progress since Skyrme’s time on multi-Skyrmion solutions, modelling medium-sized nuclei like Carbon-12. These solutions have fascinating symmetries that constrain their quantised rotational and vibrational excitations, matching known nuclear spectra quite well. A current challenge is to model nuclear reactions in terms of Skyrmion collisions.

Thursday 10th October 2024: Martin Völkl (Birmingham)

Learning about QCD from heavy-ion collisions

Understanding the properties of the strong interaction from first principles is a difficult endeavour. The large coupling strength at energies usually found in nature, as well as the fact that quarks and gluons are confined in hadrons mean that usual perturbative methods can often not be applied. Heavy-ion collisions at high energies, such as those measured by the ALICE detector at the LHC provide a laboratory to understand quantum chromodynamics in a vastly different regime. The quark-gluon plasma produced there is a state of equilibrated, deconfined, strongly interacting matter. During this seminar we will discuss what how we can learn about QCD from these collisions, what we have found out so far, and which questions remain to be explored in the future.

Thursday 17th October 2024: Eli Hawkins (York)

Quantization of Angular Momentum

I shall outline the mathematical perspective of Strict Deformation Quantization. In this context, I can prove that for a well-behaved quantization of the 2-sphere, the values of the quantization parameter (formally, Planck’s constant) are restricted. This is a robust version of the quantization of angular momentum that applies when rotational symmetry is only approximate.

Thursday 24th October 2024: Douglas Abraham (Oxford)

Phase Separation in Uni-axial Ferromagnets: Recent exact results

The phenomenological view from the 19th century of phase separation in simple fluids and the associated structure of the resulting interface will be described, along with its shortcomings. The statistical-mechanical discussion of these matters begins with the work of Peierls (formerly of this department) and continues with that of Griffiths and Dobrushin. This is combined with the exact solution approach of Kaufman and of Lieb, Mattis and Schultz to obtain new results. For the first time, an approach to the Gibbs dividing surface is given, as well as a way to incorporate fluctuations in that picture. A short discussion will be given of how the calculations work, beginning with Kaufman.

Thursday 7th November 2024: Enrico Amico (Birmingham)

Higher-order connectomics of human brain function

Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. In this talk I will introduce a novel approach to the study of interacting dynamics in brain connectomics, based on higher-order interaction models. Our method builds on recent advances in simplicial complexes and topological data analysis, with the overarching goal of exploring macro-scale and time-dependent higher-order processes in human brain networks. I will present our preliminary findings along these lines, and discuss limitations and potential future directions for the exciting field of higher-order brain connectomics.

Thursday 14th November 2024: Daniele Toniolo (UCL)

Stability of slow Hamiltonian dynamics and Dynamical generation of α-Rényi entropies

In this talk I will present two results. The first regards the stability of the slow dynamics for spin systems from the point of view of Lieb-Robinson (L-R) bounds. L-R bounds quantify the speed at which a generic local operator spreads across the system due to Heisenberg evolution. A slow dynamics happens when to spread across a region the operator takes a time proportional to the exponential of such region. This is relevant in particular for so called many-body localized systems. In this case when the system is perturbed, for example with the insertion of perturbations that would lead to regions of fast dynamics, I will show that the dynamics remains locally slow. With this theory I can also consider the non perturbative scenario of the junction among systems with fast and slow dynamics. This is based upon [1].

The second result that I will discuss is the dynamical generation of entanglement as quantified by α-Rényi entropies, with 0<α<1, including the case α=1 of the von Neuman entropy, starting from a generic product state. I will show that this follows from the Lieb-Robinson bound of the dynamics. For a generic local spin system in one dimension then the entanglement grows at most linearly in time. On the other hand when a slow dynamics is considered, like in the first part of the talk, I will obtain the log t-law of entanglement that has been shown before for MBL systems only by numerics or by assuming the existence of local integrals of motions. The second part of the talk is based upon [2], and [3].

