20 research outputs found
Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
Explaining quantum many-body dynamics is a long-held goal of physics. A
rigorous operator algebraic theory of dynamics in locally interacting systems
in any dimension is provided here in terms of time-dependent equilibrium
(Gibbs) ensembles. The theory explains dynamics in closed, open and
time-dependent systems, provided that relevant pseudolocal quantities can be
identified, and time-dependent Gibbs ensembles unify wide classes of quantum
non-ergodic and ergodic systems. The theory is applied to quantum many-body
scars, continuous, discrete and dissipative time crystals, Hilbert space
fragmentation, lattice gauge theories, and disorder-free localization, among
other cases. Novel pseudolocal classes of operators are introduced in the
process: projected-local, which are local only for some states, crypto-local,
whose locality is not manifest in terms of any finite number of local densities
and transient ones, that dictate finite-time relaxation dynamics. An immediate
corollary is proving saturation of the Mazur bound for the Drude weight. This
proven theory is intuitively the rigorous algebraic counterpart of the weak
eigenstate thermalization hypothesis and has deep implications for
thermodynamics: quantum many-body systems 'out-of-equilibrium' are actually
always in a time-dependent equilibrium state for any natural initial state. The
work opens the possibility of designing novel out-of-equilibrium phases, with
the newly identified scarring and fragmentation phase transitions being
examples.Comment: 30 pages, 6 figures. Detailed examples added. Version as accepted by
PRX. Comments are very welcom
Non-stationarity and Dissipative Time Crystals: Spectral Properties and Finite-Size Effects
We discuss the emergence of non-stationarity in open quantum many-body
systems. This leads us to the definition of dissipative time crystals which
display experimentally observable, persistent, time-periodic oscillations
induced by noisy contact with an environment. We use the Loschmidt echo and
local observables to indicate the presence of a finite sized dissipative time
crystal. Starting from the closed Hubbard model we then provide examples of
dissipation mechanisms that yield experimentally observable quantum periodic
dynamics and allow analysis of the emergence of finite sized dissipative time
crystals. For a disordered Hubbard model including two-particle loss and gain
we find a dark Hamiltonian driving oscillations between GHZ states in the
long-time limit. Finally, we discuss how the presented examples could be
experimentally realized.Comment: 31 pages, 5 figures. Submitted to NJP: Focus on Time Crystal
Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
We review recent results on an exactly solvable model of nonequilibrium
statistical mechanics, specifically the classical Rule 54 reversible cellular
automaton and some of its quantum extensions. We discuss the exact microscopic
description of nonequilibrium dynamics as well as the equilibrium and
nonequilibrium stationary states. This allows us to obtain a rigorous handle on
the corresponding emergent hydrodynamic description, which is treated as well.
Specifically, we focus on two different paradigms of Rule 54 dynamics. Firstly,
we consider a finite chain driven by stochastic boundaries, where we provide
exact matrix product descriptions of the nonequilibrium steady state, most
relevant decay modes, as well as the eigenvector of the tilted Markov chain
yielding exact large deviations for a broad class of local and extensive
observables. Secondly, we treat the explicit dynamics of macro-states on an
infinite lattice and discuss exact closed form results for dynamical structure
factor, multi-time-correlation functions and inhomogeneous quenches.
Remarkably, these results prove that the model, despite its simplicity, behaves
like a regular fluid with coexistence of ballistic (sound) and diffusive (heat)
transport. Finally, we briefly discuss quantum interpretation of Rule 54
dynamics and explicit results on dynamical spreading of local operators and
operator entanglement.Comment: Review paper, 70 pages, 17 figures. To appear in JSTAT special issue
2021 "Emergent Hydrodynamics in Integrable Many-body Systems"; v2 minor
modifications to improve presentatio
Quantum probe spectroscopy for cold atomic systems
We study a two-level impurity coupled locally to a quantum gas on an optical
lattice. For state-dependent interactions between the impurity and the gas, we
show that its evolution encodes information on the local excitation spectrum of
gas at the coupling site. Based on this, we design a nondestructive method to
probe the system's excitations in a broad range of energies by measuring the
state of the probe using standard atom optics methods. We illustrate our
findings with numerical simulations for quantum lattice systems, including
realistic dephasing noise on the quantum probe, and discuss practical limits on
the probe dephasing rate to fully resolve both regular and chaotic spectra.Comment: 17 single-column pages, 4 figures. Matches published versio
Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
We study the null space degeneracy of open quantum systems with multiple
non-Abelian, strong symmetries. By decomposing the Hilbert space representation
of these symmetries into an irreducible representation involving the direct sum
of multiple, commuting, invariant subspaces we derive a tight lower bound for
the stationary state degeneracy. We apply these results within the context of
open quantum many-body systems, presenting three illustrative examples: a
fully-connected quantum network, the XXX Heisenberg model and the Hubbard
model. We find that the derived bound, which scales at least cubically in the
system size the symmetric cases, is often saturated. Moreover, our work
provides a theory for the systematic block-decomposition of a Liouvillian with
non-Abelian symmetries, reducing the computational difficulty involved in
diagonalising these objects and exposing a natural, physical structure to the
steady states - which we observe in our examples.Comment: 19 pages, 3 figures, 3 table
Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit “Doob-transformed” dynamics that optimally realizes rare dynamical events
A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
We study quantum transport properties of an open Heisenberg XXZ spin 1/2
chain driven by a pair of Lindblad jump operators satisfying a global
`microcanonical' constraint, i.e. conserving the total magnetization. We will
show that this system has an additional discrete symmetry which is particular
to the Liouvillean description of the problem. Such symmetry reduces the
dynamics even more than what would be expected in the standard Hilbert space
formalism and establishes existence of multiple steady states. Interestingly,
numerical simulations of the XXZ model suggest that a pair of distinct
non-equilibrium steady states becomes indistinguishable in the thermodynamic
limit, and exhibit sub-diffusive spin transport in the easy-axis regime of
anisotropy Delta > 1.Comment: 14 pages with 5 pdf figures, revised version, as accepted by New
Journal of Physic