Ground states in relatively bounded quantum perturbations of classical lattice systems

Communications in Mathematical Physics

Volumn 261, Issue 3, 2006, Pages 799-819

  Yarotsky, D A ^a,b,c,d  

^a UNIVERSITY COLLEGE DUBLIN   (Ireland)

^b INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^c UNIVERSITY OF MUNICH   (Germany)

^d Irish Research Council for Science Engineering and Technology   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144463186     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-005-1456-9     Document Type: Article

References (31)

1. Affleck, I.: Quantum spin chains and the Haldane gap. J. Phys.: Condensed Matter 1, 3047-3072 (1989)
2. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59, 799-802 (1987)
3. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Valence bond ground states in isotropic quantum antiferromagnets. Commun. Math. Phys. 115, 477-528 (1987)
4. Albanese, C.: Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Commun. Math. Phys. 134, 1-27, 237-272 (1990)
5. Arovas, D.P., Auerbach, A., Haldane, F.D.M.: Extended Heisenberg model of antiferromagnetism: analogies to the fractional quantum Hall effect. Phys. Rev. Lett. 60, 531-534 (1988)
6. Bovier, A., Zahradník M.: A simple inductive approach to the problem of convergence of cluster expansions of polymer models. J. Stat. Phys. 85, 517-28 (1982)
7. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics. 2nd edn., vol 1, Berlin: Springer Verlag, 1987
8. Datta, N., Kennedy, T.: Expansions for one quasiparticle states in spin 1/2 systems. J. Stat. Phys. 108, 373-399 (2002)
9. den Nijs, M., Rommelse, K.: Preroughening transition in crystal surfaces and valence-bond phases in quantum spin chains. Phys. Rev. B. 40, 4709 (1989)
10. Fannes, M., Nachtergaele, B., Werner, R.F.: Valence bond states on quantum spin chains as ground states with spectral gap. J. Phys. A: Math. Gen. 24, L185-L190 (1991)
11. Fannes, M., Nachtergaele, B., Werner, R.F.: Finitely correlated states of quantum spin chains. Commun. Math. Phys. 144, 443-490 (1992)
12. Haldane, F.D.M.: Continuum dynamics of the 1-d Heisenberg antiferromagnet: identification with the O (3) nonlinear sigma model. Phys. Lett. A 93, 464-468 (1983)
13. Haldane. F.D.M.: Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solutions of the one-dimensional easy-axis Néel state. Phys. Rev. Lett. 50, 1153-1156 (1983)
14. Kato. T.: Perturbation theory for linear operators. Berlin: Springer-Verlag. 1976
15. Kennedy, T., Lieb, E.H., Tasaki, H.: A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state. J. Stat. Phys. 53, 383-415 (1988)
16. 2 symmetry breaking in Haldane gap antiferromagnets. Phys. Rev. B 45, 304 (1992)
17. Kennedy, T., Tasaki, H.: Hidden symmetry breaking and the Haldane phase in S = 1 quantum spin chains. Commun. Math. Phys. 147, 431-484 (1992)
18. Kirkwood, J.R., Thomas, L.E.: Expansions and phase transitions for the ground states of quantum Ising lattice systems. Commun. Math. Phys. 88, 569-580 (1983)
19. Klümper, A., Schadschneider, A., Zittartz, J.: Matrix-product ground states for one-dimensional spin-1 quantum antiferromagnets. Europhys. Lett. 24, 293 (1993)
20. Knabe, S.: Energy gaps and elementary excitations for certain VBS-antiferromagnets. J. Stat. Phys. 52, 627-638 (1988)
21. Kotecký, R., Preiss, D.: Cluster expansions for abstract polymer models. Commun. Math. Phys. 103, 491-498 (1986)
22. Malyshev, V.A., Minlos, R.A.: Gibbs Random Fields. Cluster Expansions. Dordrecht: Kluwer Academic Publishers, 1991
23. Matsui, T.: A link between quantum and classical Potts models. J. Stat. Phys. 59, 781-798 (1990)
24. Matsui, T.: Uniqueness of the translationally invariant ground state in quantum spin systems. Commun. Math. Phys. 126, 453-467 (1990)
25. Nachtergaele, B.: The spectral gap for some spin chains with discrete symmetry breaking. Commun. Math. Phys. 175, 565-606 (1996)
26. Reed, M., Simon, B.:Methods of modern mathematical physics. V. 2: Fourier analysis. Self-adjointness. N.Y.: Academic Press, 1975
27. Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics 159, Berlin-Heidelberg-New York: Springer Verlag, 1982
28. Simon, B.: The statistical mechanics of lattice gases. Princeton, NJ: Princeton University Press, 1993
29. Ueltschi, D.: Cluster expansions and correlation functions. Moscow Math. J. 4, 509-520 (2004)
30. Yarotsky, D.A.: Perturbations of ground states in weakly interacting quantum spin systems. J. Math. Phys. 45, 2134-2152 (2004)
31. Yarotsky, D.A.: Uniqueness of the ground state in weak perturbations of non-interacting gapped quantum lattice systems. J. Stat. Phys. 118, 119-144 (2005)