Critical Behavior of the Supersolid transition in Bose-Hubbard Models

TL;DR

This paper investigates the critical phenomena of superfluid to supersolid phase transitions in Bose-Hubbard models, revealing different universality classes and novel behaviors depending on the type of ordering and dimensionality.

Contribution

It provides a detailed analysis of the critical behavior of SF-SS transitions, identifying new universality classes and fluctuation-driven first-order transitions in two and three dimensions.

Findings

SF- CSS transition is in 3D XY universality class.

SF-XSS transition is driven first order by fluctuations.

Multi-critical points exhibit 3D Ising universality.

Abstract

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF--CSS transition is in the three-dimensional XY universality class. The SF--XSS transition exhibits non-trivial new critical behavior, and appears, within a $d=3-\epsilon$ expansion to be driven generically first order by fluctuations. However, within a one--loop calculation directly in $d=2$ a strong coupling fixed point with striking ``non-Bose liquid'' behavior is found. At special isolated multi-critical points of particle-hole symmetry, the system falls into the 3d Ising universality class.