Competing density-wave orders in a one-dimensional hard-boson model

TL;DR

This paper maps the phase diagram of a one-dimensional hard-boson model, revealing competing density-wave orders, incommensurate phases, and critical behaviors, with implications for optical lattice experiments and integrable systems.

Contribution

It establishes a connection between a hard-boson model and Baxter's hard-square model, providing exact solutions and phase analysis for constrained bosonic systems.

Findings

Identified density-wave orders with periods 2 and 3

Discovered a floating incommensurate phase

Developed methods to compute the Luttinger parameter in constrained systems

Abstract

We describe the zero-temperature phase diagram of a model of bosons, occupying sites of a linear chain, which obey a hard-exclusion constraint: any two nearest-neighbor sites may have at most one boson. A special case of our model was recently proposed as a description of a ``tilted'' Mott insulator of atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to generate the transfer matrix of Baxter's hard-square model. Aided by exact solutions of a number of special cases, and by numerical studies, we obtain a phase diagram containing states with long-range density-wave order with period 2 and period 3, and also a floating incommensurate phase. Critical theories for the various quantum phase transitions are presented. As a byproduct, we show how to compute the Luttinger parameter in integrable theories with hard-exclusion constraints.