ICTS

We discuss the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. We demonstrate the formation of such scars from the superposition of exact zero modes in a particular U(1) gauge theory. A class of these, called sublattice scars, seem to be perfectly structured if a particular local observable is probed even though these states are high-energy eigenstates. A "triangle relation" that connects some anomalous zero modes with other states with nonzero integer eigenvalues will be discussed.
 

We address the fate of Fermi liquids in Floquet bands coupled to heat reservoirs.

For fermionic baths, we will show that periodically driven Fermions are described by a periodic Gibbs ensemble in which the Fermi Dirac occupation is replaced by a stair-case-like function which has several step discontinuities, leading to a "Floquet Fermi Liquid” state that contains several Fermi surfaces enclosed inside each other. We will discuss several properties of these states such as quantum oscillations, how to tune their van-Hove singularities without changing the electron density, and clarify and old controversy in optoelectronics by demonstrating that current rectification is possible when the frequency of the drive is within the optical gap of the metal.

For bosonic baths, we will demonstrate the existence of a "Floquet Non-Fermi liquid state" that has no analogue in equilibrium. It features "higher order Floquet Fermi surfaces” where the occupation in momentum space displays cusp-like non-analyticities, but without an associated jump or quasiparticle residue. More intriguingly, the sharpness of these higher order Floquet Fermi surfaces survives even at finite temperatures, implying that this Floquet Non-Fermi Liquid remains quantum critical at finite temperatures, unlike equilibrium Fermi and Non-Fermi liquids where temperature acts as a relevant perturbation that renders the fluid classical with exponentially decaying correlations at sufficiently large distances.

The field of thermodynamics is one of the crown jewels of classical physics. Thanks to the advent of experiments in cold atomic systems with long coherence times, our understanding of the connection of thermodynamics to quantum statistical
mechanics has seen remarkable progress.

Extending these ideas and concepts to the non-equilibrium setting is a challenging topic, in itself of perennial interest. Here, we present perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems, whose Hamiltonians depend on time periodically, H(t + T) = H(t). For these, there is no energy conservation, and hence not even a natural concept of temperature.

We find that certain structures from equilibrium thermodynamics are lost, while entirely new non-equilibrium phenomena can arise, including a spectacular spatiotemporal `time-crystalline' form of order, recently observed experimentally on Google AI's sycamore NISQ platform.

References: for an introductory overview, see Nature Physics 13, 424–428 (2017). For an in-depth review, see arxiv:1910.10745. NISQ experiment: Nature 601, 531 (2022).

I will discuss the dynamics of monitored systems combining the ingredients of unitary evolution, measurements, and adaptive classical control. I will present various novel dynamical phases and phase transitions that arise in these systems, ranging from entanglement and teleportation phase transitions to "learnability" transitions in the ability to reconstruct quantum information from measurements. I will also discuss experimental realizations of these phenomena in noisy quantum processors.

The field of thermodynamics is one of the crown jewels of classical physics. Thanks to the advent of experiments in cold atomic systems with long coherence times, our understanding of the connection of thermodynamics to quantum statistical
mechanics has seen remarkable progress.

Extending these ideas and concepts to the non-equilibrium setting is a challenging topic, in itself of perennial interest. Here, we present perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems, whose Hamiltonians depend on time periodically, H(t + T) = H(t). For these, there is no energy conservation, and hence not even a natural concept of temperature.

We find that certain structures from equilibrium thermodynamics are lost, while entirely new non-equilibrium phenomena can arise, including a spectacular spatiotemporal `time-crystalline' form of order, recently observed experimentally on Google AI's sycamore NISQ platform.

References: for an introductory overview, see Nature Physics 13, 424–428 (2017). For an in-depth review, see arxiv:1910.10745. NISQ experiment: Nature 601, 531 (2022).

I will consider closed quantum many-body systems, time-evolving by unitary dynamics, so fully isolated from any external environment. One basic issue is whether or not a large such system can serve as a bath (or environment) for itself, bringing all of its subsystems to thermal equilibrium with each other via the system’s unitary quantum dynamics. When a system does do this, that is “thermalization”. Exceptions to thermalization include “quantum many-body
scars” and various types of integrability or near-integrability; many-body Anderson localization is one type of integrability.

As one simple example of integrability and the transition/crossover to near-integrability and thermalization, I will discuss a weakly interacting gas (time permitting). This also serves as an example of “Fock-space many-body localization”.
 

