Quantum criticality of a Bose gas in an optical lattice near the Mott transition

Abstract

We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure P(μ,T) versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m^* and scattering length a^*. m^* is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott insulating phase, while a^* is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/U between hopping amplitude and on-site repulsion.

v1) 4 pages, 6 figures. v2) Significant rewriting (new title) with more emphasis on the quantum critical behavior near the Mott transition

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Criticality in Heavy Fermion Metals
• Quantum criticality
• Quantum magnetism and criticality
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Quantum Criticality
• Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas
• Determination of the Equation of State of a Two-Component Fermi Gas at Unitarity
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Signature of Quantum Criticality in the Density Profiles of Cold Atom Systems
• Non-perturbative renormalization-group approach to the Bose-Hubbard model
• Techniques to measure quantum criticality in cold atoms
• Quantum Criticality from in-situ Density Imaging
• Trapped Resonant Fermions above Superfluid Transition Temperature

Cited by in corpus (11)

• The nonperturbative functional renormalization group and its applications
• Ultracold atoms and the Functional Renormalization Group
• Universal thermodynamics of a two-dimensional Bose gas
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Renormalization group study of Bose polarons
• Thermodynamics of a Bose gas near the superfluid--Mott-insulator transition
• A Non-Perturbative Renormalization Group approach to quantum XY spin models
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Quantum XY criticality in a two-dimensional Bose gas near the Mott transition
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition