Phys. Rev. B 43, 2615 (1991)

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Nonlinear sigma model and static holes

Khalil Bitar

Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306

Efstratios Manousakis

Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306

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-S antiferromagnetic Heisenberg model in two space dimensions, where the different spin cases map to different values of the coupling constant g of the sigma model. For the value of 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 C_ij==iS[ Sigma (r_i)+(-1)^||i-j|| Sigma (r_j)]}>, where Sigma (r_i) is the area on the unit sphere defined by the path of the spin located at the spatial lattice point r_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.

©1991 The American Physical Society.

PACS: 74.20.-z 75.10.Jm 74.65.+n

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