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'').
Highlights
In this paper we have studied the fundamentals of generalised hydrodynamics in noninteracting spin chains
generalised hydrodynamic description (GHD) was originally developed in a perturbative framework, as the asymptotic solution of time evolution in the limit of large time [35,36] or low inhomogeneity [56,57] in integrable systems
Ref. [69] made a first attempt to lift the theory into a non-perturbative level by conjecturing the existence of so-called “locally quasi-stationary states”, which are states completely characterised by a local version of the root densities of the thermodynamic Bethe Ansatz [87]
Summary
The dynamics of integrable quantum many-body systems prepared in inhomogeneous states have attracted an increasing attention for more than two decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22], arguably for their potentiality to elucidate basic questions of quantum transport. In order to overcame this weakness, there have been proposals to go beyond the infinite time/low inhomogeneity limit of the original formulation in interacting integrable systems [79, 80, 82, 83], but, at the same time, some issues in noninteracting spin chains were uncovered. The distinction between root densities and auxiliary fields is not transparent, and, without a proper definition, such fields couple to the root densities in an obscure way This issue is evident in interacting integrable systems, as the aforementioned additional fields do not even appear in the thermodynamic Bethe Ansatz [86,87], which is arguably the framework of GHD.
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