Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state

TL;DR

This paper investigates high-energy, low-entropy states in the XXZ spin chain that exhibit quantum criticality, using integrability and Luttinger theory to analyze static and dynamic correlations, revealing detailed agreement between methods.

Contribution

It introduces a detailed analysis of high-energy, low-entropy critical states in the XXZ model through integrability and effective field theory, extending understanding beyond ground states.

Findings

Correlations in high-energy states match Luttinger theory predictions.

Static and dynamic correlations show signatures of Fermi sea splitting.

Good agreement between integrability results and field theory asymptotics.

Abstract

Pumping a finite energy density into a quantum system typically leads to `melted' states characterized by exponentially-decaying correlations, as is the case for finite-temperature equilibrium situations. An important exception to this rule are states which, while being at high energy, maintain a low entropy. Such states can interestingly still display features of quantum criticality, especially in one dimension. Here, we consider high-energy states in anisotropic Heisenberg quantum spin chains obtained by splitting the ground state's magnon Fermi sea into separate pieces. Using methods based on integrability, we provide a detailed study of static and dynamical spin-spin correlations. These carry distinctive signatures of the Fermi sea splittings, which would be observable in eventual experimental realizations. Going further, we employ a multi-component Tomonaga-Luttinger model in order to predict the asymptotics of static correlations. For this effective field theory, we fix all universal exponents from energetics, and all non-universal correlation prefactors using finite-size scaling of matrix elements. The correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior. Finally, we discuss the description of dynamical correlations from a mobile impurity model, and clarify the relation of the effective field theory parameters to the Bethe Ansatz solution.