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Title: Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models

Abstract

Based on extensions of quantum Monte Carlo algorithms to incorporate magnetic fields, two criteria to detect superconductivity in two-dimensional Hubbard models are investigated. We calculate both the internal energy [ital E]([Phi],[ital T]) as well as the ground-state energy, [ital E][sub 0]([Phi]), for Hubbard models on a cylinder geometry threaded by a flux [Phi]. The temperature derivative of the superfluid density, [partial derivative][beta][ital D][sub [ital s]]([beta])/[partial derivative][beta], is obtained from the difference in internal energy of systems which differ by a phase twist [pi]/2 in the boundary condition along one lattice direction. In the framework of a Kosterlitz-Thouless transition, [partial derivative][beta][ital D][sub [ital x]]([beta])/[partial derivative][beta] scales to a Dirac [delta] function at the transition temperature. On finite-sized lattices, [partial derivative][beta][ital D][sub [ital s]]([beta])/[partial derivative][beta] shows a response which increases with lattice size. From the functional form of [ital E][sub 0]([Phi]), superconducting or nonsuperconducting ground states may be identified. In both approaches, superconductivity may be detected without prior knowledge of the symmetry and nature of the pairing correlations. For single-band Hubbard models, our results include numerical data which (a) confirm the existence and pin down the transition temperature of a Kosterlitz-Thouless-type transition in the attractive Hubbard model away from half-band filling andmore » (b) show that the quarter-filled repulsive Hubbard model is not superconducting. For the three-band Hubbard model we consider two parameter sets which take into account the differences in static magnetic structure and Fermi surfaces between La-Sr-Cu-O and Y-Ba-Cu-O materials. For both parameter sets, the finite-temperature approach showed no sign of a Kosterlitz-Thouless-type transition up to inverse temperatures [beta]=17.5, in units of Cu-O hopping.« less

Authors:
;  [1];  [2]
  1. Physikalisches Institut, Universitaet Wuerzburg, 97074 Wuerzburg (Germany)
  2. Department of Physics, University of California, Santa Barbara, California 93106-9530 (United States)
Publication Date:
OSTI Identifier:
6903794
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter; (United States)
Additional Journal Information:
Journal Volume: 50:17; Journal ID: ISSN 0163-1829
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HUBBARD MODEL; SUPERCONDUCTIVITY; FLUX QUANTIZATION; KOSTERLITZ-THOULESS THEORY; MAGNETIC FLUX; MONTE CARLO METHOD; SUPERFLUID MODEL; TWO-DIMENSIONAL CALCULATIONS; CALCULATION METHODS; CRYSTAL MODELS; ELECTRIC CONDUCTIVITY; ELECTRICAL PROPERTIES; MATHEMATICAL MODELS; NUCLEAR MODELS; PHYSICAL PROPERTIES; 665411* - Basic Superconductivity Studies- (1992-)

Citation Formats

Assaad, F F, Hanke, W, and Scalapino, D J. Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models. United States: N. p., 1994. Web. doi:10.1103/PhysRevB.50.12835.
Assaad, F F, Hanke, W, & Scalapino, D J. Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models. United States. doi:10.1103/PhysRevB.50.12835.
Assaad, F F, Hanke, W, and Scalapino, D J. Tue . "Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models". United States. doi:10.1103/PhysRevB.50.12835.
@article{osti_6903794,
title = {Temperature derivative of the superfluid density and flux quantization as criteria for superconductivity in two-dimensional Hubbard models},
author = {Assaad, F F and Hanke, W and Scalapino, D J},
abstractNote = {Based on extensions of quantum Monte Carlo algorithms to incorporate magnetic fields, two criteria to detect superconductivity in two-dimensional Hubbard models are investigated. We calculate both the internal energy [ital E]([Phi],[ital T]) as well as the ground-state energy, [ital E][sub 0]([Phi]), for Hubbard models on a cylinder geometry threaded by a flux [Phi]. The temperature derivative of the superfluid density, [partial derivative][beta][ital D][sub [ital s]]([beta])/[partial derivative][beta], is obtained from the difference in internal energy of systems which differ by a phase twist [pi]/2 in the boundary condition along one lattice direction. In the framework of a Kosterlitz-Thouless transition, [partial derivative][beta][ital D][sub [ital x]]([beta])/[partial derivative][beta] scales to a Dirac [delta] function at the transition temperature. On finite-sized lattices, [partial derivative][beta][ital D][sub [ital s]]([beta])/[partial derivative][beta] shows a response which increases with lattice size. From the functional form of [ital E][sub 0]([Phi]), superconducting or nonsuperconducting ground states may be identified. In both approaches, superconductivity may be detected without prior knowledge of the symmetry and nature of the pairing correlations. For single-band Hubbard models, our results include numerical data which (a) confirm the existence and pin down the transition temperature of a Kosterlitz-Thouless-type transition in the attractive Hubbard model away from half-band filling and (b) show that the quarter-filled repulsive Hubbard model is not superconducting. For the three-band Hubbard model we consider two parameter sets which take into account the differences in static magnetic structure and Fermi surfaces between La-Sr-Cu-O and Y-Ba-Cu-O materials. For both parameter sets, the finite-temperature approach showed no sign of a Kosterlitz-Thouless-type transition up to inverse temperatures [beta]=17.5, in units of Cu-O hopping.},
doi = {10.1103/PhysRevB.50.12835},
journal = {Physical Review, B: Condensed Matter; (United States)},
issn = {0163-1829},
number = ,
volume = 50:17,
place = {United States},
year = {1994},
month = {11}
}