Spontaneous continuous-symmetry breaking and tower of states in a comb chain

TL;DR

This paper demonstrates spontaneous continuous symmetry breaking and the existence of a tower of states in a one-dimensional antiferromagnetic Heisenberg model on a comb lattice, challenging previous assumptions about 1D systems.

Contribution

It provides the first example of a 1D system with short-range interactions exhibiting a tower of states and spontaneous symmetry breaking, supported by theoretical and numerical analysis.

Findings

Spontaneous continuous symmetry breaking occurs in a 1D comb lattice model.

A tower of states is observed in a 1D ferrimagnetic system with short-range interactions.

The study links the MLM theorem and symmetry breaking in bipartite lattices.

Abstract

Based on the study of a one-dimensional (1D) antiferromagnetic Heisenberg model on a comb lattice, this work identifies an example of spontaneous continuous symmetry breaking in a 1D system with short-range interactions. When a symmetry-preserving relevant perturbation is applied to the system, we find that this model can always be described by the Marshall-Lieb-Mattis (MLM) theorem. The Shen-Qiu-Tian theorem establishes a direct connection between the MLM theorem (in the case of bipartite lattices with unequal numbers of sites in the two sublattices) and the breaking of continuous symmetry. Moreover, although authors of previous studies have suggested that the presence of a tower of states (TOS) serves as an important numerical diagnostic of the tendency of a system toward spontaneous symmetry breaking, these investigations have primarily focused on two-dimensional systems. In 1D systems, however, the presence of long-range order does not automatically imply the emergence of a TOS. Here, we observe the existence of a TOS in a 1D realistic ferrimagnetic lattice system with short-range interactions.