Nonlinear. sigma. model and static holes

Journal Article · Fri Feb 01 04:00:00 EST 1991 · Physical Review, B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.43.2615· OSTI ID:5839385

Bitar, K ^[1]; Manousakis, E ^[2]

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306 (US)
2. Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306 (USA)

We study certain aspects of the nonlinear {sigma} model regularized on the lattice in two space and one Euclidean-time dimensions using the Monte Carlo method. For certain purposes this model is considered as the long-wavelength limit of the quantum spin-{ital S} antiferromagnetic Heisenberg model in two space dimensions, where the different spin cases map to different values of the coupling constant {ital g} of the {sigma} model. For the value of {ital g} that corresponds to the spin-1/2 case on the square lattice, we find that the most probable configurations are characterized by large-ampltiude short-range quantum fluctuations. Such configurations lack smoothness, which, however, can be achieved by means of real-space block-spin transformations. We calculate the Berry phase correlations, namely, the correlation function {ital C}{sub {ital i}{ital j}}=={l angle}exp{l brace}{ital iS}({Sigma}({bold r}{sub {ital i}})+({minus}1){sup {vert bar}{ital i}{minus}{ital j}{vert bar}}{Sigma} ({bold r}{sub {ital j}})){r brace}{r angle}, where {Sigma}({bold r}{sub {ital i}}) is the area on the unit sphere defined by the path of the spin located at the spatial lattice point {bold r}{sub {ital i}} during its Euclidean-time evolution. We find that the contribution to hole-hole attraction from such correlations is limited to distances of a few lattice spacings. Finally, we examine the possible presence of topological monopole singularities in configurations, and we find only spin-wave excitations.

• DOE Contract Number: FC05-85ER25000
• OSTI ID: 5839385
• Journal Information: Physical Review, B: Condensed Matter; (USA), Journal Name: Physical Review, B: Condensed Matter; (USA) Vol. 43:4; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656100* -- Condensed Matter Physics-- Superconductivity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPUTERIZED SIMULATION
CRYSTAL MODELS
HEISENBERG MODEL
HIGH-TC SUPERCONDUCTORS
HOLES
MATHEMATICAL MODELS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
SIMULATION
SUPERCONDUCTORS
TWO-DIMENSIONAL CALCULATIONS