Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1203.4848 · Physical Review B

Accurate computation of low-temperature thermodynamics for quantum spin chains

Yukun Huang, Pochung Chen, Ying-Jer Kao

Published Dec 3, 2012• 25 citations
arXivHTMLPDF

Abstract

We apply the biorthonormal transfer-matrix renormalization group (BTMRG) [Huang, Phys. Rev. E 83, 036702 (2011)] to study low-temperature properties of quantum spin chains. Simulations on anisotropic Heisenberg spin-$1/2$ chains demonstrate that the BTMRG outperforms the conventional transfer-matrix renormalization group by successfully accessing far lower temperature than previously reported, while retaining the same level of accuracy. The power of the method is further illustrated by the calculation of the low-temperature specific heat for a frustrated spin chain.

DOI
10.1103/physrevb.86.235102

Related papers

Thermodynamics of quantum Heisenberg spin chains

Tao Xiang

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.

arXiv:cond-mat/9808179•Physical review. B, Condensed matter•Oct 1, 1998•92 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.

arXiv:cond-mat/9706152•Journal of the Physical Society of Japan•Aug 15, 1997•149 citations

Thermodynamics of Frustrated Quantum Spin Chains

K. Maisinger, Ulrich Schollwöck

We apply the transfer-matrix density matrix renormalization group (DMRG) approach to frustrated quantum spin chains, down to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.025\mathrm{K}$ in the thermodynamic limit. The incommensurability problem of exact diagonalization and the negative sign problem of quantum Monte Carlo vanish completely. For illustration, we give results for chains with next-nearest-neighbor frustration and for the delta chain, which has been a testbed for many thermodynamic methods. The DMRG approach proves to be an extremely powerful method for the old problem of the thermodynamics of frustrated systems.

arXiv:cond-mat/9803122•Physical Review Letters•Jul 13, 1998•44 citations

Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices

Yukun Huang

A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special E·S·E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.

Physical Review E•Mar 10, 2011•13 citations

Linearized Tensor Renormalization Group Algorithm for the Calculation of Thermodynamic Properties of Quantum Lattice Models

Wei Li, Shi-Ju Ran, Shou-Shu Gong +4 more

A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum XY spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.

arXiv:1011.0155•Physical Review Letters•Mar 22, 2011•95 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/9609001•Journal of Physics Condensed Matter•Sep 30, 1996•152 citations
We apply the biorthonormal transfer-matrix renormalization group (BTMRG) [Huang, Phys. Rev. E 83, 036702 (2011)] to study low-temperature properties of quantum spin chains. Simulations on anisotropic Heisenberg spin-1/21/21/2 chains demonstrate that the BTMRG outperforms the conventional transfer-matrix renormalization group by successfully accessing far lower temperature than previously reported, while retaining the same level of accuracy. The power of the method is further illustrated by the calculation of the low-temperature specific heat for a frustrated spin chain.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
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.
We apply the transfer-matrix density matrix renormalization group (DMRG) approach to frustrated quantum spin chains, down to T=0.025KT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.025\mathrm{K}T=0.025K in the thermodynamic limit. The incommensurability problem of exact diagonalization and the negative sign problem of quantum Monte Carlo vanish completely. For illustration, we give results for chains with next-nearest-neighbor frustration and for the delta chain, which has been a testbed for many thermodynamic methods. The DMRG approach proves to be an extremely powerful method for the old problem of the thermodynamics of frustrated systems.
A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special E·S·E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.
A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum XY spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.