Perturbations of ground states in weakly interacting quantum spin systems

Journal of Mathematical Physics

Volumn 45, Issue 6, 2004, Pages 2134-2152

  Yarotsky, D A ^a  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942655436     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1705718     Document Type: Article

References (20)

1. Albanese, C., "On the spectrum of the Heisenberg Hamiltonian," J. Stat. Phys. 55, 297-309 (1989).
2. Angelescu, N., Minlos, R. A., and Zagrebnov, V. A., "The lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model," edited by R. A. Minlos, S. Shlosman, and Yu, M. Suhov, in On Dobrushin's Way. From Probability Theory to Statistical Physics, Am. Math. Soc. Transl., 2000, Vol. 198, pp. 1-11.
3. Angelescu, N., Minlos, R. A., and Zagrebnov, V. A., "The one-particle energy spectrum of weakly coupled quantum rotators," J. Math. Phys. 41, 1-23 (2000).
4. Datta, N., and Kennedy, T., "Expansions for one quasiparticle states in spin 1/2 systems," J. Stat. Phys. 108, 373-399 (2002).
5. Datta, N., and Kennedy, T., "Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature," Commun. Math. Phys. 236, 477-511 (2003).
6. Ginibre, J., "Existence of phase transitions for quantum lattice systems," Commun. Math. Phys. 14, 205 (1969).
7. 2 symmetry breaking in Haldane gap antiferromagnets," Phys. Rev. B 45, 304-307 (1992).
8. Kennedy, T., and Tasaki, H., "Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains," Commun. Math. Phys. 147, 431-484 (1992).
9. Kirkwood, J. R., and Thomas, L. E., "Expansions and phase transitions for the ground states of quantum Ising lattice systems," Commun. Math. Phys. 88, 569-580 (1983).
10. Kondratiev, Yu. G., and Minlos, R. A., "One-particle subspaces in the stochastic XY model," J. Stat. Phys. 87, 613-642 (1997).
11. Malyshev, V. A., and Minlos, R. A., Gibbs Random Fields. Cluster Expansions (Kluwer Academic, Dordrecht, 1991).
12. Malyshev, V. A., and Minlos, R. A., Linear Operators in Infinite Particle Systems (AMS, Providence, RI, 1995).
13. Matsui, T., "A link between quantum and classical Potts models," J. Stat. Phys. 59, 781-798 (1990).
14. Matsui, T., "Uniqueness of the translationally invariant ground state in quantum spin systems," Commun. Math. Phys. 126, 453-467 (1990).
15. Minlos, R. A., "Invariant subspaces of the stochastic Ising high temperature dynamics," Markov Processes Relat. Fields 2, 263-284 (1996).
16. Minlos, R. A., and Suhov, Yu. M., "On the spectrum of the generator of an infinite system of interacting diffusions," Commun. Math. Phys. 206, 463-489 (1999).
17. Thomas, L. E., and Yin, Z., "Low temperature expansions for the Gibbs states of weakly interacting quantum Ising lattice systems," Commun. Math. Phys. 91, 405-417 (1983).
18. Thomas, L. E., and Yin, Z., "Low temperature expansions for the Gibbs states of quantum Ising lattice systems," J. Math. Phys. 25, 3128-3134 (1984).
19. Yarotsky, D. A., "Scattering of quasi-particle excitations in weakly coupled stochastic lattice spin systems," submitted to Commun. Math. Phys. (to be published).
20. Zhizhina, E. A., Kondratiev, Yu. G., and Minlos, R. A., "Lower branches of the spectrum of Hamiltonians of infinite quantum systems with a compact space of "spins," Trans. Moscow Math. Soc. 60, 225-262 (1999).