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Title: Time discretization of functional integrals
Authors: Samson, J.H.
Issue Date: 2000
Publisher: © IOP Publishing
Citation: SAMSON, J.H., 2000. Time discretization of functional integrals. Journal of Physics A - Matehmatical and General, 33 (16), pp.3111-3120.
Abstract: Numerical evaluation of functional integrals usually involves a finite (Lslice) discretization of the imaginary-time axis. In the auxiliary-field method, the L-slice approximant to the density matrix can be evaluated as a function of inverse temperature at any finite L as ˆρL(β) = [ˆρ1(β/L)]L, if the density matrix ˆρ1(β) in the static approximation is known. We investigate the convergence of the partition function ZL(β) ≡ Tr ˆρL(β), the internal energy and the density of states gL(E) (the inverse Laplace transform of ZL), as L → ∞. For the simple harmonic oscillator, gL(E) is a normalized truncated Fourier series for the exact density of states. When the auxiliary-field approach is applied to spin systems, approximants to the density of states and heat capacity can be negative. Approximants to the density matrix for a spin-1/2 dimer are found in closed form for all L by appending a self-interaction to the divergent Gaussian integral and analytically continuing to zero self-interaction. Because of this continuation, the coefficient of the singlet projector in the approximate density matrix can be negative. For a spin dimer, ZL is an even function of the coupling constant for L < 3: ferromagnetic and antiferromagnetic coupling can be distinguished only for L ≥ 3, where a Berry phase appears in the functional integral. At any non-zero temperature, the exact partition function is recovered as L→∞.
Version: Accepted for publication
DOI: 10.1088/0305-4470/33/16/305
URI: https://dspace.lboro.ac.uk/2134/11610
Publisher Link: http://dx.doi.org/10.1088/0305-4470/33/16/305
ISSN: 0305-4470
Appears in Collections:Published Articles (Physics)

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