Marin Bukov (Dresden), François Huveneers (London), Andrea De Luca (Cergy), David Luitz (Bonn), Markus Mueller (Villigen), Wojciech De Roeck (Leuven), Silvia Pappalardi (Koeln), Simone Warzel (Muenchen).

Wojciech De Roeck (Leuven): TBA.

TBA

Marin Bukov (Dresden): Geometric Floquet Theory.

We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential U(1)->Z. This allows us to introduce a unique gauge-invariant formulation, decomposing the dynamics into a purely geometric and a purely dynamical evolution. The dynamical Kato operator provides an unambiguous sorting of the quasienergy spectrum, identifying a unique Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands.

François Huveneers (London): Absence of Normal Transport in an Interacting Disordered Spin Chain.

Many-body localization (MBL) is an out-of-equilibrium phase of matter featuring emergent integrability: There exists a complete set of local integrals of motion. As a result, an MBL system remembers its initial state for arbitrarily long times if the system is thermally isolated. This implies, in particular, a total absence of transport. Demonstrating this with mathematical rigor proves highly challenging. In this talk, I will present a theorem stating that the diffusion constant of such systems vanishes, indicating that transport is at most sub-diffusive. An interesting aspect of the proof is that it relies on establishing MBL in some portions of the chains that are immune from resonances. Additionally, it rules out some numerical results that suggested MBL would not exist at all. Our work represents thus a step forward in rigorously establishing the existence of the MBL phase in one-dimensional systems.
From a work with W. De Roeck, L. Giacomin and O. Prosniak.

Andrea De Luca (Cergy): New universal behaviors of unitary and nonunitary chaotic quantum dynamics.

I will discuss how many natural quantities that characterize quantum dynamics spontaneously lend themselves to analysis in terms of replicas. A common example is the study of entanglement entropies and thus entropy production mechanisms. I will introduce a class of models, known as random circuits, characterized by a local random matrix structure. For the latter, averaging over the ensemble of random matrices leads to an interaction in the space of replicas and interesting statistical physics models. I will show how this approach provides generic predictions for entanglement, correlation functions, and the structure of many-body wave functions. Finally, I will discuss in the same framework the case of nonunitary dynamics induced by the presence of quantum measures that can lead to phase transitions in the space of replicas.

David Luitz (Bonn): Eigenstate Correlations, the Eigenstate Thermalization Hypothesis, and Quantum Information Dynamics in Chaotic Many-Body Quantum Systems.

We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterize entanglement dynamics and operator spreading. In order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider Floquet systems in which there are no conserved densities. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalization hypothesis (ETH). In particular, ETH provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations among sets of four or more eigenstates. We establish the simplest correlation function that captures these correlations and discuss features of its behavior that are expected to be universal at long distances and low energies. We also propose a maximum-entropy ansatz for the joint distribution of a small number 𝑛 of eigenstates. In the case 𝑛=2, this ansatz reproduces ETH. For 𝑛=4 it captures both the growth with time of entanglement between subsystems, as characterized by the purity of the time-evolution operator, and also operator spreading, as characterized by the behavior of the out-of-time-order correlator. We test these ideas by comparing results from Monte Carlo sampling of our ansatz with exact diagonalization studies of Floquet quantum circuits.
Dominik Hahn, David J. Luitz, and J. T. Chalker Phys. Rev. X 14, 031029

Markus Mueller (Villigen): Exact solution of the classical and quantum Heisenberg mean field spin glasses.

While the physics of classical and quantum Ising spin glasses has been understood rather thoroughly, glasses of Heisenberg (vector) spins have remained a difficult and largely unsolved problem, including especially its quantum version, which governs the local moments in randomly doped, strongly correlated materials.
I will present the numerically exact mean field solution of quantum and classical Heisenberg spin glasses, based on the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time Quantum Monte Carlo. I will compare the exact solution of the SU(2) problem to its by now very popular SU(M) version in the large M limit, known as the Sachdev-Ye-Kitaev (SYK) model.
We find that the Heisenberg (vector) spin glasses have a rougher energy landscape than their Ising analogues, affecting their avalanche response to external stimuli. The short time quantum dynamics and collective excitations exhibit a surprisingly slow evolution with temperature, that, at asymptotically low temperatures, tend to the superuniversal form found so far in all insulating mean field glasses. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, similar to those found at the melting quantum critical point. Interestingly, they strongly resemble the Planckian dynamics of the SYK model, even though the underlying physical mechanisms are different.

Silvia Pappalardi (Koeln): Theory of robust quantum many-body scars in long-range interacting systems.

Quantum many-body scars are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this talk, I will describe how clean, long-range interacting quantum spin systems generically host robust quantum many-body scars. Our theory unveils the stability mechanism of such states for arbitrary system size and predicts instances of its breakdown, e.g. near dynamical critical points or in the presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for the presence or absence of heating under periodic driving for sufficiently long-range decay of two-body interaction.

Simone Warzel (Muenchen): Rigorous results on quantum p-spin glasses.

In this talk, I will give an overview of rigorous results on quantum versions of mean-field spin glasses in which the interaction is of p-body type. In particular, this will address their free energy as expressed through a quantum Parisi formula and their phase diagrams.
For the p-spin Ising model in a transversal magnetic field, a recent proof of the convergence of the quantum free energy as p tends to infinity towards the free energy of the quantum random energy model will be sketched.

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