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arXiv:0812.0128 · Journal of Physics Condensed Matter

A quantum transfer matrix method for one-dimensional disordered electronic systems

L P Yang, Y J Wang, Wenhu Xu, Mingpu Qin, Tao Xiang

Published Mar 13, 2009• 4 citations
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Abstract

We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of 2 × 2 local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.

DOI
10.1088/0953-8984/21/14/145407

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We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of 2 × 2 local transfer matrices. We demonstrate this method by applying it to the 1D disordered Anderson model. Thermodynamic quantities of this model are calculated and discussed.
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The transfer matrix DMRG method for one dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than 10−310^{-3}10−3 down to T=0.01JT=0.01JT=0.01J with 80 states kept.
The transfer-matrix density-matrix renormalization-group method for one-dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than ${10}^{\ensuremath{-}3}$ down to T=0.01JT=0.01JT=0.01J with 80 states kept.