[1] D. Toniolo, S. Bose, arXiv:2405.05958

[2] D. Toniolo, S. Bose, arXiv:2408.00743

[3] D. Toniolo, S. Bose, arXiv:2408.02016

Thursday 21st November 2024: Michele Simoncelli (Cambridge)

Unified theories of transport in solids: from crystals to glasses, and from diffusion to viscous hydrodynamics

Crystals and glasses have dramatically different properties which intrigued scientists long before the development of atomistic theories, and nowadays play a pivotal role in a variety of technologies. I will explore the quantum mechanisms that determine the macroscopic conduction properties of solids, extending established formulations[1] and developing the computational framework[2] to solve them. Starting from a density matrix formalism, I will show how the semiclassical Boltzmann equation for heat transport is missing a tunneling term that becomes pivotal in disordered or defective materials[3]. Second, I will discuss how this formulation can be extended to describe coupled transport phenomena — involving, e.g., heat and light, charge, or spin — which are critical for applications ranging from zero-carbon jet engines[4] to neuromorphic computing. Finally, I will elucidate how the microscopic transport equations can be coarse-grained into mesoscopic, viscous equations; these transcend ordinary diffusion, rationalizing the recent observation of hydrodynamic behaviour[5] and paving the way for its control and technological exploitation.

[1] M. Simoncelli, N. Marzari, and F. Mauri, Phys. Rev. X 12, 041011 (2022).
[2] B. Póta, P. Ahlawat, G. Csányi, and M. Simoncelli, arXiv:2408.00755.
[3] A. F. Harper, K. Iwanowski, W. C. Witt, M. C. Payne, and M. Simoncelli, Phys. Rev. Mater. 8, 043601 (2024).
[4] A. Pazhedath, L. Bastonero, N. Marzari, and M. Simoncelli, Phys. Rev. Appl. 22, 024064 (2024).
[5] J. Dragašević and M. Simoncelli, arXiv:2303.12777.

Thursday 28th November 2024: Benedikt Placke (Oxford)

Topological Quantum Spin Glasses: the low temperature phase of qLDPC codes with expansion

Understanding the nature of glasses and the glass transition remains one of the most important unsolved problems in statistical mechanics, with wide ranging implications, from materials to machine learning and optimisation problems. Here, we establish a rigorous connection between (spin-)glass order and expansion, a property of classical and quantum error-correcting codes defined on non-Euclidean graphs that guarantees efficient decodability. This allows us to rigorously prove the existence of finite-temperature spin glass order in classical error correcting codes, as well as the existence of a novel form of topological quantum spin glass order in quantum error correcting codes with expansion. Topological Quantum Spin Glasses are characterized by the same complex (free) energy landscape as their classical counterparts, but with every local and global minimum corresponding to a topologically ordered quantum state. We complement our rigorous results by extensive numerical studies and argue that (topological) glassiness may be observed in a large class of (quantum) error correcting codes.

Thursday 5th December 2024: Nick Jones (Oxford)

Symmetry, topology and entanglement in the chiral clock family

Global symmetries greatly enrich the phase diagram of quantum many-body systems. As well as symmetry-breaking phases, symmetry-protected topological (SPT) phases have symmetric ground states that cannot be connected to a trivial state without a phase transition. There can also be symmetry-enriched critical points between these phases of matter, and ‘unnecessary’ critical points. I will demonstrate these phenomena in phase diagrams constructed using an integrable family of N-state chiral clock chains, where an underlying Onsager algebra allows for many exact results.

The talk is based on joint work with Abhishodh Prakash and Paul Fendley arXiv:2406.01680 and ongoing work.

Thursday 12th December 2024: Ilya Gruzberg (Ohio State)

Multifractals and conformal invariance at Anderson transitions

Multifractal measures arise in such diverse subjects as dynamical chaos, weather and climate, turbulence, fractal growth, critical clusters in statistical mechanics, disordered magnets and other random critical points, Anderson transitions, mathematical finance, random energy landscapes, Gaussian multiplicative chaos, and rigorous approaches to conformal field theory. A multifractal measure is characterized by a continuous spectrum of multifractal exponents Δ_q that describe the scaling of the moments of the measure with the system size. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators with scaling dimensions Δ_q in a field-theory description of the transitions. The operators O_q satisfy the so-called Abelian fusion expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum Δ_q must be quadratic in its arguments in any dimension d ≥ 2 (parabolicity of the spectrum). We confront this finding with available numerical and analytical data for various Anderson transitions that unambiguously show clear deviations of the multifractal spectra Δ_q from parabolicity and discuss possible reasons for the discrepancy.