Then I will focus on many-body localization in one-dimensional systems with only short-range interactions and hoppings. I will review our present understanding of the phase diagram of such systems and discuss two key phenomena that are important in such systems, namely the “avalanche” instability, and many-body resonances. This will serve as an introduction to later lectures by John Imbrie.
 

Refs:
Crowley and Chandran, arXiv:2012.14393
Morningstar, et al., arXiv:2107.05462
Sels, arXiv:2108.10796
Bulchandani, et al., arXiv:2112.14762
Long, et al., arXiv:2207.05761
Ha, Morningstar and Huse, arXiv:2301.04658

In recent years, superconducting qubits have emerged as one of the leading platforms for quantum computation and simulation. We utilize these Noisy Intermediate Scale Quantum (NISQ) processors to study nonequilibrium quantum dynamics and simulate quantum phases of matter. I will present some of our recent works in studying robustness of bound states of photons [1], measurement-induced quantum information phases [2], and the universality classes of dynamics in the 1D Heisenberg chain [4]. A goal for this talk is to provide a sense of what NISQ discoveries to anticipate and a time scale for them.

[1] Morvan et al., Nature 612, 240–245 (2022)
[2] Hoke et al., Nature 622, 481–486 (2023)
[3] Rosenberg et al., Arxiv.org/abs/2306.09333

We will discuss how quantum jumps affect localized regimes in driven-dissipative disordered many-body systems featuring a localization transition. We introduce a deformation of the Lindblad master equation that interpolates between the standard Lindblad and the no-jump non-Hermitian dynamics of open quantum systems. We probe both the statistics of complex eigenvalues of the deformed Liouvillian and dynamical observables of physical relevance. We show that reducing the number of quantum jumps, achievable through realistic post-selection protocols, can promote the emergence of the localized phase. We will also discuss eigenvector correlations across the localization transition in non-Hermitian power-law banded random matrices.

Understanding the out-of-equilibrium dynamics of a closed quantum system driven across a quantum phase transition is an important problem with widespread implications for quantum state preparation and adiabatic algorithms. While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the subsequent and significant coarsening processes lie beyond its scope. Here, we develop a universal description of such coarsening dynamics---and their interplay with the Kibble-Zurek mechanism---in terms of scaling theories. Our comprehensive theoretical framework applies to a diverse set of ramp protocols and encompasses various coarsening scenarios involving both quantum and thermal fluctuations. Moreover, we highlight how such coarsening dynamics can be directly studied in today's "synthetic" quantum many-body systems, including Rydberg atom arrays, and present a detailed proposal for their experimental observation.

I will discuss our recently introduced information lattice as an intuitive way to organise entanglement or quantum information into scales. I will then show how this gives useful information about both localised states and thermalising dynamics and will outline an efficient algorithm for many-body dynamics. In the second part of the talk I will quickly advertise new results on ultraslow growth of number entropy in l-bit model of many-body localization.

I will discuss how one can define chaos in Hamiltonian systems through adiabatic transformations. I will explain how complexity of the adiabatic gauge potential, which is the generator of such transformations, is behind seemingly different phenomena such as chaos, ergodicity,  and integrability, long time response of physical observables, emergence of conservation laws, Schrieffer–Wolff  transformations, hydrodynamic response, counter-diabatic driving and other phenomena. Using this probe I will argue that integrable and ergodic regimes are always separated by an intermediate universal chaotic but non-ergodic phase characterized by slow glassy-type response. This intermediate regime can be termed as maximally chaotic, because the adiabatic transformations have the largest complexity. The fact that systems are most chaotic near integrability is in fact well known from our everyday experience as weakly interacting nearly integrable gases with large Reynolds numbers often lead to very chaotic turbulent flows, while stronger interactions lead to simpler laminar flows. I will argue that this intermediate regime was mistakenly identified in the past as a thermodynamically stable many body localized phase and will discuss some common mistakes made in the MBL literature (both analytical and numerical). I will also explain the mechanism of instability of localized integrals of motion through the operator growth. I will illustrate this maximally chaotic regime with other examples both quantum and classical systems including Floquet systems close to integrability. At the end I will mention some open questions.

Starting from a pure initial state, the local properties of chaotic many-body quantum systems are expected to quickly thermalize under unitary dynamics. The remaining evolution from local to global equilibrium is described by the classical equations of hydrodynamics. However, the advent of quantum simulator platforms has made it possible to measure not only local expectation values, but also their full quantum statistics, fluctuations and space-time correlations. In this talk, I will discuss a theory of diffusive fluctuations in chaotic many-body quantum systems, and establish its validity in random unitary quantum circuits with charge conservation. I will also discuss exceptions to this conventional behavior in integrable quantum spin chains, as well as Dirac fluids as a result of Lorentz invariance and particle-hole symmetry. In particular, I will argue that charge noise in the hydrodynamic regime of Dirac fluids is parametrically enhanced relative to that in conventional diffusive metals.

The Dicke model exhibits a rich variety of phase transitions. In this talk, we will try to cover the following points.
1) The usefulness of studying various eigenvector properties to characterize the phase transitions of the Dicke and the anisotropic Dicke model.
2) The effect of periodic and quasiperiodic drive on the Dicke model.
3) We introduce and study a disordered Dicke model. We show how analytical expressions for the quantum and thermal phase transitions can be obtained.

Consider equal antiferromagnetic Heisenberg coupling between qubits sitting at the nodes of a complex, generally nonbipartite, network. We ask the question: What property of the network determines the net magnetization of the ground state? I will present strong evidence that graph heterogeneity, as measured by the presence of (disassortative) hubs, is the key ingredient to obtain nonzero total spin, not how frustrated the graph is. Additionally, the magnetization falls with the number of bonds per node. I will present statistics over different families of random graphs to corroborate this finding. I will also show how to construct frustrated non-random networks where the magnetization can be tuned over its entire range, across both continuous and discontinuous transitions, which can be solved exactly. These findings pose open questions and strongly motivate further exploration of frustrated magnetism beyond regular lattices.

Being motivated by intriguing phenomena such as the breakdown of conventional bulk boundary correspondence and emergence of skin modes in the context of non-Hermitian (NH) topological insulators, we here propose a NH second-order topological superconductor (SOTSC) model that hosts Majorana zero modes (MZMs). Employing the non-Bloch form of NH Hamiltonian, we topologically characterize the above modes by biorthogonal nested polarization and resolve the apparent breakdown of the bulk boundary correspondence. Unlike the Hermitian SOTSC, we notice that the MZMs inhabit only one corner out of four in the two-dimensional NH SOTSC. Such localization profile
of MZMs is protected by mirror rotation symmetry and
remains robust under on-site random disorder. We extend the static MZMs into the realm of Floquet drive. We find anomalous $\pi$-mode following low-frequency mass-kick in addition to the regular $0$-mode that is usually engineered in a high-frequency regime. We further characterize the regular $0$-mode with biorthogonal Floquet nested polarization. Our proposal is not limited to the $d$-wave superconductivity only and can be realized in the experiment with strongly correlated optical lattice platforms.

The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). We explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models.

Surprising signatures of anomalous spin transport have been reported in the spin-half Heisenberg spin chain at the isotropic point, in a number of recent work. The talk will discuss: (i) analogous results for classical integrable spin chains and (ii) properties of coupled Burgers equations that have been proposed as effective hydrodynamic descriptions of integrable spin chains.

Glassy dynamics have time-reparametrization `softness': glasses fluctuate, and respond to external perturbations, primarily by changing the pace of their evolution. Remarkably, the same situation also appears in toy models of quantum field theory such as the Sachdev-Ye-Kitaev (SYK) model, where the excitations associated to reparametrizations play the role of an emerging `gravity'. I describe here how these two seemingly unrelated systems share common features, arising from a technically very similar origin. Apart from the curiosity that this correspondence naturally arouses, there is also the hope that developments in each field may be useful for the other.

We show that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size (`creep')
that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time
scale, i.e., of a naive "clock rate"; however, the concept of an "internal clock" survives, at least in an ensemble sense.

We observe that the average entropy appropriately models the ensemble-averaged internal clock and reduces fluctuations. We take the tendency for faster-than-logarithmic growth of entanglement and smooth dependency on the disorder of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.

Understanding ergodicity and its breakdown in isolated quantum systems has been one of the central problems in recent times. A nonergodic behavior may arise in the presence of strong disorder leading to a many-body localization (MBL) phase or phases intermediate between ergodic and MBL, e.g., the so-called non-ergodic extended (NEE) phase. I will discuss real-space and Fock-space (FS) characterizations of ergodic, NEE, and MBL phases in an interacting quasiperiodic system, which possesses a mobility edge in the noninteracting limit. I will show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. Based on a finite-size scaling analysis of the typical local FS self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.

