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Density matrix renormalisation group study of the one-dimensional Holstein model of spinless fermions

Robert J. Bursill, Ross H. McKenzie, Chris J. Hamer

Jan 1, 19980 citations

Chain Representations of Open Quantum Systems and Their Numerical Simulation with Time-Adaptive Density Matrix Renormalisation Group Methods

Alex W. Chin, Susana F. Huelga, Martin Bodo Plenio

Semiconductors and semimetalsJan 1, 201117 citations

Applications of the density matrix renormalisation group to problems in magnetism

G A Gehring, Robert J. Bursill, Tao Xiang

We review White's density matrix renormalisation group method, an increasingly popular method for the solution of low dimensional quantum Hamiltonians. We describe some applications to frustrated spin systems, quantum critical phenomena, two dimensional classical and one dimensional quantum systems at non-zero temperature, and low energy properties of two dimensional quantum models such as the Hubbard and Heisenberg Hamiltonians.

arXiv:cond-mat/9608127Aug 27, 19960 citations

The density matrix renormalization group for a quantum spin chain at non-zero temperature

Robert J. Bursill, Tao Xiang, G A Gehring

We apply a recent adaptation of White's density matrix renormalization group (DMRG) method to a simple quantum spin model, the dimerized XY chain, in order to assess the applicability of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low-temperature results are found to be most accurate in the case when there is a substantial energy gap.

arXiv:cond-mat/9609001Journal of Physics Condensed MatterSep 30, 1996152 citations

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Y.J. Kim, M. Greven, U.‐J. Wiese +1 more

arXiv:cond-mat/9712257The European Physical Journal BAug 1, 199856 citations

Dynamic density-density correlations in interacting Bose gases on optical lattices

Satoshi Ejima, Holger Fehske, Florian Gebhard

In order to identify possible experimental signatures of the superfluid to Mott-insulator quantum phase transition we calculate the charge structure factor S ( k , ω ) for the one-dimensional Bose-Hubbard model using the dynamical density-matrix renormalisation group (DDMRG) technique. Particularly we analyse the behaviour of S ( k , ω ) by varying – at zero temperature–the Coulomb interaction strength within the first Mott lobe. For strong interactions, in the Mott-insulator phase, we demonstrate that the DDMRG results are well reproduced by a strong-coupling expansion, just as the quasi-particle dispersion. In the super-fluid phase we determine the linear excitation spectrum near k = 0. In one dimension, the amplitude mode is absent which mean-field theory suggests for higher dimensions.In order to identify possible experimental signatures of the superfluid to Mott-insulator quantum phase transition we calculate the charge structure factor S ( k , ω ) for the one-dimensional Bose-Hubbard model using the dynamical density-matrix renormalisation group (DDMRG) technique. Particularly we analyse the behaviour of S ( k , ω ) by varying – at zero temperature–the Coulomb interaction strength within the first Mott lobe. For strong interactions, in the Mott-insulator phase, we demonstrate that the DDMRG results are well reproduced by a strong-coupling expansion, just as the quasi-particle dispersion. In the super-fluid phase we determine the linear excitation spectrum near k = 0. In one dimension, the amplitude mode is absent which mean-field theory suggests for higher dimensions.

arXiv:1110.4498Journal of Physics Conference SeriesDec 14, 20126 citations

Density matrix renormalisation group study of a one-dimensional quantum spin chain at non-zero temperature

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Density matrix renormalisation group study of a one-dimensional quantum spin chain at non-zero temperature

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