New Directions in far from Equilibrium Integrability and beyond: March 11, 2024 – May 10, 2024

MINI COURSE SCHEDULE

WEEK 1: MARCH 11-15, 2024

Monday  3/11/24 – 10:30AM-11:30AM- Seminar Room – 313
Friday 3/15/24 – 1:30PM-2:30PM – Seminar Room – 313

Topic: Kardar-Parisi-Zhang physics in integrable Heisenberg models
Lecturer: Romain Vasseur (University of Massachusetts, Amherst)

Abstract: The field of hydrodynamics of quantum systems has experienced a revival in the past decade, as an effective field theory describing how many-body quantum systems evolve from local to global equilibrium. This has been largely driven by the advent of new experimental platforms, from strongly interacting ultracold gases to pristine solid-state systems with strong interactions and long mean free times. Hydrodynamics is particularly rich for low-dimensional fluids, featuring transport anomalies such as long-time tails, and proximity of many realistic systems to integrability. In these lectures, I will focus on the hydrodynamics of systems close to integrable limits, featuring infinitely-many approximate conservation laws and long-lived quasiparticle excitations. I will briefly review recent successes of this theory, and use it to argue that integrable isotropic magnets in one dimension exhibit a breakdown of Fick’s diffusion law; corresponding to anomalous, superdiffusive transport properties with associated dynamical exponent z=3/2 and scaling functions falling into the celebrated Kardar-Parisi-Zhang universality class. Time permitting I will also discuss recent results including the stability of superdiffusion against integrability-breaking perturbations, as well fluctuations and full counting statistics.

WEEK 2: MARCH 18-22, 2024

Monday 3/18/24 – 10:30AM-11:30AM – Seminar Room – 313
Wednesday 3/20/24 – 10:30AM-11:30AM – Seminar Room – 313
Thursday 3/21/24 – 10:30AM – 11:30AM – Seminar Room – 313

Topic: Field Theory of Many-Body Lindbladian Dynamics
Lecturer: Alex Kamenev (W. I. Fine Theoretical Physics Institute, University of Minnesota)

Abstract: Quantum driven-dissipative systems may often be described within Markovian approximation, leading to the so-called Lindblad equation. The latter is known to be extremely useful within NMR and quantum optics contexts, where it is typically applied to one- or few-body systems. The rapid development of qubit arrays requires a better understanding of many-body Lindbladian dynamics.  The lectures will focus on field-theoretical tools recently developed for the description of many-body driven-dissipative systems. I will place them within a general context of Schwinger-Keldysh formalism and illustrate for a few paradigmatic examples. The latter include Gaussian models, parametric oscillators, quantum heating and activation, and semiclassical methods to describe dissipative tunneling.

Friday 3/22/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic:  The “Universal Lindblad Equation:” what is it, why do we need it, and how accurate are its steady states?
Lecturer: Mark Rudner (University of Washington)

Abstract: With the exception of the universe as a whole, the evolution of a quantum system is generically non-unitary due to the coupling between the system and its environment. In quantum optics, the powerful framework of Lindblad master equations has been developed and employed for many years to describe the effective evolution of atomic-like systems in the presence of electromagnetic and other environmental degrees of freedom. Importantly, explicit derivations of Lindblad master equations have traditionally relied on highly restrictive assumptions on energy level spacings that limit its applicability to few-level/few-body systems. In this talk I will describe a new route to obtaining the Lindblad equation which circumvents all restrictive assumptions on the nature of the system at hand. This “universal Lindblad equation” (ULE) can therefore be applied to a wide range of many-body systems, including emerging quantum hardware with several to many coupled qubits and many-body systems driven far from equilibrium. I will discuss rigorous bounds on the errors incurred by the approximations leading to the ULE, and on the deviations of steady states observables calculated from the ULE relative to their exact values.  I will conclude with a discussion of future prospects and applications of this new framework.

WEEK 3: MARCH 25-29, 2024

Monday 3/25/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic:  Thermodynamics based on neural networks
Lecturer: Andreas Klümper (University of Wuppertal)

Abstract: This is joint work with Dennis Wagner and Jesko Sirker. We present three different neural network (NN) algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows for the exact calculation of the operator trace. The second one is based on a sampling of the trace using minimally entangled states, whereas the third one makes use of quantum typicality. In the latter case, we approximate a typical infinite-temperature state by wave functions which are given by a product of a
projected pair and a NN part and evolve this typical state in imaginary time.

