• Amanda Gatto (UIUC)
  
      Long-range entanglement and (de)localization

A result by Gioia and Wang [Phys Rev X 12, 031007 (2022)] showed that translationally symmetric states having nonzero momentum are necessarily long range entangled (LRE). In this talk, I will consider the question: can a notion of momentum for non-translation symmetric states directly encode the nature of their entanglement, as it does for translation symmetric states? We show that this is the case for states in 1D systems with periodic boundary conditions, where localization properties serve as a proxy for entanglement properties. We show how, for 1D systems with periodic boundary conditions, the magnitude |<T>| and phase arg<T> of the expectation value of the translation operator encode (de)localization and entanglement properties of states which break translation symmetry. In particular, we show that, in the continuum limit, |<T>| -> 1 for delocalized states, a proxy for LRE states in 1D systems. This result can be seen as a momentum-space version of Resta's formula for the localization length. We investigate how accurate our results are in different lattice models with and without well-defined continuum limits. 

• Malte Henkel  (Université de Lorraine Nancy)
  
    Generalized Time-Translation Invariance and Physical Ageing".

Physical ageing out of equilibrium is characterized by slow dynamics, the absence of time-translation invariance, and dynamical        scaling.However, we shall show that a generalised form of time-translation invariance allows one to recover the known generic phenomenology of ageing. This behaviour arises in classical many-body systems after a rapid quench from an initially disordered state to a temperature ( T \leq T_c ), i.e., at or below the critical temperature ( T_c ). Generalised time-translation invariance is obtained, out of equilibrium, through a change of representation of the generators of the Lie algebra of dynamical symmetries associated with scale invariance and time-translation invariance.

• Paulo Mourão (Sapienza University of Rome)

The Physics of Associative Memories

• Andrea Pizzi (Cambridge University)

Genuine quantum scars in many-body spin systems

Chaos makes isolated systems of many interacting particles quickly thermalize and forget their past. While this picture applies to simple observables such as order parameters and correlators, it need not extend to more complex quantities like wavefunction amplitudes, that are becoming accessible in quantum computers and simulators and can reveal a richer structure. In this talk, I will show that although the quantum eigenstates are thermal and strongly entangled, many of them are genuinely scarred, that is, have an enlarged amplitude along underlying classical unstable periodic orbits. For a wide family of spin models, scarring produces non-Porter-Thomas amplitude statistics and makes the system more likely to revisit the orbit it was initialized on, retaining memory of its past and weakly breaking ergodicity. Some features of scarring even extend beyond periodic orbits, giving rise to "quantum trails" along generic trajectories. These findings prove structure in spite of chaos in many-body quantum systems.

• Clayton Peacock (New York University)

Integrability and single particle localization in Krylov space 

• Miguel Gonçalves (Princeton University)

Excitations in moiré fractional Chern insulators 

• Pedro Ninhos (University of Southern Denmark)

Microscopic screening theory for excitons in two-dimensional materials: A bridge between effective model and ab initio descriptions 

• Paul McClarty (Max Planck Institute)

Brief review of Kitaev quantum double models 

Review of spontaneous breaking of continuous symmetries in 1D quantum systems

• Federico Balducci (Max Planck Institute)

Non-Hermitian many-body localization: singular value decomposition and transport properties 

In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. In this talk, I discuss some recent results on the fate of many-body localization in open systems described by a non-Hermitian Hamiltonian, which can be obtained from Markovian dynamics conditioned on null measurement. First, I show how the singular value decomposition can be used as an effective tool for characterizing dynamical phases, with a crossover of the singular value statistics from Wigner-Dyson to Poisson, and of the singular vectors from delocalized to localized. Second, I shift the focus to dynamical probes, specifically the steady-state spin current, and investigate transport properties. I show that the steady-state current in an interacting Hatano-Nelson model remains finite at all accessible disorders, with no evidence of a transition. These results reveal a stark discrepancy between spectral and singular indicators on one side, which suggest localization, and transport behavior on the other side, which indicates delocalization.

• Jacopo Gliozzi (University of Illinois Urbana-Champaign)

Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions