Emergent Gravity at a Lifshitz Point from a Bose Liquid on the Lattice

TL;DR

This paper introduces a lattice boson model that exhibits a stable algebraic Bose liquid phase, which manifests as emergent quantum gravity at a Lifshitz fixed point, and explores phase transitions between different gravity phases.

Contribution

It presents a lattice model realizing emergent quantum gravity at a Lifshitz point and analyzes phase transitions between different algebraic Bose liquid phases.

Findings

Stable algebraic Bose liquid phase at low energy.

Emergent quantum gravity at a z=3 Lifshitz fixed point.

Phase transition to a z=2 Lifshitz gravity phase.

Abstract

We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1 dimensions. The stability of this algebraic Bose liquid phase is guaranteed by the gauge symmetry of gravitons and self-duality of the low energy field theory. By tuning one parameter in the lattice boson model we can drive a phase transition between the z = 3 Lifshitz gravity and another algebraic Bose liquid phase, described by gravity at the z = 2 Lifshitz point.