Monday 3/25/24 – 1:30PM-2:30PM – Seminar Room 313

Topic: Bosonization and Regularization at the Boundaries of Equilibrium
Lecturer: Carlos Bolech (University of Cincinnati)

Abstract: In this talk, we will critically reexamine the bosonization-debosonization procedure for systems including localized features or boundaries. After highlighting possible inconsistencies that can adversely affect the results of all types of calculations, we will introduce a novel “consistent bosonization-debosonization (BdB)” scheme that we have developed to resolve the non-equilibrium transport puzzle in a simple 1D electron junction [1] and argue that it should be widely applicable. This new framework takes the form of additional considerations, related to the regularization of fermionic bilinears, that supplement the conventional refermionization procedure and can be carried over to the study of other systems. We will then discuss its application to the two-lead Kondo junction and the discussion will be focused on the Toulouse limit [2]. Subsequently, we will consider the (multi)-two-channel Kondo model and discuss its “compactification” [3]. A combination of exact results and an extended RG analysis will be used to argue in favor of the new consistent BdB procedure and to put it into perspective.”

Tuesday 3/26/24 – 10:30AM-11:30AM – Seminar Room – 313
Wednesday 3/27/24 – 10:30AM-11:30AM – Seminar Room – 313
Thursday 3/28/24 – 10:30AM – 11:30AM – Seminar Room – 313

Topic: Integrable circuit dynamics
Lecturer: Pieter Claeys (Max Planck Institute for the Physics of Complex Systems)

Abstract: Unitary circuits have gained intense attention in the past few years as minimal models for many-body quantum dynamics. In such circuits a quantum state is evolved in a discrete time through the repeated application of unitary gates, with the resulting dynamics being either chaotic or integrable. These models have the additional advantage of being experimentally realizable in current quantum computing setups, which natively realize unitary gates. These lectures will present an introduction to integrable circuit dynamics, first showing how integrable circuits and their conserved charges can be derived starting from the Yang-Baxter equation and incorporated in the framework of the algebraic Bethe ansatz. I will discuss how integrable circuits naturally appear as the discretization of integrable Hamiltonian dynamics, with an inbuilt discrete time step, and exhibit so-called Trotter transitions as this discrete time step is varied. For a large Trotter step certain integrable models have the additional property of being dual-unitary, exhibiting a space-time duality particular to circuit models, and I will review the interplay of integrability and dual-unitarity and its constraints on quasiparticle dynamics and conservation laws. I will conclude by discussing recent experiments on integrable circuit dynamics in current digital quantum simulators, focusing on transport and magnon dynamics.

Friday 3/29/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic:  Probing anyon correlations and blackhole-like dynamics in the quantum Hall bulk
Lecturer: Smitha Vishveshwara (University of Illinois at Urbana-Champaign).

Abstract: The recent interferometric and beam-splitter experiments signaling the presence of anyons in quantum Hall systems has created of resurgence of interest in the topic. Here, I will present a theoretical description of coherent state bulk anyons and their signatures in two particle correlators and dynamics. I will demonstrate how a saddle potential, for instance created in a pinched point contact geometry, can model a beam-splitter. Anyon dynamics in such a potential reflects Hanbury-Brown Twiss correlations that can directly probe fractional statistics.  I will also illustrate how the same setting can probe dynamics akin to that found in the astrophysical realm of black holes. Specifically, point-contact geometries can exhibit phenomena parallel to Hawking-Unruh radiation and black hole quasinormal modes associated with ringdowns in gravitational wave detection.

WEEK 4: APRIL 1-5, 2024

Monday 4/1/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Limit Shape Transition in Full Counting Statistics
Lecturer: Dimitri Gangardt (University of Birmingham)

Abstract: Full Counting Statistics (FCS) is a way to characterise non-local correlations in many body systems. We calculate the generating function of FCS of the particle number on a macroscopic interval in a system of free fermions and reveal the existence of 3rd order phase transition as a function of the rescaled counting parameter. We characterise the transition as a topological change of the dominant configuration (instanton) in the coarse grained hydrodynamical fields similar to Limit Shape transitions in fluctuating statistical phenomena.

