# Tensor network simulation of the Kitaev-Heisenberg model at finite temperature

## TL;DR

This paper employs tensor network methods to study the finite-temperature properties of the Kitaev-Heisenberg model, estimating critical temperatures and benchmarking against Monte Carlo results, thus advancing tensor network applications in complex quantum systems.

## Contribution

It introduces an efficient tensor network approach for finite-temperature simulation of the Kitaev-Heisenberg model on a hexagonal lattice, including a novel lattice mapping and benchmarking against Monte Carlo data.

## Key findings

- Critical temperatures are an order of magnitude lower than coupling constants.
- The tensor network method accurately captures spin ordering crossover.
- The approach is validated against Monte Carlo results for the pure Kitaev model.

## Abstract

We investigate the Kitaev-Heisenberg (KH) model at finite temperature using the exact environment full update (eeFU), introduced in Phys. Rev. B 99, 035115 (2019), which represents the purification of a thermal density matrix on an infinite hexagonal lattice by an infinite projected entangled pair state (iPEPS). We show that thanks to a dynamical mapping from a hexagonal to a rhombic lattice, the eeFU on the hexagonal lattice is as efficient as the simple full update (FU) algorithm. Critical temperatures for coupling constants in the stripy and the antiferromagnetic phase are estimated. They are an order of magnitude less than the couplings in the Hamiltonian. By a duality transformation, these results can be mapped to, respectively, the ferromagnetic and zigzag phases. For the special case of the pure Kitaev model, which is tractable by quantum Monte-Carlo but the most challenging for tensor networks, the algorithm is benchmarked against the Monte-Carlo results. It recovers accurately the crossover to spin ordering and qualitatively the one to flux ordering.