Thursday 23rd January 2025: Shovan Dutta (Raman Research Institute, Bangalore)

Anti-thermalization: Heating by cooling and vice versa

Common intuition tells us that if one part of a connected system is cooled continuously, the other parts should also cool down. This is at the heart of sympathetic cooling, a key experimental protocol for preparing synthetic quantum matter. I will talk about a surprising scenario where the fate of the system is reversed, namely, as one part is cooled to its ground state, the other part heats towards its most excited state, realizing an “automated Maxwell’s demon.” This anti-thermal dynamics arise in a broad class of number-conserving systems and can be tested with two qubits in existing setups. We show that the mechanism allows one to prepare a number of exotic states that are otherwise unstable, including mid-spectrum nonclassical states and highly athermal states where subspaces heat in the presence of overall cooling. These findings reveal a rich interplay between symmetry and resonance effects in the dynamics of thermalization.

Ref: arXiv:2412.07630

Thursday 30th January 2025: Oleksandr Gamayun (London Institute for Mathematical Sciences)

Effective form factors for asymptotics of finite-temperature correlation functions

The behaviour of correlation functions in one-dimensional quantum systems at zero temperature is now very well understood in terms of linear and non-linear Luttinger models. The “microscopic” justification of these models consists in the exact accounting for soft-mode excitations around the vacuum state and at most few high-energy excitations. At finite temperature, or more generically for finite entropy states, this direct approach is not strictly applicable due to the different structure of “soft” excitations. We focus on physical systems where the strong interaction makes it possible to present correlation functions in terms of Fredholm determinants of the generalized sine kernels. Based on “microscopic” resummations, we develop a phenomenological approach of the effective form factors that allows us to describe the asymptotic behaviour of these Fredholm determinants. We demonstrate how this works for correlation functions in the XY model, mobile impurity, and the generic Toeplitz determinants.

Thursday 13th February 2025: Pavel Kos (MPQ Munich)

Dual-isometric Projected Entangled Pair States

Efficient characterization of higher dimensional many-body physical states presents significant challenges. In this talk, I will discuss a new class of Project Entangled Pair State (PEPS) that incorporates two isometric conditions. This new class of tensor network states facilitates the efficient calculation of general local observables and certain two-point correlation functions, which have previously been shown to be intractable for general PEPS, or PEPS with only a single isometric constraint. Despite incorporating two isometric conditions, the class preserves the rich physical structure while enhancing the analytical capabilities. It features a large set of tunable parameters, with only a subleading correction compared to that of general PEPS. It can encode universal quantum computations and can represent a transition from topological to trivial order.

Based on X. Yu, J. I. Cirac, P. Kos*, G. Styliaris* Phys. Rev. Lett. 133, 190401 (2024) [arXiv:2404.16783].

Thursday 20th February 2025: Janne Ruostekoski (Lancaster University)

Long-range interactions between atoms: radiative quantum phase transitions, unconventional interactions and macroscopic responses

Light-matter interfaces with periodic configurations can exhibit strong cooperative responses. We demonstrate how long-range interactions between atoms can lead to quantum phase transitions, realising many-body extensions of well-studied canonical phase transition models, unconventional interactions, and macroscopic behaviour that is not expected to be found in natural atomic media, such as negative refraction of light.

Thursday 27th February 2025: Paul Newman (University of Birmingham)

The Quark and Gluon Structure of Matter and the Electron Ion Collider

An early perspective is presented on the Electron-Ion Collider (EIC), which is currently under intense development towards realisation in the early 2030s at the Brookhaven National Laboratory in the USA. After a historically-themed reminder of Deep Inelastic lepton-hadron Scattering and how it leads us to an understanding of proton structure, overviews of the physics motivation, accelerator and detector concepts of the EIC are given. Finally, the international ‘ePIC’ experimental collaboration is introduced, including the substantial involvement of the Birmingham nuclear and particle physics groups.

Thursday 6th March 2025: Juan P. Garrahan (University of Nottingham)

Generative diffusion models, classical and quantum

Diffusion models are a class of generative machine learning methods used to sample a target distribution by transforming samples of a trivial distribution using a learned stochastic dynamics. I will discuss this problem from the point of view of non-equilibrium statistical mechanics. I will show how by using tensor networks one can efficiently define and sample (discrete) diffusion models without explicitly having to solve a stochastic differential equation. I will then extend some of these ideas to quantum stochastic dynamics, discussing similarities and differences between the classical and quantum cases.

