Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

TL;DR

This paper demonstrates how superposing symmetric PEPS tensors can effectively describe spontaneous discrete lattice symmetry breaking, exemplified by a nematic spin liquid in a frustrated spin-1 Heisenberg model.

Contribution

It introduces a novel PEPS superposition method to accurately model symmetry-breaking phases in frustrated quantum spin systems.

Findings

Superposition of PEPS tensors captures nematic phase properties.

Method agrees with ED and DMRG results.

Demonstrates discrete symmetry breaking in a 2D spin model.

Abstract

Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $\pi/2$-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results.