LSM and CPT

TL;DR

This paper investigates 1+1d lattice models with anti-unitary symmetries, exploring their anomalies, constraints on phases, and how these anomalies manifest or are matched in continuum theories, including emergent symmetries.

Contribution

It provides a detailed analysis of anomalies in lattice models with anti-unitary symmetries and their relation to continuum CPT symmetry, revealing new insights into symmetry matching and emergent phenomena.

Findings

Identification of mod 8 anomaly in Majorana chain

Discovery of mod 2 anomalies in spin chains

Different mechanisms for anomaly matching in continuum theories

Abstract

We study a number of 1+1d lattice models with anti-unitary symmetries that simultaneously reflect space and reverse time. Some of these symmetries are anomalous, leading to Lieb-Schultz-Mattis-type constraints, thus excluding a trivially gapped phase. Examples include a mod 8 anomaly in the Majorana chain and various mod 2 anomalies in the spin chain. In some cases, there is an exact, non-anomalous lattice symmetry that flows in the continuum to CPT. In some other cases, the CPT symmetry of the continuum theory is emergent or absent. Depending on the model, the anomaly of the lattice model is matched in the continuum in different ways. In particular, it can be mapped to an emergent anomaly of an emanant symmetry.