Symmetry breaking gives rise to energy spectra of three states of matter

TL;DR

This paper introduces a unified theoretical framework using symmetry breaking in an interacting phonon Hamiltonian to explain the energy spectra of solids, liquids, and gases, linking microscopic interactions to macroscopic phases.

Contribution

It proposes a novel approach that unifies the description of all three states of matter through symmetry breaking in a phonon Hamiltonian.

Findings

Symmetry breaking leads to energy gaps in shear excitations.

The approach explains the emergence of different phases from microscopic Hamiltonians.

Goldstone theorem underpins the formation of energy spectra across phases.

Abstract

A fundamental task of statistical physics is to start with a microscopic Hamiltonian, predict the system's statistical properties and compare them with observable data. A notable current fundamental challenge is to tell whether and how an interacting Hamiltonian predicts different energy spectra, including solid, liquid and gas phases. Here, we propose a new idea that enables a unified description of all three states of matter. We introduce a generic form of an interacting phonon Hamiltonian with ground state configurations minimising the potential. Symmetry breaking, from the group of rotations in reciprocal space to its subgroup, leads to emergence of energy gaps of shear excitations as a consequence of the Goldstone theorem, and readily results in the emergence of energy spectra of solid, liquid and gas phases.