# Generalized criteria of symmetry breaking. A strategy for quantum time crystals

## TL;DR

This paper introduces a new criterion for spontaneous symmetry breaking based on pure phases, applicable to models including quantum time crystals, without relying on ground state properties or time-dependent Hamiltonians.

## Contribution

It proposes a generalized symmetry breaking criterion that broadens applicability, especially to quantum time crystals, by focusing on pure phases rather than ground states.

## Key findings

- Developed a criterion applicable to a wider class of models
- Demonstrated models exhibiting quantum time crystal behavior
- Avoided reliance on time-dependent Hamiltonians

## Abstract

The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis of the standard approach, this criterion applies to a wider class of models. An interesting application is the breaking of time translations. Indeed, we discuss explicit theoretical models which exhibit the prototypical features of quantum time crystals, without the need of a time-dependent Hamiltonian.