Quantum XY criticality in a two-dimensional Bose gas near the Mott transition

Abstract

We derive the equation of state of a two-dimensional Bose gas in an optical lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of the multicritical points where the quantum phase transition between the Mott insulator and the superfluid phase occurs at fixed density and belongs to the three-dimensional XY model universality class. Using a nonperturbative renormalization-group approach, we compute the pressure $P(\mu ,T)$ as a function of chemical potential and temperature. Our results compare favorably with a calculation based on the quantum O(2) model -- we find the same universal scaling function -- and allow us to determine the region of the phase diagram in the vicinity of a quantum multicritical point where the equation of state is universal. We also discuss the possible experimental observation of quantum XY criticality in a ultracold gas in an optical lattice.

v1) 6 pages, 4 figures. v2) Revised version

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum criticality
• Quantum Criticality
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Monte Carlo study of two-dimensional Bose-Hubbard model
• The Higgs mode in a two-dimensional superfluid
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Universal thermodynamics of a two-dimensional Bose gas
• Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems
• Quantum Criticality from in-situ Density Imaging
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• Trapped Resonant Fermions above Superfluid Transition Temperature

Cited by in corpus (12)

• The nonperturbative functional renormalization group and its applications
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Thermodynamics of the two-dimensional XY model from functional renormalization
• Quantum criticality at the superconductor to insulator transition revealed by specific heat measurements
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Goldstone Boson Interaction in D=2+1 (Pseudo-)Lorentz-Invariant Systems with a Spontaneously Broken Internal Rotation Symmetry
• Non-local correlation and entanglement of ultracold bosons in the two-dimensional Bose-Hubbard lattice at finite temperature
• Quantitative Studies on the Quantum Critical Regime near Superfluid to Mott Insulator Transition
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Operator product expansion coefficients from the nonperturbative functional renormalization group