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Journal of Anhui University

Bosonization of one-dimensional spin-1/2XY model in external magnetic field

LI Chang-ling

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

By using bosonization technique and Jordan-Wigner transformation,we study the spin(-1/2XY) model in external magnetic field.The bosonization procedure is changed in the presence of an external field.We study the model without external field firstly,and then the perturbation due to the external magnetic field is bosonized separately.We solve the incommensurability problem by redefining the bononic field operator,and correlation functions are calculated.Lastly,we talk simply about virtues of bosonization compared with other techniques.

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By using bosonization technique and Jordan-Wigner transformation,we study the spin(-1/2XY) model in external magnetic field.The bosonization procedure is changed in the presence of an external field.We study the model without external field firstly,and then the perturbation due to the external magnetic field is bosonized separately.We solve the incommensurability problem by redefining the bononic field operator,and correlation functions are calculated.Lastly,we talk simply about virtues of bosonization compared with other techniques.
By using Haldane's harmonic-fluid approach-bosonization, we study the spin-1/2XY model in external magnetic field. The bosonization procedure is changed in the presence of an external field. We study the model without external field firstly, and then the perturbation due to the external magnetic field is bosonized separately, We add the bosonized perturbation to the Hamiltonian of the one-dimensional spin-1/2 model, then we get the exactly bosonized model in external magnetic field. In terms of bosonized haimitonian, incommensurability problem can be solved by moving Fermi point. Therefore, we redefine the bononic field operator and get a new Hamiltonian, and the problem duo to perturbation is sovled, but the correlation functions are changed at the same time. Lastly the correlation functions are calculated newly. And we talk simply about the change of correlation function duo to shifting Fermi point, and virtues of bosonization compared with other techniques.
The Jordan-Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan-Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J1-J2 Heisenberg models, as well as to the pairing or reduced Bardeen-Cooper-Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.
The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to definite values at zero magnetic field around various Fermi points.