Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part II: Application to the Many-Body Problem

TL;DR

This paper explores the phase diagram of constrained lattice bosons, revealing an Ising transition from atomic to dimer superfluidity, and identifies a new collective mode and quantum critical point through analytical methods.

Contribution

It introduces an analytical framework for studying the many-body phase diagram of constrained bosons, uncovering new collective phenomena and critical behavior beyond mean field approaches.

Findings

Identified shifts in phase boundaries at low densities.

Discovered a new collective mode in the strong coupling limit.

Established the existence of a true Ising quantum critical point near half filling.

Abstract

We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [11]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean field plus spin wave approach. First, we determine shifts in the mean field phase border, which are most pronounced in the low density regime. Second, the investigation of the strong coupling limit reveals the existence of a new collective mode, which emerges as a consequence of enhanced symmetries in this regime. Third, we show that the Ising type phase transition, driven first order via the competition of long wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.