Models of interacting bosons with exact ground states: a unified approach

TL;DR

This paper introduces a broad class of exactly solvable bosonic lattice models with ground states linked to classical lattice gas weights, unifying various known models and enabling systematic construction of new phases.

Contribution

It presents a unified framework for constructing frustration-free bosonic models with exact ground states related to classical statistical weights, encompassing many known and novel quantum phases.

Findings

Exact ground states with specified density distributions

Representation of known solvable models like toric code and dimer models

Construction of models with quantum spin liquids, supersolids, and Bose surfaces

Abstract

We define an infinite class of ``frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer and vertex models, toric code, and certain Levin-Wen string-net models. We also systematically construct solvable models with other interesting ground states, including ``quantum spin liquids,'' supersolids, ``Bose-Einstein insulators,'' Bose liquids with ``Bose surfaces'', and Bose-Einstein condensates that permit adiabatic evolution from a non-interacting limit to a Gutzwiller-projected limit.