Finite-temperature degenerate perturbation theory for bosons in optical lattices
arXiv:1906.09661 · doi:10.1103/PhysRevA.100.043609
Abstract
Bosonic atoms confined in optical lattices can exist in two different phases, Mott-insulator and superfluid, depending on the strength of the system parameters, such as the on-site interaction between particles and the hopping parameter. This work is motivated by the fact that non-degenerate perturbation theory applied to the mean-field approximation of the Bose-Hubbard Hamiltonian at zero and finite temperature fails to give consistent results in the vicinity of the Mott-insulator-superfluid phase transition, e.g., the order parameter calculated via non-degenerate perturbation theory reveals an unphysical behavior between neighboring Mott lobes, which is an explicit consequence of degeneracy problems that artificially arise from such a treatment. Therefore, in order to fix this problem, we propose a finite-temperature degenerate perturbation theory approach based on a projection operator formalism which ends up solving such degeneracy problems in order to obtain physically consistent results for the order parameter near the phase transition.
References in corpus (21)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
- Bose-Fermi Mixtures in a Three-dimensional Optical Lattice
- Localization of bosonic atoms by fermionic impurities in a 3d optical lattice
- Atomic quantum gases in Kagomé lattices
- Formation of spatial shell structures in the superfluid to Mott insulator transition
- Coherent collisional spin dynamics in optical lattices
- Interference pattern and visibility of a Mott insulator
- Boson Mott insulators at finite temperatures
- Quantum Phase Diagram of Bosons in Optical Lattices
- Effective Action Approach for Quantum Phase Transitions in Bosonic Lattices
- Visibility of Cold Atomic Gases in Optical Lattices for Finite Temperatures
- Superfluid-Insulator Transitions in Attractive Bose-Hubbard Model with Three-Body Constraint
- Tuning the Quantum Phase Transition of Bosons in Optical Lattices via Periodic Modulation of s-Wave Scattering Length
- Excitation Spectra of Bosons in Optical Lattices from Schwinger-Keldysh Calculation
- Superfluid and Mott Insulating shells of bosons in harmonically confined optical lattices
- Reference data for phase diagrams of triangular and hexagonal bosonic lattices
- Real-Time Ginzburg-Landau Theory for Bosons in Optical Lattices
- Improving Mean-Field Theory for Bosons in Optical Lattices via Degenerate Perturbation Theory
Cited by in corpus (3)
- Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study
- 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