Stable Gapless Bose Liquid Phases without any Symmetry

TL;DR

This work demonstrates an infinite family of stable gapless bosonic phases, called algebraic Bose liquids (ABL), that do not require symmetry breaking. By enforcing rotationally invariant, derivative-based Gauss-law constraints on rank-n tensor fields, the authors construct emergent gauge theories with self-duality, ensuring that all gap-opening perturbations are irrelevant at the Gaussian fixed point. They show that these phases exhibit gapless excitations with tunable dispersions, and possess a form of topological order on $T^3$ characterized by $6k$ integers. The results significantly expand the landscape of quantum spin liquids and related spinless bosonic phases, linking higher-rank gauge theories to gravity-like excitations and robust, topology-protected gaplessness.

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.

Figures (1)

• Figure 1: The unit cell for the simplest rank-3 model. The red site is three-fold degenerate ($n_{xxx}$), the green sites are two-fold degenerate ($n_{xxy}$) and the blue site is nondegenerate ($n_{xyz}$).