Abstract
The critical properties and the spectrum of the quantum Ashkin-Teller chain are investigated by perturbation expansion around the exactly soluble Ising decoupling limit. The critical exponents are found to satisfy the hyperscaling relation and they are consistent with the conjectured values. The critical Hamiltonian in the finite-size scaling limit is transformed into a two-band spin-1/2 Fermi system, where the interaction energy in first order is the product of the band magnetizations. The complete spectrum is shown to exhibit a conformal structure with infinite primary operators, the anomalous dimensions of which are consistent with a Gaussian form.
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References
J. Cardy, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1987).
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,J. Stat. Phys. 34:763 (1984).
D. Friedan, Z. Qui, and S. Shenker,Phys. Rev. Lett. 52:1575 (1984).
J. Cardy,J. Phys. A 17:L385 (1984).
M. N. Barber, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1983).
G. V. Gehlen, V. Rittenberg, and H. Ruegg,J. Phys. A 19:107 (1986).
H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale,Phys. Rev. Lett. 56:742 (1986).
I. Affleck,Phys. Rev. Lett. 56:746 (1986).
J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson,Phys. Rev. B 16:1217 (1977); L. P. Kadanoff andf A. C. Brown,Ann. Phys. 121:318 (1979).
B. Nienhuis, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1987).
F. C. Alcaraz, M. Baake, U. Grimm, and V. Rittenberg,J. Phys. A 21:L117 (1988).
G. von Gehlen and V. Rittenberg,J. Phys. A 20:227 (1987).
M. Baake, G. von Gehlen, and V. Rittenberg,J. Phys. A 20:L479, L487 (1987).
S. K. Yang,Nucl. Phys. B 285:183 (1987).
S. K. Yang and H. B. Zheng,Nucl. Phys. B 285:410 (1987).
H. Saleur,J. Phys. A 20:L1127 (1987).
H. Saleur,J. Stat. Phys. 50:475 (1988).
G. von Gehlen, V. Rittenberg, and G. Schütz,J. Phys. A 21:2805 (1988).
H. J. de Vega and F. Woynarovich,Nucl Phys. B 251[FS13]:439 (1985).
F. Woynarovich,Phys. Rev. Lett. 59:259 (1987).
F. C. Alcaraz, M. N. Barber, and M. T. Batchelor,Phys. Rev. Lett. 58:771 (1987).
C. J. Hamer, G. R. W. Quispel, and M. T. Batchelor,J. Phys. A 20:5677 (1987).
C. J. Hamer and M. T. Batchelor,J. Phys. A 21:L173 (1988).
M. T. Batchelor and H. W. J. Blöte,Phys. Rev. Lett. 61:138 (1988).
M. T. Batchelor, M. N. Barber, and P. A. Pearce,J. Stat. Phys. 49:1117 (1987).
F. Iglói,Nucl. Phys. B 5A:15 (1988).
M. Kohmoto, M. den Nijs, and L. P. Kadanoff,Phys. Rev. B 24:5229 (1981).
F. Iglói and J. Sólyom,J. Phys. A 17:1531 (1984).
E. Lieb, T. Schultz, and D. Mattis,Ann. Phys. (N.Y.)16:407 (1961).
P. Pfeuty,Ann. Phys. (N.Y.)57:79 (1970).
G. G. Cabrera and R. Jullien,Phys. Rev. B 35:7062 (1987).
L. P. Kadanoff and F. J. Wegner,Phys. Rev. B 4:3989 (1971).
J. Zittartz,Z. Phys. B 41:75 (1981).
F. Iglói and J. Zittartz,Z. Phys. B 73:125 (1988).
J. Zittartz,Z. Phys. B 41:65 (1981).
I. S. Gradshteyn and J. M. Ryzhik,Table of Integrals, Series and Products (Academic Press, New York, 1980).
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Iglói, F. Quantum Ashkin-Teller model near the decoupling limit. J Stat Phys 55, 311–330 (1989). https://doi.org/10.1007/BF01042602
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DOI: https://doi.org/10.1007/BF01042602