Ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping

Abstract

We compute the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the 1d to the 2d system. We find that the tip of the lobe lies on a curve controlled by the 1d limit over the full anisotropy range while the universality class is always the same as in the isotropic 2d system. This behavior can be derived analytically from the lowest RG equations and has a form typical for the underlying Kosterlitz-Thouless transition in 1d. We also compute the phase boundary of the Mott lobe for strong anisotropy and compare it to the 1d system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.

4 pages + references, 4 figures

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• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• Bose-Hubbard lattice as a controllable environment for open quantum systems
• Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders
• Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal
• Anisotropic superfluidity of two-dimensional excitons in a periodic potential
• Competing instabilities at long length scales in the one-dimensional Bose-Fermi-Hubbard model at commensurate fillings
• Quantum phase transition of the Bose-Hubbard model on cubic lattice with anisotropic hopping
• Phase transitions of the dimerized Kane-Mele model with/without the strong interaction
• Mott-insulating phases of the Bose-Hubbard model on quasi-1D ladder lattices