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

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.043634· OSTI ID:21454818

Hen, Itay; Rigol, Marcos ^[1]

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1. Department of Physics, Georgetown University, Washington, DC 20057 (United States)

We study the ground-state properties of trapped inhomogeneous systems of hardcore bosons in two- and three-dimensional lattices. We obtain 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 density, and compressibility. In the presence of a trap, there is in general a spatial coexistence of superfluid and insulating domains. 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. Our analysis can be used to describe bosons in optical lattices where the onsite interaction U is much larger than the hopping amplitude t.

• OSTI ID: 21454818
• Journal Information: Physical Review. A, Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevA.82.043634; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BOSONS
COMPARATIVE EVALUATIONS
COMPRESSIBILITY
DENSITY
EQUATIONS OF STATE
FLUCTUATIONS
FREE ENERGY
GROUND STATES
KINETIC ENERGY
MEAN-FIELD THEORY
MONTE CARLO METHOD
NUMERICAL ANALYSIS
SPIN WAVES
SUPERFLUIDITY
THREE-DIMENSIONAL CALCULATIONS
TRAPPING
CALCULATION METHODS
ENERGY
ENERGY LEVELS
EQUATIONS
EVALUATION
MATHEMATICS
MECHANICAL PROPERTIES
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
VARIATIONS