Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices

Abstract

We study the ground-state properties of trapped inhomogeneous systems of hardcore bosons in two- and three-dimensional lattices. We obtain our results both numerically, using quantum Monte Carlo techniques, and via several analytical approximation schemes, such as the Gutzwiller-mean-field approach, a cluster-mean-field method and a spin-wave analysis which takes quantum fluctuations into account. We first study the homogeneous case, for which simple analytical expressions are obtained for all observables of interest, and compare the results with the numerical ones. We obtain the equation of state of the system along with other thermodynamic properties such as the free energy, kinetic energy, superfluid density, condensate fraction and compressibility. In the presence of a trap, superfluid and insulating domains coexist in the system. We show that the spin-wave-based method reproduces the quantum Monte-Carlo results for global as well as for local quantities with a high degree of accuracy. We also discuss the validity of the local density approximation in those systems. Our analysis can be used to describe bosons in optical lattices where the onsite interaction U is much larger than the hopping amplitude t.

14 pages, 14 figures

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Local quantum criticality in confined fermions on optical lattices
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Spatial correlations of trapped 1d bosons in an optical lattice
• Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
• Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice
• Phases of a 2D Bose Gas in an Optical Lattice
• Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice
• Trapping and cooling fermionic atoms into the Mott and Néel states
• Superfluid to Mott-insulator transition of hardcore bosons in a superlattice
• Phase diagram of the hardcore Bose-Hubbard model on a checkerboard superlattice
• Numerical simulations of strongly correlated fermions confined in 1D optical lattices
• Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap
• Phases of Bosons or Fermions in confined optical lattices
• Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing

Cited by in corpus (10)

• Coherent and dissipative dynamics at quantum phase transitions
• Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder
• Dynamics of Disordered States in the Bose-Hubbard Model with Confinement
• Semiclassical approach to ground-state properties of hard-core bosons in two dimensions
• Atom-atom correlations in time-of-flight imaging of ultra-cold bosons in optical lattices
• Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator
• Critical parameters from trap-size scaling in trapped particle systems
• Temperature-dependent excitation spectra of ultra-cold bosons in optical lattices
• Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions