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

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.

30 pages, 12 figures; v2: minor revisions; Submitted to SciPost Physics

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Cited by in corpus (13)

• Quantum Generalized Hydrodynamics
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• Edge singularities and quasi-long-range order in non-equilibrium steady states
• Entanglement entropies of inhomogeneous Luttinger liquids
• Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics
• Interplay between transport and quantum coherences in free fermionic systems
• The Whitham approach to Generalized Hydrodynamics
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Spin-1/2 $XX$ chain in a transverse field with regularly alternating $g$-factors: Static and dynamic properties
• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy