On the compressibility of deformable spin chains in a vicinity of quantum critical points

TL;DR

This paper investigates how quantum critical points in deformable spin chains influence their elastic properties, particularly compressibility, revealing distinct behaviors near criticality for different models.

Contribution

It provides a comparative analysis of compressibility behavior near quantum critical points across several spin chain models, including the Heisenberg-Ising and XX chains.

Findings

Inverse compressibility shows hysteresis near the critical point in the XX chain.

Compressibility diminishes continuously near the critical point in the Ising and Heisenberg-Ising chains.

Different spin models exhibit distinct elastic responses at quantum criticality.

Abstract

We calculate the ground-state compressibility of a deformable spin-1/2 Heisenberg-Ising chain with Dzyaloshinskii-Moriya interaction to discuss how a quantum critical point inherent in this spin system may manifest itself in the elastic properties of the underlying lattice. We compare these results with the corresponding ones for the spin-1/2 Ising chain in a longitudinal or transverse field and the spin-1/2 $XX$ chain in a transverse field. The inverse compressibility of the spin-1/2 $XX$ chain in a transverse field exhibits a hysteresis in a vicinity of quantum critical point that is accompanied with the finite jump of compressibility. Contrary to this, the inverse compressibility diminishes continuously close to a quantum critical point of the spin-1/2 Ising chain in a transverse field and the spin-1/2 Heisenberg-Ising bond alternating chain.