1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction

TL;DR

This paper demonstrates that non-Hermitian constructions enable spontaneous symmetry breaking and long-range order at finite temperatures in one-dimensional systems, challenging traditional Hermitian limitations.

Contribution

It introduces a novel non-Hermitian approach to achieve symmetry breaking in 1D models, revealing new phases and topological features.

Findings

Spontaneous symmetry breaking occurs at finite temperatures in non-Hermitian 1D models.

Order parameters and specific heat support the existence of ordered phases.

Non-Hermitian effects inhibit domain-wall proliferation, enabling long-range order.

Abstract

Spontaneous symmetry breaking generally circumvents one-dimensional systems with local interactions in thermal equilibrium. Here, we analyze a category of one-dimensional Hermitian models via local non-Hermitian constructions. Notably, spontaneous symmetry breaking and long-range order may emerge at finite temperatures in such systems under periodic boundary conditions, in sharp contrast to Hermitian constructions. We demonstrate clear numerical evidence, such as order parameters and specific heat, supporting phase diagrams with robust ordered phases. Non-Hermitian physics plays a vital role in prohibiting domain-wall proliferation and promoting spontaneous symmetry breaking. The fermions exhibit an exotic topological nature in their path-integral windings, which uphold nonzero integers -- commonly a non-Hermitian signature -- in the ordered phases, thus offering a novel and spontaneous origin for both symmetry breaking and non-Hermiticity.