Many-body physics of spontaneously broken higher-rank symmetry: from fractonic superfluids to dipolar Hubbard model

TL;DR

This paper explores the theory of spontaneous higher-rank symmetry breaking in many-body systems, leading to exotic phases like fractonic superfluids, and discusses models, ground states, excitations, and potential experimental realizations.

Contribution

It introduces new theoretical insights into higher-rank symmetry breaking, including models, order parameters, and physical phenomena in many-fracton systems.

Findings

Development of minimal models for HRS

Identification of Goldstone modes and order parameters

Analysis of hydrodynamics and KT-like physics in fractonic systems

Abstract

Fractonic superfluids are exotic phases of matter in which bosons are subject to mobility constraints, resulting in features beyond those of conventional superfluids. These exotic phases arise from the spontaneous breaking of higher-rank symmetry (HRS) in many-body systems with higher-moment conservation, such as dipoles, quadrupoles, and angular moments. The aim of this paper is to introduce exciting developments on the theory of spontaneous symmetry breaking in such systems, which we refer to as ``many-fracton systems''. More specifically, we introduce exciting progress on general aspects of HRS, minimal model construction, realization of symmetry-breaking ground states, order parameter, off-diagonal long-range order (ODLRO), Noether currents with continuity equations, Gross-Pitaevskii equations, quantum fluctuations, Goldstone modes, specific heat, generalized Mermin-Wagner theorem, critical current, Landau criterion, symmetry defects, and Kosterlitz-Thouless (KT)-like physics, hydrodynamics, and dipolar Hubbard model realization. This paper is concluded with several future directions.