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Physical Review Letters

Critical exponents in multiparticle 1D quantum systems from finite-size effects in conformal field theories

Andrei Dmitrievich Mironov, Anton Vladimirovich Zabrodin

Published Feb 4, 1991• 11 citations
Publisher

Abstract

The scaling dimensions and the asymptotic behavior of correlation functions of the main operators in a continuous model of a spinless 1D Bose or Fermi gas with a rather general pairwise interaction are obtained using finite-size effects.
DOI
10.1103/physrevlett.66.534

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Using the finite-size effects, the scaling dimensions and correlation functions of the main operators in continuous and lattice models of 1d spinless Bose-gas with pairwise interaction of rather general form are obtained. The long-wave properties of these systems can be described by the Gaussian model with central charge c=1. The disorder operators of the extended Gaussian model are found to correspond to some nonlocal operators in the XXZ Heisenberg antiferromagnet. This same approach is applicable to fermionic systems. Scaling dimensions of operators and correlation functions in the systems of interacting Fermi-particles are obtained. We present a universal treatment for 1d systems of different kinds which is independent of the exact integrability and which gives universal expressions for critical exponents through the thermodynamic characteristics of the system.
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