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Emptiness formation probability at finite temperature for the isotropic Heisenberg chain

Frank Göhmann, Andreas Klümper, Alexander Seel

arXiv:cond-mat/0406611Physica B Condensed MatterFeb 26, 200513 citations

High temperature expansion of the emptiness formation probability for the isotropic Heisenberg chain

Zengo Tsuboi, Masahiro Shiroishi

Recently, Göhmann, Klümper and Seel have derived novel integral formulae for the correlation functions of the spin-1/2 Heisenberg chain at finite temperature. We have found that the high temperature expansion (HTE) technique can be effectively applied to evaluate these integral formulae. Actually, as for the emptiness formation probability P ( n ) of the isotropic Heisenberg chain, we have found a general formula of the HTE for P ( n ) with arbitrary up to O (( J / T ) 4 ). If we fix a magnetic field to a certain value, we can calculate the HTE to much higher order. For example, the order up to O (( J / T ) 42 ) has been achieved in the case of P (3) when h = 0. We have compared these HTE results with the data by quantum Monte Carlo simulations. They exhibit excellent agreement.Recently, Göhmann, Klümper and Seel have derived novel integral formulae for the correlation functions of the spin-1/2 Heisenberg chain at finite temperature. We have found that the high temperature expansion (HTE) technique can be effectively applied to evaluate these integral formulae. Actually, as for the emptiness formation probability P ( n ) of the isotropic Heisenberg chain, we have found a general formula of the HTE for P ( n ) with arbitrary up to O (( J / T ) 4 ). If we fix a magnetic field to a certain value, we can calculate the HTE to much higher order. For example, the order up to O (( J / T ) 42 ) has been achieved in the case of P (3) when h = 0. We have compared these HTE results with the data by quantum Monte Carlo simulations. They exhibit excellent agreement.

arXiv:cond-mat/0502569Journal of Physics A Mathematical and GeneralMay 3, 200521 citations

The Validity of the Low-Temperature Expansions for the Anisotropic Heisenberg Models

M. J. Škrinjaŕ, D. Kapor, Jovan P. Šetrajčić

De Gruyter eBooksDec 31, 19840 citations

Thermodynamics of the Anisotropic Heisenberg Chain Calculated by the Density Matrix Renormalization Group Method

Naokazu Shibata

The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the imaginary time direction. The magnetic susceptibility and the specific heat are calculated down to T=0.01J and compared with the Bethe ansatz results. The agreement including the logarithmic correction in the magnetic susceptibility at the isotropic point is fairly good.The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the imaginary time direction. The magnetic susceptibility and the specific heat are calculated down to T=0.01J and compared with the Bethe ansatz results. The agreement including the logarithmic correction in the magnetic susceptibility at the isotropic point is fairly good.

arXiv:cond-mat/9706152Journal of the Physical Society of JapanAug 15, 1997149 citations

New method of deriving high temperature expansions for the Heisenberg model

Cyril Domb, David W. Wood

Physics LettersJan 1, 196421 citations

Effect of Anisotropy on the Critical Behaviour of Three- Dimensional Heisenberg Ferromagnets

R. Shanker, R. A. Singh

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

Zeitschrift für Naturforschung AJan 1, 19763 citations

A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain

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