Thursday 13th March 2025: Thomas Hird (University of Birmingham)

Single Photon Storage with Optimised Atom-Light Interactions

An optical quantum memory, a device capable of storing and retrieving an arbitrary quantum state at the single photon level, is a cornerstone of photonic quantum technologies. These technologies have applications ranging from synchronising processing steps in optical quantum computers to constructing quantum repeaters for faithful transmission of quantum states over long distances.

In this seminar, I will discuss the foundations and plans of my newly created group at Birmingham, focusing on storing a photon as a delocalised excitation in an atomic ensemble. This excitation can be modelled as a matter-bosonic excitation, where the time-varying atomic interaction acts like a non-stationary beam splitter in high-dimensional qudit space. I will describe my investigations into novel photon statistics characterization methods, quantum Zeno effects in atom ensembles, and optimizing light-matter interactions by manipulating the amplitude and phase of the driving light field. These phenomena have significant implications for both fundamental quantum optics and practical applications in a range of photonic quantum technologies.

Thursday 20th March 2025: Federico Carollo (Coventry University)

Biasing open dynamics and exploring many-body effects in “digital” quantum trajectories through a thermodynamic approach

Noisy intermediate-scale quantum devices have recently become available and provide a useful environment for research on quantum dynamics. Building on this opportunity, we will explore open-system dynamics that are simulated on a quantum computer by coupling a system of interest to an ancilla. After each interaction the ancilla is measured and the sequence of measurements defines a quantum trajectory. Using a thermodynamic analogy, which identifies trajectories as microstates, we will show how to bias open-system dynamics to enhance the probability of quantum trajectories with desired properties, e.g., specific measurement patterns or temporal correlations. We will discuss how such a biased dynamics can be implemented on a unitary, gate-based quantum computer and show proof-of-principle results on a publicly accessible machine. We will conclude by discussing an application of the formalism to a many-body system displaying heterogeneous dynamics.

Thursday 27th March 2025: Vladimir Yudson (HSE University, Moscow)

Beyond the RKKY: dissipation in a system of spin impurities coupled to an electron reservoir

The seminal RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction of spin impurities weakly coupled to an electron reservoir is usually described by an effective spin Hamiltonian derived by perturbative exclusion of electron degrees of freedom. The RKKY Hamiltonian determines eigenstates and eigenenergies of the spin system but there are no dissipation effects within this framework. To describe the decay of excited states one should go beyond the effective Hamiltonian approximation. Here we develop a field-theoretical approach to the problem using the Majorana representation of the spin operators in order to define a ‘fermionic’ functional integral over Grassmann variables. This allows us to calculate dynamic spin-spin correlation functions which bear information about the decay rates of excited spin states. For a particular system of a pair of spins coupled with a helical electron edge state we have found the existence of ‘bright’ and ‘dark’ (long-living) excited spin states.

Thursday 3rd April 2025: Jorge Quintanilla (University of Kent)

Quantum-assisted coordination of mobile agents

Many problems in Operational Research, such as the so-called “rendezvous problem”, involve non-signal coordination of mobile agents. I will discuss quantum advantages that may emerge when the players have access to entangled quantum memories, illustrating them through Rendezvous and Domination problems on graphs. I will present theoretical and simulation results (the latter using both classical and quantum processors) discussing how the quantum advantages come about in each case. I will also describe evolutionary algorithms for the automatic generation of optimal strategies. I will end by arguing that quantum-assisted, non-signal coordination of mobile agents represents a brand new area of application for quantum technologies.

Thursday 22nd May 2025: Julia D. Hannukainen (University of Cambridge)

Local Topological Markers: Characterising topology beyond perfect crystals

Topological phases of matter are traditionally studied in crystalline systems using momentum-space methods. Recent experiments have demonstrated topological edge states in amorphous materials, motivating the development of new tools for systems lacking translation invariance. In this work, we introduce real space local topological markers for characterising topology in odd dimensions.

I will begin with an introduction to topological insulators, demonstrating how our description of topological phases and topological invariants is based on notions of translation invariance and the existence a Bloch basis even though topology does not require translation invariance. I will introduce the local Chern marker—the Chern number expressed in terms of the Fourier transformed Chern character—which is an easily applicable, commonly used real space invariant in even dimensions.

