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Title: 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 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.

Authors:
;  [1]
  1. Department of Physics, Georgetown University, Washington, DC 20057 (United States)
Publication Date:
OSTI Identifier:
21454818
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.82.043634; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Hen, Itay, and Rigol, Marcos. Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.043634.
Hen, Itay, & Rigol, Marcos. Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices. United States. https://doi.org/10.1103/PHYSREVA.82.043634
Hen, Itay, and Rigol, Marcos. 2010. "Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices". United States. https://doi.org/10.1103/PHYSREVA.82.043634.
@article{osti_21454818,
title = {Analytical and numerical study of trapped strongly correlated bosons in two- and three-dimensional lattices},
author = {Hen, Itay and Rigol, Marcos},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.82.043634},
url = {https://www.osti.gov/biblio/21454818}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 82,
place = {United States},
year = {Fri Oct 15 00:00:00 EDT 2010},
month = {Fri Oct 15 00:00:00 EDT 2010}
}