Classification of a supersolid: Trial wavefunctions, Symmetry breakings and Excitation spectra

TL;DR

This paper reviews theoretical approaches to supersolids, focusing on symmetry breaking, wavefunctions, and excitation spectra, and introduces a new effective lattice Hamiltonian to better understand their properties.

Contribution

It presents a new effective supersolid Hamiltonian on a lattice and offers insights into symmetry breaking, order parameters, and excitation spectra in supersolids.

Findings

Comparison of supersolids in different systems

Introduction of a new lattice Hamiltonian

Analysis of excitation spectra and detection methods

Abstract

A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal $ U(1) $ symmetry. Here, we review some past and recent works in phenomenological Ginsburg-Landau theories, ground state trial wavefunctions and microscopic numerical calculations. We also write down a new effective supersolid Hamiltonian on a lattice. The eigenstates of the Hamiltonian contains both the ground state wavefunction and all the excited states (supersolidon) wavefunctions. We contrast various kinds of supersolids in both continuous systems and on lattices, both condensed matter and cold atom systems. We provide additional new insights in studying their order parameters, symmetry breaking patterns, the excitation spectra and detection methods.