Abstract
The TPQ formulation is not only interesting for the foundation of statistical mechanics, but also useful for practical applications. I compare this formulation to other numerical methods and explain its advantage in 2D frustrated spin and electron systems. As an illustration, I show the numerical results for antiferromagnetic Heisenberg model on the Kagome lattice.
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References
M. Hyuga, S. Sugiura, K. Sakai, A. Shimizu, Phys. Rev. B 90, 121110(R) (2014)
M. Suzuki, Quantum Monte Carlo Methods in Condensed Matter Physics (World Scientific, Singapore, 1993). editor
S.R. White, Phys. Rev. Lett. 69, 2863 (1992)
V. Vidal, Phys. Rev. Lett. 99, 220405 (2007)
V. Murg, F. Verstraete, J.I. Cirac, Phys. Rev. A 75, 033605 (2007)
S.R. White, A.E. Feiguin, Phys. Rev. Lett. 93, 076401 (2004)
S.R. White, Phys. Rev. Lett. 102, 190601 (2009)
M. Imada, M. Takahashi, J. Phys. Soc. Jpn. 55, 3354 (1986)
J. Jaklič, P. Prelovšek, Adv. Phys. 49, 1 (2000)
A. Weiße, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006)
T.J. Rivlin, Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory, Pure and Applied Mathematics, 2nd edn. (Wiley, New York, 1990)
S. Sugiura, A. Shimizu, Phys. Rev. Lett. 111, 010401 (2013)
H. Nakano, T. Sakai, J. Phys. Soc. Jpn. 83, 104710 (2014)
S. Depenbrock, I.P. McCulloch, Phys. Rev. Lett. 109, 067201 (2012)
M. Punk, D. Chowdhury, S. Sachdev, Nat. Phys. 10, 289 (2014)
V. Elser, Phys. Rev. Lett. 62, 2405 (1989)
N. Elstner, A.P. Young, Phys. Rev. B 50, 6871 (1994)
P. Sindzingre, G. Misguich, C. Lhuillier, B. Bernu, L. Pierre, Ch. Waldtmann, H.-U. Everts, Phys. Rev. Lett. 84, 2953 (2000)
M. Isoda, H. Nakano, T. Sakai, J. Phys. Soc. Jpn 80, 084704 (2011)
H. Kawamura, K. Watanabe, T. Shimokawa, J. Phys. Soc. Jpn. 83, 103704 (2014)
A.M. Läuchli, J. Sudan, E.S. Sørensen, Phys. Rev. B 83, 212401 (2011)
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Sugiura, S. (2017). Application to Numerical Calculation. In: Formulation of Statistical Mechanics Based on Thermal Pure Quantum States. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-1506-9_7
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DOI: https://doi.org/10.1007/978-981-10-1506-9_7
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