Quantum XX-model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium

TL;DR

This paper exactly solves a quantum XX-model with competing interactions, revealing rich phase diagrams including ferromagnetic, antiferromagnetic, and XY phases, and explores non-equilibrium dynamics such as quenches and dynamical phase transitions.

Contribution

It provides an exact solution for the one-dimensional quantum XX-model with competing interactions and analyzes its equilibrium phases and non-equilibrium relaxation dynamics.

Findings

Identified ferromagnetic, antiferromagnetic, and XY phases in the model.

Discovered remanent order and dynamical phase transitions after quenches.

Linked the phases to supersolid states in the equivalent Bose-Hubbard model.

Abstract

We consider the quantum XX-model in the presence of competing nearest-neighbour and global-range interactions, which is equivalent to a Bose-Hubbard model with cavity mediated global range interactions in the hard core boson limit. Using fermionic techniques the problem is solved exactly in one dimension in the thermodynamic limit. The ground state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY-phase having quasi-long-range order. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF-phase beyond a static metastability line AF order arises on top of remanent XY quasi-long-range order, which corresponds to dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.