Critical behavior of the supersolid transition in Bose-Hubbard models

Abstract

We study the phase transitions of interacting bosons at zero temperature between superfluid ͑SF͒ and supersolid ͑SS͒ 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 ͑X͒ and collinear ͑C͒, 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 nontrivial critical behavior, and appears, within a dϭ3Ϫ⑀ expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in dϭ2 a strong-coupling fixed point with striking ''non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.

Superfluidity and phase transitions in a resonant Bose gas

“…2 the MSF-ASF transition takes place at a critical value of detuning ν c (T, n) determined by the strength of atomic and molecular interactions, shifting it away from its noninteracting value of 0. At zero temperature this is a continuous quantum phase transition that for a d-dimensional system is in the (d+1)-dimensional classical Ising universality class 49,50,51 with 10) where g 1 , g 12 , and g 2 are, respectively, the atomatom, atom-molecule and molecule-molecule interaction strengths, related in the standard way to the corresponding scattering lengths, 15 and α is the Feshbach resonance coupling. The transition at ν c is characterized, upon approach from the MSF side, by the vanishing of the singleatom excitation gap E gap MSF (ν), and, upon approach from the ASF side, by the disappearance of the atomic condensate n 10 (ν).…”

“…However, as will be seen, a coupling of the scalar order parameter to the strongly-fluctuating Goldstone mode of the MSF phase has a nontrivial effect on the Ising transition, quite likely driving it first order sufficiently close to the transition. 50,51 Bose-condensation of atoms (ordering ofψ 1 ) directly from the normal state breaks the full U (1) × Z 2 symmmetry and corresponds to a direct, continuous N-AMSF phase transition. Since it is associated with the ordering of a complex scalar field, one expects (and finds) it also to be in the well-studied XY-model universality class, and to exhibit a single Goldstone mode corresponding to common (locked) phase fluctuations of the condensate fields Ψ 01 and Ψ 02 .…”

Quantum Phase Transition in an Atomic Bose Gas with a Feshbach Resonance

“…These field theories have the familiar φ 4 form, except that at T = 0 there is also a marginal coupling to dynamic density fluctuations of the superfluid which apparently drives the transition weakly first-order [25] (the T > 0 transition can remain second order). The critical precursors of the transition lead to a large density of states for collective low energy excitations, which will strongly damp single-particle excitations.…”

Excitations in Correlated Superfluids near a Continuous Transition into a Supersolid

“…(1), and could be, in principle, derived using functional integral methods as outlined for a related model in Ref. [12]. Here we treat the coefficients as phenomenological parameters.…”