Monday 4/1/24 – 1:30PM-2:30PM – Seminar Room – 313

Topic: Optimal realization of Yang-Baxter gate on quantum computers
Lecturer: Vladimir Korepin (C. N. Yang Institute of Theoretical Physics of the Stony Brook University)

Abstract: Quantum computers provide a promising method to study the dynamics of many-body systems beyond classical simulation. On the other hand, the analytical methods developed and results obtained from the integrable systems provide deep insights into the many-body system. Quantum simulation of the integrable system not only provides a valid benchmark for quantum computers but is also the first step in studying integrable-breaking systems. The building block for the simulation of an integrable system is the Yang-Baxter gate. It is vital to know how to optimally realize the Yang-Baxter gates on quantum computers. Based on the geometric picture of the Yang-Baxter gates, we present the optimal realizations of two types of Yang-Baxter gates with a minimal number of CNOT or Rzz gates. We also show how to systematically realize the Yang-Baxter gates via the pulse control. We test and compare the different realizations on IBM quantum computers. We find that the pulse realizations of the Yang-Baxter gates always have a higher gate fidelity compared to the optimal CNOT or Rzzrealizations. On the basis of the above optimal realizations, we demonstrate the simulation of the Yang-Baxter equation on quantum computers. Our results provide a guideline and standard for further experimental studies based on the Yang-Baxter gate.

Wednesday 4/3/24 – 10:30AM-11:30AM – Seminar Room – 313
Thursday 4/4/24 – 10:30AM – 11:30AM – Seminar Room – 313
Friday 4/5/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Integrable Lindblad Equations
Lecturer: Fabian Essler (University of Oxford)

Abstract: I discuss Lindblad equations for open many-particle quantum systems , where the system is coupled to an environment in the bulk. I show how such master equations are related to non-Hermitian two-leg ladder “spin” models. The latter can be Yang-Baxter integrable, and I will give an overview of known cases. I then discuss how physical properties in such Lindblad equations are related to Bethe ansatz wave functions. Finally, I will introduce the quantum symmetry simple exclusion process of stochastic quantum dynamics and show how its average evolution gives rise to a Lindblad equations that is Yang-Baxter solvable in a novel way.

WEEK 5: APRIL 8-12, 2024

Tuesday 4/9/24 – 10:30AM – 11:30AM – Seminar Room – 313

Topic: Quantum transport and out-of-equilibrium phenomena in quantum devices
Lecturer: Thierry Giamarchi (University of Geneva)

Abstract: I will present in this talk several realizations of quantum transport occurring in quantum systems of bosons or fermions connected to reservoirs. The system can be put out of equilibrium either by the reservoirs themselves or by coupling it to an external environment, such as a time-dependent noise or losses of particles or pairs. I will show how we can address some of these questions using field theory techniques such as Keldysh.
I will also examine the case of the Hall transport for systems which are put under a (synthetic)magnetic field. In addition to the pure theoretical aspects, I will also make contact with recent experimental realizations of such problems in cold atomic systems.

Wednesday 4/10/24 – 10:30AM-11:30AM – Seminar Room – 313
Thursday 4/11/24 – 10:30AM – 11:30AM – Seminar Room – 313
Friday 4/12/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Generalized hydrodynamics and Bethe ansatz
Lecturer: Olalla Castro Alvaredo (University of London)

Abstract: In this short course, I will review the main ideas underlying the Generalised Hydrodynamics (GHD) approach. I will do this in the context of Integrable Quantum Field Theory (IQFT), the class of theories that we considered in our original work (with B. Doyon and T. Yoshimura, 2016). In this context, GHD combines hydrodynamics principles with a very specific description of quasiparticle excitations. The latter is based on the Thermodynamic Bethe Ansatz (TBA) approach, as developed for IQFTs by Zamolodchikov at the beginning of the 90s. Since TBA and GHD go hand in hand, I will start these lectures by reviewing the TBA approach and its generalisation to non-thermal states. I will then proceed to explain how the TBA results for physical quantities can be employed to solve a particular out-of-equilibrium protocol, namely the Partitioning Protocol, where two copies of an IQFT are equilibrated with certain (distinct) generalised temperatures and then joined at time zero and let to evolve. GHD allows us to answer the question: what are the long-time averages of conserved densities and currents in the non-equilibrium steady state that emerges after joining the two parts of the system? I will give examples of solutions of this protocol, describe how a zero-mass limit of the TBA resulst allows us to recover results at criticality and time permiting, give examples of interesting (unusual!) IQFTs where GHD has been successfully applied.