In our work we extend the Chern marker to odd dimensions, something previously lacking in the literature. I will explain why we cannot Fourier transform the odd dimensional invariants to obtain local markers, and how we can use dimensional reduction to overcome this problem. This requires the reformulation of the Chern character in terms of a single particle density matrix, which is a projector onto the filled bands. We introduce a one-parameter family Pϑ of single-particle density matrices interpolating between a trivial state and the topological state of interest in odd dimensions. By interpreting the parameter ϑ as an additional dimension, we express the Chern character in terms of the family Pϑ. Integrating over ϑ gives a closed form expression for local markers in odd dimensions. These new markers include the chiral marker, a Z invariant equivalent to the chiral winding number, and a Chern-Simons marker, a Z2 invariant characterizing all nonchiral phases in odd dimensions, including topological insulators in three dimensions.

The single-particle density matrix formalism has the advantage that the markers can be used to characterise the topology of a given quantum state, where no knowledge of the parent Hamiltonian is required. This formalism extends to interacting systems through the one-particle density matrix. While the one-particle density matrix of an interacting state is no longer a projector, as long as its spectrum remains gapped, it can be adiabatically flattened to a topologically equivalent free fermion-like form. The local markers provide a practical approach to identifying topological phases in both disordered and interacting quantum systems.

References:
Phys. Rev. Lett. 129, 277601 (2022)
Phys. Rev. Research. 6, L032045 (2024)

Wednesday 11th Jun 2025: Max McGinley (University of Cambridge)

Entanglement and complexity in shallow quantum circuits

Highly entangled many-body quantum systems are generally thought to be too complex to be simulated on classical computers. Because of this, quantum simulation is regarded as one of the most promising applications of future quantum computers. But what about simulating weakly entangled quantum states, which are in some sense much simpler? In this talk, I will discuss the problem of simulating shallow quantum circuits, i.e. the evolution of quantum many-body states over short timescales. Even though the states produced in this setting have only weak, short-ranged entanglement, I will provide new evidence that simulating this kind of quantum dynamics is still a hard problem for classical computers. Using new theoretical techniques, we analyse a phenomenon known as measurement-induced entanglement (MIE), and prove that in two spatial dimensions and above, MIE can proliferate across a many-body system in circuits of constant depth. I will discuss the implications of our work for demonstrating the computational advantage of quantum computers, and for the wider study of entanglement and complexity in many-body quantum dynamics.

Thursday 12th Jun 2025: Colin Rylands (Coventry University)

Entanglement and symmetry dynamics in dual unitary circuits with impurities

The most common protocol for studying far-from-equilibrium quantum systems is the quantum quench. The system is prepared in a non-equilibrium state and evolved unitarily via Hamiltonian or circuit dynamics. Typically, the time evolution operator is translationally invariant, and, in such cases, many universal results have been obtained concerning local relaxation, the growth of entanglement and lately, also, the dynamics of broken symmetries. In this talk, I will discuss some interesting phenomena which arise when translational invariance is broken by the presence of an impurity in the system. Concentrating on a specify example— dual unitary quantum circuits— I will show how the inclusion of an impurity gate which is not dual unitary can change the growth of entanglement. At short times this can be calculated exactly while at longer times this is not possible. I will discuss two complementary effective theories, the quasiparticle and membrane pictures, which allow access to the late time regime, exhibiting markedly different behaviour. If the impurity breaks a symmetry of the bulk system, the physics is richer. A competition takes place between the bulk which restores the symmetry and the impurity which breaks it, thereby facilitating novel phenomena like the quantum Mpemba effect. If time permits, I will also discuss the case when the impurity is not unitary, and more specifically represents a projective measurement. In this case the entanglement growth shows a strong dependence on the placement of the impurity: in some cases, entanglement is suppressed, in others it is enhanced.

Thursday 26th Jun 2025: Tomaž Prosen (University of Ljubljana)

Multifractal dynamical response

Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. I will discusss an unusual type of nonergodic behavior in a many-body discrete-time dynamical system, specifically a multiperiodic response with multifractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bipartite lattice. Although the models display strong fragmentation of phase space of configurations, I will demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories.