Speaker:   Lenart Zadnik
Title:   Elusive hierarchy of relaxation times in quantum kinetically constrained models
Abstract:   I will discuss the mechanism of slow heterogeneous relaxation in quantum kinetically constrained models (KCMs) in which the strength of the potential energy is controlled by a coupling parameter. I will focus on the regime of slow dynamics which includes the large-coupling limit. By performing a large coupling expansion around that limit we find a nested hierarchy of states that remain frozen on time scales determined by powers of the coupling. Classification of such states, together with the evolution of their Krylov complexity, reveal that these time scales are related to the distances between the sites where facilitated dynamics is allowed by the kinetic constraint. While correlations within frozen states relax slowly and exhibit metastable plateaus that persist on time scales set by powers of the coupling parameter, the correlations in the rest of the states decay rapidly. I will describe how to compute the plateau heights in correlation functions and discuss the elusive nature of the time-scale hierarchy in thermodynamically large systems. The results presented in this talk explain the observed slow relaxation in quantum KCMs and elucidate dynamical heterogeneity in such models by relating the relaxation times to the spatial separations between the active regions. If time permits, I will also discuss how the large coupling expansion and its nested hierarchy of frozen states can be used to access the low-temperature glassy dynamics in the classical stochastic KCMs.
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Speaker:    Sarang Gopalakrishnan 
Title:   Persistence of local quantum coherence in high-temperature states
Abstract:   We explore the autocorrelation functions of "non-hydrodynamic" operators (e.g., the single-particle Green's function) at high temperature, under energy-conserving or charge-conserving quantum dynamics. These operators are strictly orthogonal to hydrodynamic modes, but are nevertheless indirectly affected by hydrodynamic fluctuations: in one or two dimensions, we show that their relaxation is subexponential at all temperatures. This subexponential decay is strictly a quantum-coherent effect, which is immediately destabilized by adding extrinsic noise. Our results imply that there are no well-defined Ruelle-Pollicott resonances in low-dimensional systems with charge conservation, even in sectors that are non-hydrodynamic. We develop a framework relating the dynamics of non-hydrodynamic operators to large deviations in classical hydrodynamics. 

E. McCulloch, J. A. Jacoby, C. von Keyserlingk, SG, Phys. Rev. Lett. 136, 190403 (2026)
E. McCulloch, J. A. Jacoby, SG, arXiv:2604.27074

Speaker:   Tianci Zhou
Title:   Compressing the Influence Matrices for Local Quantum Dynamics

Abstract:   The influence matrices provide an alternative route to the classical simulation of quantum dynamics. These objects describe the effective bath seen by a finite subsystem and, since they retain information only on the local dynamics, they are expected to be easier to simulate than the full wavefunction. Recent work, however, has shown that the influence matrices carry strong temporal correlations even in maximally chaotic systems, which rules out their efficient representation. In this work, we demonstrate that one can nevertheless efficiently store the reduced transition matrix, the combination of influence matrices that directly determines local expectation values. We will first show that the truncation errors are controlled by the singular spectrum of this object, which naturally motivates a low-rank approximation. We then prove that, for chaotic dual-unitary circuits, the associated entropy grows at most logarithmically in time. Our conclusions follow from exact results for random dual-unitary circuits and are supported by numerical results for fixed instances of both dual-unitary circuits and generic circuits.

Speaker:   Kavan Modi
Title:   Quantum Chaos and Volumetric Spatiotemporal Correlations
Abstract:   Chaotic systems are highly sensitive to a small perturbation, and are ubiquitous throughout biological sciences, physical sciences and even social sciences. Taking this as the underlying principle, we construct an operational notion for quantum chaos. Namely, we demand that the future state of a many-body, isolated quantum system is sensitive to past multitime operations on a small subpart of that system. By 'sensitive', we mean that the resultant states from two different perturbations cannot easily be transformed into each other. That is, the pertinent quantity is the complexity of the effect of the perturbation within the final state. From this intuitive metric, which we call the Butterfly Flutter Fidelity, we use the language of multitime quantum processes to identify a series of operational conditions on chaos, particularly the scaling of the spatiotemporal entanglement. Our criteria already contain routine notions and well-known diagnostics for quantum chaos. We then extend the criteria to include projected process ensembles, motivated by studies on deep thermalisation. Our results account for previous attempts to make sense of quantum chaos, such as the Peres-Loschmidt Echo, Dynamical Entropy, Tripartite Mutual Information, and Local-Operator Entanglement. Finally, we will present numerical results using the XXZ model and discuss how chaos leads to equilibration, Markovianisation, and thermalisation.

Reference: N Dowling, K Modi, PRX Quantum 5, 010314 (2024)

Speaker:   Robert Koenig
Title:   Fault-tolerant quantum computing and classical simulation Part 1
Abstract:   This minicourse will introduce basic notions of quantum computing and quantum fault-tolerance. In Part I, I will discuss models of computation, noisy quantum circuits, quantum error-correcting codes, fault-tolerant gadgets, and the threshold theorem. In Part II, I will turn to the classical simulation of (noisy) quantum circuits and discuss how efficient simulations of quantum many-body dynamics can give insights into the fault-tolerance properties of quantum information-processing proposals.

Speaker:   Robert Koenig
Title:   Fault-tolerant quantum computing and classical simulation Part 2
Abstract:   This minicourse will introduce basic notions of quantum computing and quantum fault-tolerance. In Part I, I will discuss models of computation, noisy quantum circuits, quantum error-correcting codes, fault-tolerant gadgets, and the threshold theorem. In Part II, I will turn to the classical simulation of (noisy) quantum circuits and discuss how efficient simulations of quantum many-body dynamics can give insights into the fault-tolerance properties of quantum information-processing proposals.

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