WEEK 6: APRIL 15-19, 2024

Monday 4/15/24 – 10:30AM-11:30AM – Auditorium – 103
Wednesday 4/17/24 – 10:30AM-11:30AM – Auditorium – 103

Topic: Defining quantum and classical chaos through adiabatic complexity
Lecturer: Anatoli Polkovnikov (Boston University)

Abstract: I will start from a general introduction to relations between chaos and thermalization in quantum and classical systems and discuss different ideas of defining quantum chaos through random matrix theory, operator spreading and out of time order correlation functions. Then I will move to the main theme of these lectures connecting chaos with adiabatic complexity. In particular, I will explain how this notion can be used to to define and probe chaos in both quantum and classical systems. Mathematically this complexity is encoded in the properly regularized fidelity susceptibility or more broadly in the geometric tensor. In classical systems this measure reflects complexity of trajectory-preserving canonical transformations under infinitesimal deformations of the Hamiltonian, while in quantum systems it reflects the complexity of the eigenstate transformations. I will discuss how the fidelity susceptibility is related to the low frequency response of the spectral functions of the operators deforming the Hamiltonian, i.e. to their fluctuations or noise. I will argue that generically integrable and ergodic regimes are separated by a buffer chaotic but non-ergodic KAM glassy region where the adiabatic complexity reaches the maximum. According to this measure the maximum chaos precedes ergodicity/thermalization. The KAM regime can be either transient but very long-lived in the thermodynamic limit or can last for infinite times in few-particle systems. In gases or fluids this KAM regime is familiar to us through emergence of highly chaotic but non-thermal turbulent cascades at small interaction strengths. I will also discuss that this KAM regime is manifested in interacting disordered systems sometimes referred to as MBL systems, which are not integrable as often stated in the literature but rather strongly chaotic and transient in infinite systems. I will also argue that in extensive systems close to integrability generally time evolution of observables can be described by three distinct regimes: integrable, glassy/chaotic KAM, and locally thermal hydrodynamic with very sharp crossovers between them.Finally I will show evidence that the transition from integrable to ergodic/mixing regimes is generally described by a two-parameter finite time scaling theory with integrable points playing a similar role to critical points for continuous phase transitions and the KAM regime being analogous to the critical slowing down.

Wednesday 4/17/24 – 1:30PM-2:30PM – Auditorium – 103

Topic: Quantum-classical approach to the problem of thermalization in one-dimensional spin systems
Lecturer: Felix Izrailev (Instituto de Fisica, Benemerita Universidad de Puebla, Mexico) 

Abstract: We investigate the quench dynamics of L interacting spins in a 1D lattice, demonstrating a strong chaos in both classical and quantum descriptions. Our focus spans various timescales, characterizing the dynamics from the early stages of evolution up to relaxation. Utilizing insights from the quantum-classical correspondence developed in [Phys. Rev. B 107, 155143 (2023)], we aim to elu- cidate the mechanisms behind the system’s relaxation process. This process involves two distinct mechanisms: one arising from linear parametric instability and the other from non-linearity. We demonstrate that the relaxation of the total energy associated with the unperturbed basis (a global quantity) and on-site magnetization (a local observable) is primarily due to the first mechanism, referred to as linear chaos. Our analytical findings indicate that the relaxation timescales for both quantities are independent of the system size in both classical and quantum models. While the mathematical explanation lies in the quasi-homogeneity of the single-particle frequency, the physical reasons trace back to the conservation of the L angular momenta length, significantly influencing the dynamical properties of spin systems. The observables with a well-defined classical limit conform to this physically sound dependence. However, our study of the participation ratio, lacking a classical limit, reveals a more intricate scenario. In this case, the situation is much more complicated, indicating the absence of thermalization in the thermodynamic limit.

Thursday 4/18/24 – 10:30AM – 11:30AM – Seminar Room – 313
Friday 4/19/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Quantum chaos versus integrability
Lecturer: Marcos Rigol (Penn State University)

Abstract: Integrable interacting many-body quantum systems are paradigms of mathematical beauty and exact solvability. Their properties are now routinely studied with nearly-integrable ultracold 1D gases. In my first lecture, I’ll describe recent experiments that measured the momentum distribution of the quasi-particles that underlie a 1D Bose gas with contact interactions (the rapidity distribution), and used it to probe near-integrable dynamics involving large distances and long times, testing the recently proposed theory of generalized hydrodynamics. By means of “high-energy” quenches implemented via a Bragg scattering pulse, the experiments have also unveiled equilibration at the shortest available time scales, a process known as hydrodynamization in the context of relativistic heavy-ion collisions, which precedes local prethermalization. I will discuss the experimental results as well as their theoretical understanding and modeling. As the counterpart to integrability, we generically have quantum chaos. In my second lecture I’ll discuss recent progress in the understanding of the entanglement properties of typical eigenstates of quantum-chaotic and integrable interacting many-body quantum systems. They both exhibit a typical bipartite entanglement entropy whose
leading term scales with the volume of the subsystem, but the coefficient is fundamentally different depending of whether the model is quantum chaotic or integrable. I will also discuss the nature of the subleading corrections that emerge as a consequence of the presence of abelian and nonabelian symmetries in such models.

