Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model

TL;DR

This paper uses advanced tensor network algorithms to provide numerical evidence of an Ising phase transition at finite temperature in the collinear phase of the spin-1/2 J1-J2 Heisenberg model on a square lattice, revealing how the critical temperature varies with interaction ratios.

Contribution

It introduces an SU(2) invariant tensor network method to accurately study thermal phase transitions in quantum Heisenberg models, avoiding artifacts of symmetry breaking in previous approaches.

Findings

Critical temperature peaks at T_c/J_2 ≈ 0.18 near J_2/J_1 ≈ 1.0.

T_c is suppressed near the zero-temperature boundary of the collinear phase.

T_c vanishes as 1/log(J_2/J_1) in the large J_2/J_1 limit.

Abstract

Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. In units of $J_2$, the critical temperature reaches a maximal value of $T_c/J_2\simeq 0.18$ around $J_2/J_1\simeq 1.0$. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase $J_2/J_1\simeq 0.6$, and it vanishes as $1/\log(J_2/J_1)$ in the large $J_2/J_1$ limit, as predicted by Chandra, Coleman and Larkin [Phys. Rev. Lett. 64, 88, 1990]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.