Spontaneous Symmetry Breaking and Frustrated Phases

TL;DR

This paper explores a frustrated quantum lattice system with rich phase transitions, spontaneous symmetry breaking, and emergent phenomena like generalized symmetries and fractonic phases, providing detailed analysis of critical behavior and excitations.

Contribution

It introduces a comprehensive study of quantum phase transitions and symmetry breaking in a frustrated lattice model, highlighting the emergence of generalized symmetries and fractonic phases.

Findings

Multiple quantum phase transitions identified

Spontaneous breaking of spatial and internal symmetries

Emergence of generalized polynomial shift symmetries

Abstract

We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system undergoes several quantum phase transitions from both gapped-to-gapless and gapless-to-gapless phases, providing a very rich phase structure with disordered, homogeneous and modulated ordered phases meeting in a quantum Lifshitz point. The gapless phases spontaneously break spatial lattice translations as well as internal symmetries of the form $U(1)^{\mathsf{N}_c}$, where $\mathsf{N}_c$ is the number of independent pitch vectors that arise in the homogeneous and modulated ordered phases. We carry out a detailed analysis of the quantum critical behavior discussing the mechanism leading to the phase transitions. We also discuss a proper characterization of all the gapless phases as well as the nature of the Goldstone excitations. We study the behavior of the correlation functions and identify regions in the phase diagram where the system exhibits generalized symmetries, such as polynomial shift symmetry. This type of symmetry plays an important role in the so-called fractonic phases, which is an exotic form of matter recently discovered.