Stable Gapless Bose Liquid Phases without any Symmetry

TL;DR

This paper generalizes stable algebraic Bose liquid phases to include more exotic gapless excitations, demonstrating their stability and topological properties without relying on symmetry constraints.

Contribution

It introduces new stable algebraic Bose liquid phases with exotic excitations and constructs their topological invariants, extending previous models.

Findings

Existence of stable phases with graviton-like excitations.

Presence of algebraic topological ground state degeneracy.

Construction of topological invariants for these phases.

Abstract

It is well-known that a stable algebraic spin liquid state (or equivalently an algebraic Bose liquid (ABL) state) with emergent gapless photon excitations can exist in quantum spin ice systems, or in a quantum dimer model on a bipartite $3d$ lattice. This photon phase is stable against any weak perturbation without assuming any symmetry. Further works concluded that certain lattice models give rise to more exotic stable algebraic Bose liquid phases with graviton-like excitations. In this paper we will show how these algebraic Bose liquid states can be generalized to stable phases with even more exotic types of gapless excitations and then argue that these new phases are stable against weak perturbations. We also explicitly show that these theories have an (algebraic) topological ground state degeneracy on a torus, and construct the corresponding topological invariants.