Helicity modulus in the two-dimensional Hubbard model

Journal Article · Sun Mar 14 23:00:00 EST 1993 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.47.6256· OSTI ID:6742950

Denteneer, P J.H.; An, G; van Leeuwen, J M.J. ^[1]

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1. Instituut-Lorentz, University of Leiden, P.O. Box 9506, 2300 RA Leiden (Netherlands)

The helicity modulus, which is the stiffness associated with a twisted order parameter, for the two-dimensional Hubbard model is calculated for the equivalent cases of (i) attractive on-site interaction (negative [ital U]) with arbitrary strength, arbitrary electron density, and zero magnetic field and (ii) repulsive on-site interaction (positive [ital U]) with arbitrary strength, at half-filling and in an arbitrary magnetic field. An explicit formula for the helicity modulus is derived using the Bogoliubov-Hartree-Fock approximation. An improved value for the helicity modulus is obtained by performing variational Monte Carlo calculations using a Gutzwiller projected trial wave function. To within a small correction term the helicity modulus is found to be given by [minus]1/8 the average kinetic energy. The variational Monte Carlo calculation is found to increase the value of the helicity modulus by a small amount (about 5% for intermediate values of the interaction strength) compared to the results from the Bogoliubov-Hartree-Fock approximation. In the case of attractive interaction, from a comparison with the Kosterlitz-Thouless relation between critical temperature and helicity modulus, the critical temperature for a Kosterlitz-Thouless transition is calculated and a phase diagram is obtained. An optimal critical temperature is found for an intermediate value of [ital U]. We discuss connections of our results with results in the literature on the Hubbard model using the random-phase approximation and quantum Monte Carlo calculations.

• OSTI ID: 6742950
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 47:11; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

665411* -- Basic Superconductivity Studies-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BCS THEORY
CALCULATION METHODS
CONFIGURATION
CRYSTAL MODELS
DATA
HELICAL CONFIGURATION
INFORMATION
MAGNETIC FIELDS
MATHEMATICAL MODELS
MONTE CARLO METHOD
NUMERICAL DATA
ORDER PARAMETERS
PHYSICAL PROPERTIES
STRESSES
THEORETICAL DATA
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
TWO-DIMENSIONAL CALCULATIONS