WEEK 7: APRIL 22-26, 2024 

Monday 4/22/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Chiral Kondo lattices as platforms for anyons
Lecturer:  Alexei Tsvelik (Brookhaven National Laboratory)

Abstract:We describe the chiral Kondo chain model based on the symplectic Kondo effect and demonstrate that it has a quantum critical ground state populated by non-Abelian anyons. We show that the fusion channel of two arbitrary anyons can be detected by locally coupling the two anyons to an extra single channel of chiral current and measuring the corresponding conductance at finite frequency. Based on such measurements, we propose that the chiral Kondo chain model with symplectic symmetry can be used for implementation of measurement-only topological quantum computations, and it possesses a number of distinct features favorable for such applications. The sources and effects of errors in the proposed system are analyzed, and possible material realizations are discussed.

Tuesday 4/23/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Out-of-time-order correlators: chaos, integrability and classical approach to equilibrium
Lecturer: Ignacio Garcia-Mata (Instituto de Investigaciones Físicas de Mar del Plata)

Abstract: The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems and thus the OTOC is widely used as a measure of chaos. For short times exponential growth is related to the classical Lyapunov exponent, sometimes known as butterfly effect. However, this behavior is not universal. In this talk I will review some aspects of short and long time behavior of the OTOC, some measures of chaos and integrability based on long time fluctuations, and relations to classical relaxation rates.

Wednesday 4/24/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Thermalization Universality Classes for Weakly Nonintegrable Many-Body Dynamics
Lecturer: Sergej Flach (Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea)

Abstract: We observe different universality classes in the slowing down of thermalization of many-body dynamical systems upon approaching integrable limits. We identify two fundamentally distinct long-range and short-range classes defined by the nonintegrable perturbation network spanned amongst the (set of countable) actions of the corresponding integrable limit. Weak two-body interactions (nonlinearities) induce long-range networks in translationally invariant lattices. Weak lattice coupling (hopping) instead induce short-range networks. For classical systems we study the scaling properties of the full Lyapunov spectrum. The long-range class results in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging time control parameter and the rescaled spectrum approaching an analytical function [4,6]. The short-range class results in a dramatic slowing down of thermalization and a rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one. Disorder induces transitions from long-range to short-range classes. For quantum spin chains we compute ergodization time scales within the framework of the Eigenstate Thermalization Hypothesis and the Lyapunov time from operator growth methods using Krylov Complexity. The comparison of both time scales confirms the existence of the above universality classes for quantum many body dynamics as well.

Thursday 4/25/24 – 10:30AM -11:30AM – Seminar Room – 313

Topic: Two-parameter renormalization group for Anderson localization on Random Regular Graph
Lecturer: Vladimir Kravtsov (ICTP, Trieste)

Abstract: We suggest a “poor-men” renormalization group equations for Anderson localization of random regular graphs and show that it must be a two-parameter one. Physical arguments are supported by the novel numerical studies on the Anderson model on Random Regular Graph (RRG). Furthermore, we apply the same numerical formalism to localization on d-dimensional lattices with d=2,3,4,5,6 and demonstrate how the role of irrelevant operators progressively increases with increasing d to become marginally relevant on RRG. On the other hand, on RRG in its delocalized phase, for any initial conditions the single-parameter scaling is restored at sufficiently large system size, while for the localized phase and for a critical flow the two-parameter scaling is crucial. Another important issue is the choice between the linear and volumic scaling which are equivalent on d-dimensional lattices but are different on the expander graphs like a Cayley tree or RRG. We show that the volumic scaling holds in the delocalized phase in the asymptotic single-parameter regime, while scaling in the localized phase and in the near-critical extended phase is linear in the two-parameter RG regime.

Friday 4/26/24 – 10:30AM-11:30AM – Seminar Room – 313

Lecturer: Ilya A. Gruzberg (Ohio State University)
Topic: Multifractals and conformal invariance at Anderson transitions.

Abstract: 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.

WEEK 8: APRIL 29 – MAY 3, 2024

Workshop: New Directions in far from Equilibrium Integrability and beyond

WEEK 9: MAY 6-10, 2024

Monday 5/6/24 – 10:30AM-11:30AM – Seminar Room – 313

Topic: Bethe state preparation
Lecturer: Rafael I Nepomechie (University of Miami)

Abstract: We consider the problem of preparing exact eigenstates of the spin-1/2 Heisenberg quantum spin chain on a quantum computer. We begin by briefly reviewing the basics of coordinate Bethe ansatz and quantum computing. We then describe an efficient construction of Dicke states, and finally its generalization to Bethe states. The algorithm is explicit, deterministic, and does not use ancillary qubits.