Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice

TL;DR

This paper reveals that frustration in quantum antiferromagnets on the triangular lattice induces spontaneous parity breaking, shaping nontrivial phases, with findings supported by advanced tensor network calculations.

Contribution

It introduces a systematic rule linking frustration to spontaneous parity breaking, predicting phase emergence in quantum antiferromagnets and classifying phases by their parity features.

Findings

Parity-broken phases appear only at intermediate spin values.

Enhanced frustration in bilayer systems leads to supersolid phases.

Tensor network methods confirm the phase predictions.

Abstract

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In this work, we show that phases induced by frustration are systematically shaped by an implicit rule of thumb associated with spontaneous parity breaking. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears only at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.