| Автор | J H Samson |
| Дата выпуска | 2000-04-28 |
| dc.description | Numerical evaluation of functional integrals usually involves a finite (L-slice) 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 <sub>L</sub>(β) = [<sub>1</sub>(β/L)]<sup>L</sup>, if the density matrix <sub>1</sub>(β) in the static approximation is known. We investigate the convergence of the partition function Z<sub>L</sub>(β) ≡ Tr <sub>L</sub>(β), the internal energy and the density of states g<sub>L</sub>(E) (the inverse Laplace transform of Z<sub>L</sub>), as L→∞. For the simple harmonic oscillator, g<sub>L</sub>(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-½ 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, Z<sub>L</sub> 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→∞. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Time discretization of functional integrals |
| Тип | paper |
| DOI | 10.1088/0305-4470/33/16/305 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 33 |
| Первая страница | 3111 |
| Последняя страница | 3120 |
| Аффилиация | J H Samson; Department of Physics, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK |
| Выпуск | 16 |
