Experimental evidence for Hilbert-space fragmentation in tilted Fermi-Hubbard chains
Speaker: Monika Aidelsburger (Ludwig-Maximilians-Universität München)
Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems relevant to a variety of research areas, ranging from condensed matter to high-energy physics. In particular, out-of-equilibrium phenomena constitute natural applications of quantum simulators, which have already successfully demonstrated simulations in regimes that are beyond reach using state-of-the-art numerical techniques. This enables us to shed new light on fundamental questions about the thermalization of isolated quantum many-body systems. While generic models are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), violation of ETH is believed to occur mainly in two types of systems: integrable models and manybody localized systems. In between these two extreme limits there is, however, a whole range of models that exhibit more complex dynamics, for instance, due to an emergent fragmentation of the Hilbert space into many dynamically disconnected subspaces. Here, I report on the realization of the tilted 1D Fermi-Hubbard model which lies at the interface of what is commonly known as Stark-MBL and Hilbertspace fragmentation. We observe a robust memory of the initial state over a wide range of parameters, even down to small values of the tilt [1], and observe strong initial-state dependent thermalization in the large tilt limit - a smoking-gun signature of Hilbert-space fragmentation [2].
[1] S. Scherg et al., arXiv:2010.12965 (2020)
[2] T. Kohlert et al., in preparation (2021)
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Real-frequency responses at finite temperature
Speaker: Igor Tupitsyn (UMass Amherst)
Abstract: Nearly all finite temperature calculations are done in the Matsubara representation on the imaginary time or imaginary frequency axis and real-frequency results can only be recovered by performing the numerical analytic continuation (NAC) procedure. Until recently, the infamous NAC problem standing on the way of accurate theoretical descriptions of experimentally relevant observables was considered unavoidable. Here I am going to present a simple generic solution to this problem and demonstrate that the Diagrammatic Monte Carlo technique allows one to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether the diagrammatic series are based on bare or renormalized propagators/interactions. By eliminating the need for NAC from the Matsubara representation, our technique opens the door for studies of spectral densities of arbitrary complexity with controlled accuracy. To demonstrate how it works in practice, I consider the problem of the plasmon line-width in the uniform electron gas.
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Dual-unitary circuit dynamics
Speaker: Pieter Claeys (University of Oxford)
Quantum lattice models with time evolution governed by local unitary quantum circuits can serve as a minimal model for the study of general unitary dynamics governed by local interactions. Although such circuit dynamics exhibit many of the features expected of generic many-body dynamics, exact results generally require the presence of randomness in the circuit. Dual-unitary models are a special class of circuits characterized by an underlying space-time symmetry, allowing their correlations to be calculated exactly without the need for randomness or integrability. We present and discuss exactly solvable (Floquet) models for ergodic and non-ergodic thermalization and prethermalization for correlations and the scrambling of out-of-time-order correlators, and briefly discuss a class of perturbed dual-unitary models.
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Multistage thermalization and a non-Hermitian phantom in many-body systems
Speaker: Marko Znidaric (University of Ljubljana)
A study of random quantum circuits and their rate of producing bipartite entanglement reveals that the relaxation rate is not necessarily given by the gap of the relevant transfer matrix. Due to non-Hermiticity and related non-orthogonality of eigenvectors a many-body explosion of expansion coefficients can happen, resulting in the rate that is either faster, or, even more interestingly, slower than predicted by the largest eigenvalue. This new phenomenon leading to a multistage thermalization is identified in a number of different random circuits, including the fastest possible scramblers.