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Prog. Theor. Phys. Supplement No.145 (2002) pp. 204-207
Matrix Product State Approximation for the Maximum-Eigenvalue Eigenstate of the Quantum Transfer Matrix
Nobuya Maeshima,1,*
Yasuhiro Hieida,2
Tomotoshi Nishino3 and
Kouichi Okunishi4
1Department of Physics, Graduate School of Science,
Osaka University, Toyonaka 560-0043, Japan
2Computer and Network Center, Saga University, Saga 840-8502, Japan
3Department of Physics, Graduate School of Science,
Kobe University, Kobe 657-8501, Japan
4Department of Physics, Niigata University, Niigata 950-2181, Japan
(Received December 20, 2001)
Abstract:
We propose a matrix product state (MPS) formulation to calculate
thermodynamic quantities of one dimensional (1D) quantum systems.
The maximum-eigenvalue eigenstate of the quantum transfer matrix
is represented as the product of local matrices, which are
obtained by the DMRG method for the two dimensional (2D) classical
system mapped from the original 1D quantum system. This MPS
formulation is successfully applied to the S=1/2 XY model.
URL :
http://ptp.ipap.jp/link?PTPS/145/204/
DOI : 10.1143/PTPS.145.204
References:
- M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 1999), and references therein.
-
H. Betsuyaku, Phys. Rev. Lett. 53 (1984), 629[APS].
- T. Tiang and X. Wang, in “Density-Matrix Renormalization” Lecture Notes in Phys., ed. I. Peschel, X. Wang, M. Kaulke and K. Hallberg (Springer Verlag, 1999).
-
S. Rommer and S. Eggert, Phys. Rev. B 59 (1999), 6301[APS].
B. Ammon, M. Troyer, T. M. Rice and N. Shibata, Phys. Rev. Lett. 82 (1999), 3855[APS].
-
M. Fannes, B. Nachtergaele and R. F. Werner, Europhys. Lett. 10 (1988), 633[CrossRef].
-
T. Nishino, J. Phys. Soc. Jpn. 64 (1995), 3598[JPSJ].
-
M. Suzuki, Prog. Theor. Phys. 56 (1976), 1454[PTP].
-
M. Barma and B. S. Shastry, Phys. Rev. B 18 (1978), 3351[APS].
-
M. Suzuki, Phys. Rev. B 31 (1985), 2957[APS].
-
M. Inoue and M. Suzuki, Prog. Theor. Phys. 79 (1988), 645[PTP].
