Abstract
We extend cluster perturbation theory to quantum spin systems. As an application, we calculate the spectral function and the density of states of one-particle excitations of a chain of spin-1/2 particles with alternating exchange interaction.
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M. Potthoff, M. Aichhorn, and C. Dahnken, Phys. Rev. Lett., 91, 206402 (2003).
G. Kotliar, S. Savrasov, G. Pálsson, and G. Biroli, Phys. Rev. Lett., 87, 186401 (2001).
M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Phys. Rev. B, 58, R7475–R7479 (1998).
T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Rev. Modern Phys., 77, 1027–1080 (2005).
C. Gros and R. Valentí, Phys. Rev. B, 48, 418–425 (1993).
D. Sénéchal, D. Perez, and M. Pioro-Ladrière, Phys. Rev. Lett., 84, 522–525 (2000).
D. Sénéchal, D. Perez, and D. Plouffe, Phys. Rev. B, 66, 075129 (2002).
M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Phys. Rev. B, 58, R7475–R7479 (1998).
A. Tahvildar-Zadeh, M. Jarrell, and J. Freericks, Phys. Rev. B, 55, R3332–R3335 (1997).
M. G. Zacher, R. Eder, E. Arrigoni, and W. Hanke, Phys. Rev. Lett., 85, 2585–2588 (2002).
A. Izyumov, F. A. Kassan-ogly, and Yu. N. Skryabin, Field Methods in Theory of Ferromagnetism [in Russian], Nauka, Moscow (1974).
Y. Hosokoshi, Y. Nakazawa, K. Inoue, K. Takizawa, H. Nakano, M. Takahashi, and T. Goto, Phys. Rev. B, 60, 12924–12932 (1999).
T. Goto, N. V. Mushnikov, Y. Hosokoshi, K. Katoh, and K. Inoue, Phys. B, 329-333, 1160–1161 (2003).
I. Affleck, Phys. Rev. B, 41, 6697–6702 (1990); T. Giamarchi and A. M. Tsvelik, Phys. Rev. B, 59, 11398-11407 (1999).
T. M. Rice, Science, 298, 760–761 (2002).
E. Dagotto, Rev. Modern Phys., 66, 763–840 (1994).
A. I. Larkin, Sov. Phys. JETP, 10, 186–191 (1959).
V. G. Vaks, A. I. Larkin, and S. A. Pikin, Sov. Phys. JETP, 24, 240 (1967).
Yu. A. Izyumov and F. A. Kassan-ogly, Fiz. Met. Metalloved., 26, 385 (1968).
M. A. Savchenko and V. V. Tarasenko, Fiz. Tverd. Tela, 9, 3284 (1967).
S. A. Pikin, Sov. Phys. JETP, 27, 995.
E. M. Pikalev, M. A. Savchenko, and J. Solyom, Sov. Phys. JETP, 28, 734 (1969).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum [in Russian], Nauka, Moscow (1975); English transl., World Scientific, Teaneck, N. J. (1988).
I. G. Bostrem, A. S. Ovchinnikov, and V. E. Sinitsyn, Theor. Math. Phys., 149, 1527–1544 (2006).
V. E. Sinitsyn, I. G. Bostrem, and A. S. Ovchinnikov, J. Phys. A, 40, 645–668 (2007).
C. Dahnken, M. Aichhorn, W. Hanke, E. Arrigoni, and M. Potthoff, Phys. Rev. B, 70, 245110 (2004).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 162, No. 2, pp. 216–226, February, 2010.
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Ovchinnikov, A.S., Bostrem, I.G. & Sinitsyn, V.E. Cluster perturbation theory for spin Hamiltonians. Theor Math Phys 162, 179–187 (2010). https://doi.org/10.1007/s11232-010-0013-7
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DOI: https://doi.org/10.1007/s11232-010-0013-7