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This article is cited in 5 scientific papers (total in 5 papers)
Functional Integration with an “Automorphic” Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model
K. L. Malyshev St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
For the generating function of static correlators of the third components of spins in the $XX$ Heisenberg model, we derive a new representation given by a combination of Gaussian functional integrals over anticommuting variables. A peculiarity of the resulting functional integral is that a part of the integration variables depend on the imaginary time automorphically: these variables are multiplied by a certain complex number under the shift of the imaginary time by the period. The other variables satisfy the standard boundary conditions of the fermionic/bosonic type. Functional integration results are represented as determinants of matrix operators. We finally evaluate the generating function of correlators and the partition function of the model in the zeta-function regularization. The consistency of the suggested functional definition is confirmed by calculating several correlation functions of the third components of spins at a nonzero temperature.
Keywords:
functional integration, $XX$ Heisenberg model, correlators, generalized zeta function.
Received: 23.08.2002
Citation:
K. L. Malyshev, “Functional Integration with an “Automorphic” Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model”, TMF, 136:2 (2003), 285–298; Theoret. and Math. Phys., 136:2 (2003), 1143–1154
Linking options:
https://www.mathnet.ru/eng/tmf221https://doi.org/10.4213/tmf221 https://www.mathnet.ru/eng/tmf/v136/i2/p285
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