Quantum interfaces

Bruno Nachtergaele

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 321-329
  • ISSN: 0137-6934

Abstract

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We review recent results on interface states in quantum statistical mechanics.

How to cite

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Nachtergaele, Bruno. "Quantum interfaces." Banach Center Publications 43.1 (1998): 321-329. <http://eudml.org/doc/208853>.

@article{Nachtergaele1998,
abstract = {We review recent results on interface states in quantum statistical mechanics.},
author = {Nachtergaele, Bruno},
journal = {Banach Center Publications},
keywords = {quantum interfaces; Falicov-Kimball model; XXZ Heisenberg model; stability of interfaces},
language = {eng},
number = {1},
pages = {321-329},
title = {Quantum interfaces},
url = {http://eudml.org/doc/208853},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Nachtergaele, Bruno
TI - Quantum interfaces
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 321
EP - 329
AB - We review recent results on interface states in quantum statistical mechanics.
LA - eng
KW - quantum interfaces; Falicov-Kimball model; XXZ Heisenberg model; stability of interfaces
UR - http://eudml.org/doc/208853
ER -

References

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  1. [1] C. Borgs, J. Chayes and J. Fröhlich, Dobrushin states for classical spin systems with complex interactions, to appear in J. Stat. Phys. Zbl0945.82516
  2. [2] C. Borgs, J. Chayes and J. Fröhlich, Dobrushin states in quantum lattice systems, Commun. Math. Phys. 189 (1997), 591. Zbl0888.60093
  3. [3] O. Bratteli, A. Kishimoto and D. Robinson, Ground states of quantum spin systems, Commun. Math. Phys. 64 (1978), 41-48. Zbl0399.46052
  4. [4] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, 2 volumes, Springer Verlag-Berlin-Heidelberg-New York, 2nd edition, 1987 and 1996. Zbl0905.46046
  5. [5] R. L. Dobrushin, Gibbs states describing the coexistence of phases for a three-dimensional Ising model, Theor. Prob. Appl. 17 (1972), 582. Zbl0275.60119
  6. [6] N. Datta, A. Messager and B. Nachtergaele, Rigidity of interfaces in the Falicov-Kimball model, archived as math-ph/9804008. Zbl0973.82017
  7. [7] C.-T. Gottstein and R. F. Werner, Ground states of the infinite q-deformed Heisenberg ferromagnet, preprint archived as cond-mat/9501123. 
  8. [8] F. C. Alcaraz, S. R. Salinas and W. F. Wreszinski, Anisotropic ferromagnetic quantum domains, Phys. Rev. Lett. 75 (1995), 930. 
  9. [9] G. Albertini, V. E. Korepin and A. Schadschneider, XXZ model as an effective Hamiltonian for generalized Hubbard models with broken η-symmetry, J. Phys. A: Math. Gen. 25 (1995), L303-L309. 
  10. [10] T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long-range order, Physica 138A (1986), 320-358. Zbl1002.82508
  11. [11] L. M. Falicov and J. C. Kimball, Phys. Rev. B 22 (1969), 997. 
  12. [12] M. Fannes and R. F. Werner, Boundary conditions for quantum lattice systems, Helv. Phys. Acta 68 (1995), 635-657. Zbl0848.60096
  13. [13] T. Matsui, On Ground States of the One-Dimensional Ferromagnetic XXZ Model, Lett. Math. Phys. 37 (1996), 397-403. Zbl0855.46048
  14. [14] T. Matsui, On the spectra of kink for ferromagnetic XXZ models, Lett. Math. Phys. 42 (1997), 229. Zbl0892.60099
  15. [15] T. Matsui, Translation Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1+1 Dimensions, Commun. Math. Phys. 189 (1997), 127. Zbl0898.46059
  16. [16] A. Messager and S. Miracle-Solé, Low temperature states in the Falicov-Kimball model, Rev. Math. Phys. 8 (1996), 271. Zbl0856.60106
  17. [17] T. Koma and B. Nachtergaele, The spectral gap of the ferromagnetic XXZ chain, Lett. Math. Phys. 40 (1997), 1-16. Zbl0880.60103
  18. [18] T. Koma and B. Nachtergaele, The complete set of ground states of the ferromagnetic XXZ chains, preprint archived as cond-mat/9709208, to appear in Adv. Theor. Math. Phys. Zbl0958.82012
  19. [19] T. Koma and B. Nachtergaele, in preparation. 
  20. [20] A. W. Majewski and B. Zegarliński, Quantum Stochastic Dynamics I, Math. Phys. Electronic J. 1, No2 (1995), 37. 
  21. [21] A. W. Majewski, R. Olkiewicz and B. Zegarliński, this volume. 
  22. [22] J. Propp, private communication. 
  23. [23] R. H. Schonmann and S. B. Shlosman, Wulff droplets and the metastable relaxation of kinetic Ising models, archived as mparc # 97-272. 
  24. [24] B. Simon, The Statistical Mechanics of Lattice Gases, Vol 1, Princeton University Press, 1993. Zbl0804.60093

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