The dynamics of interacting quantum many-body systems has two seemingly disparate but fundamental facets. The rst is the dynamics of real-space local observables, and if and how they thermalise. The second is to interpret the dynamics of the many-body state as that of a fictitious particle on the underlying Hilbert-space graph. In this work, we derive an explicit connection between these two aspects of the dynamics. We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. As such, the latter has the same functional form in time as the decay of autocorrelations but with renormalised parameters. Our analytical treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.

Quantum chaos can be diagnosed through the analysis of level statistics using the spectral form factor. This is the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole), when the system is chaotic. The spectral form factor captures both short- and long-range level correlations even in the presence of symmetries and it does not require unfolding. We discuss how this structure can be detected through the dynamics of two physical quantities accessible to experimental many-body quantum systems -- the survival probability and the spin autocorrelation function -- and how this manifestation of many-body quantum chaos implies relaxation times that grow exponentially with system size. However, quantities that exhibit the correlation hole are non-self-averaging. This means that the correlation hole is only visible after large averages over initial states or disorder realizations are performed, which is computationally and experimentally costly. We explain how self-averaging can be ensured by opening the system to an environment. 

Understanding the dynamics of non-equilibrium quantum many-body systems is a central challenge in modern physics, with relevance across different branches of physics. As such, solvable models of quantum dynamics are valuable; but they are rare. In this talk, I will introduce a family of quantum circuits generated by the kicked Ising model in 1+1 dimensions which have interactions alternating between odd and even bonds in time, and prove that their entanglement dynamics can be analytically solved, yielding rich and varied phenomenology. Underpinning this solvability are the properties of global tri-unitary (three 'arrows of times'), as well as local "second-level dual-unitarity", a recently discovered property which constrains the behavior of pairs of local gates underlying the circuit under a space-time rotation. The phenomenology uncovered ranges from linear growth at half the maximal speed allowed by locality, followed by saturation to maximum entropy (i.e., thermalization to infinite temperature); to entanglement growth with saturation to extensive but sub-maximal entropy. We also find at certain special system parameters an apparently novel class of analytically-solvable dynamics which is non-chaotic, but neither integrable nor Clifford. Our findings extend our knowledge of interacting quantum systems whose thermalizing dynamics can be efficiently and analytically computed, going beyond the well-known examples of integrable models, Clifford circuits, and dual-unitary circuits.

TBA

We investigate many-body dynamics where the evolution is governed by unitary circuits through the lens of `Krylov complexity', a recently proposed measure of complexity and quantum chaos. We extend the formalism of Krylov complexity to unitary circuit dynamics and focus on Floquet circuits arising as the Trotter decomposition of Hamiltonian dynamics. For short Trotter steps the results from Hamiltonian dynamics are recovered, whereas a large Trotter step results in different universal behavior characterized by the existence of local maximally ergodic operators: operators with vanishing autocorrelation functions, as exemplified in dual-unitary circuits. These two regimes are separated by a crossover in chaotic systems. Conversely, we find that free integrable systems exhibit a nonanalytic transition between these different regimes, where maximally ergodic operators appear at a critical Trotter step.

I discuss three robust routes to ergodicity breaking in quantum dynamics: many body localization, fractonic symmetries, and higher form symmetries. I’ll explain how each of these works, their key properties, and degree of robustness.

Quantum mechanics is ruled by Hermitian generators inducing unitary propagation, nevertheless, when tracing out some degrees of freedom one can end up with non-Hermitian operators. An example is entanglement or out-of-time-ordered correlation functions in random circuits, where the relaxation dynamics is described by a non-Hermitian Markovian matrix with a finite spectral gap. Naturally one would expect that the relaxation, i.e., the rate of generating entanglement, will be given by this finite gap. However, this is not the case. Rather, in the thermodynamic limit the rate is given by a phantom eigenvalue -- an "eigenvalue" that is not in the spectrum. Resolution of this puzzle will lead to a pseudospectrum and a realization that when dealing with non-Hermitian matrices being exact can actually be wrong, while being slightly wrong is correct.

Quantum critical engines, i.e., quantum engines operating close to quantum phase transitions, show universal features in their output, following the Kibble-Zurek mechanism. I will discuss universality in the work output of finite-time quantum critical engines, operating at finite temperatures.