Quantum phase transitions and thermodynamics of quantum antiferromagnets with competing interactions

TL;DR

This paper investigates quantum phase transitions and thermodynamic properties of an isotropic Heisenberg chain with competing interactions, identifying transition lines and analyzing low-temperature behavior through integrability-based methods.

Contribution

It provides a detailed phase diagram and thermodynamic analysis of the Heisenberg chain with competing interactions using integrability techniques, including numerical and analytical solutions.

Findings

Identified first and second order phase transition lines.

Determined critical exponents for low-temperature asymptotics.

Constructed the ground state phase diagram under various interactions.

Abstract

We study the isotropic Heisenberg chain with nearest and next-nearest neighbour interactions. The ground state phase diagram is constructed in dependence on the additonal interactions and an external magnetic field. The thermodynamics is studied by use of finite sets of non-linear integral equations resulting from integrabiliy. The equations are solved numerically and analytically in suitable limiting cases. We find second and first order transition lines. The exponents of the low temperature asymptotics at the phase transitions are determined.