Locally quasi-stationary states in noninteracting spin chains

Abstract

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

42 pages, 2 figures (with numerical checks and an improved analysis of inhomogeneous Hamiltonians)

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Cited by in corpus (42)

• Finite-temperature transport in one-dimensional quantum lattice models
• Correlation functions and transport coefficients in generalised hydrodynamics
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• A short introduction to Generalized Hydrodynamics
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• Diffusion and superdiffusion from hydrodynamic projections
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Interplay between transport and quantum coherences in free fermionic systems
• BBGKY Hierarchy and Generalised Hydrodynamics
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Global Quenches after Localised Perturbations
• Scaling of fronts and entanglement spreading during a domain wall melting
• The Whitham approach to Generalized Hydrodynamics
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• On the Hydrodynamics of Unstable Excitations
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• The Staircase Model: Massless Flows and Hydrodynamics
• Connected correlations in partitioning protocols: a case study and beyond
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy
• Quantum fluctuating theory for one-dimensional shock waves
• A hydrodynamic approach to Stark localization
• Wavelet representation of hardcore bosons
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Kinetics of Quantum Reaction-Diffusion systems
• Anomalous charge transport in the sine-Gordon model
• Asymptotic behaviour of determinants through the expansion of the Moyal star product
• Enhanced correlations due to ballistic transport
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Analytical solution of a free-fermion chain with time-dependent ramps
• Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion