Exact few-body results for strongly correlated quantum gases in two dimensions

Journal Article · Sun Aug 01 04:00:00 EDT 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.82.054524· OSTI ID:21421385

Xiaji, Liu; Hui, Hu; Drummond, Peter D ^[1]

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1. ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing phenomena in solid materials, such as high-T{sub c} superconductivity and the fractional quantum-Hall effect. However, theoretical methods are plagued by the existence of significant quantum fluctuations. Here, we present two- and three-body exact solutions for both fermions and bosons trapped in a two-dimensional harmonic potential with an arbitrary s-wave scattering length. These few-particle solutions link in a natural way to the high-temperature properties of many-particle systems via a quantum virial expansion. As a concrete example, using the energy spectrum of few fermions, we calculate the second and third virial coefficients of a strongly interacting Fermi gas in two dimensions, and consequently investigate its high-temperature thermodynamics. Our thermodynamic results may be useful for ongoing experiments on two-dimensional Fermi gases. These exact results also provide an unbiased benchmark for quantum Monte Carlo simulations of two-dimensional Fermi gases at high temperatures.

• OSTI ID: 21421385
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 5 Vol. 82; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CALCULATION METHODS
COMPUTERIZED SIMULATION
DIMENSIONS
ENERGY SPECTRA
EXACT SOLUTIONS
FERMI GAS
FERMIONS
FLUCTUATIONS
FLUIDS
GASES
HARMONIC POTENTIAL
HIGH-TC SUPERCONDUCTORS
LENGTH
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
NUCLEAR POTENTIAL
PARTIAL WAVES
PHYSICAL PROPERTIES
POTENTIALS
S WAVES
SCATTERING LENGTHS
SIMULATION
SOLIDS
SPECTRA
SUPERCONDUCTORS
THERMODYNAMIC PROPERTIES
THREE-BODY PROBLEM
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
TYPE-II SUPERCONDUCTORS
VARIATIONS