Non-zero entropy density in the XY chain out of equilibrium

Letters in Mathematical Physics

Volumn 79, Issue 1, 2007, Pages 1-16

  Aschbacher, Walter H ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Non equilibrium steady state; Toeplitz operators; Von Neumann entropy; XY chain

Indexed keywords

EID: 33846129729     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-006-0115-1     Document Type: Article

References (28)

1. Antal, T., Rácz, Z., Rákos, A., Schütz, G.M.: Isotropic transverse XY chain with energy and magnetization currents. Phys. Rev. E 57, 5184 (1998)
2. Araki, H.: On quasifree states of CAR and Bogoliubov automorphisms. Publ. RIMS Kyoto Univ. 6, 385 (1971)
3. Araki, H.: On the XY-model on two-sided infinite chain. Publ. RIMS Kyoto Univ. 20, 277 (1984)
4. Araki, H., Ho, T.G.: Asymptotic time evolution of a partitioned infinite two-sided isotropic XY-chain. Proc. Steklov Inst. Math. 228, 191 (2000)
5. Aschbacher, W.H., Barbaroux, J.-M.: Out of equilibrium correlations in the XY chain. Lett. Math. Phys. 77, 11 (2006)
6. Aschbacher, W.H., Jakšić, V., Pautrat, Y., Pillet, C.-A.: Topics in non-equilibrium quantum statistical mechanics. In: Lecture Notes in Mathematics, vol. 1882, Springer, Berlin Heidelberg New York (2006)
7. Aschbacher, W.H., Pillet, C.-A.: Non-equilibrium steady states of the XY chain. J. Stat. Phys. 112, 1153 (2003)
8. Böttcher, A., Silbermann, B.: Analysis of Toeplitz Operators. Springer, Berlin Heidelberg New York (2006)
9. Böttcher, A., Silbermann, B.: Introduction to Large Truncated Toeplitz Matrices. Springer, Berlin Heidelberg New York (1999)
10. Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum statistical Mechanics, vol. 2. Springer, Berlin Heidelberg New York (1997)
11. Callan, C.G., Wilczek, F.: On geometric entropy. Phys. Lett. B 333, 55 (1994)
12. Castella, H., Zotos, X., Prelovšek, P.: Integrability and ideal conductance at finite temperatures. Phys. Rev. Lett. 74, 972 (1995)
13. Eisler, V., Zimborás, Z.: Entanglement in the XX spin chain with an energy current. Phys. Rev. A 71, 042318 (2005)
14. Fiola, T.M., Preskill, J., Strominger, A., Trivedi, S.P.: Black hole thermodynamics and information loss in two dimensions. Phys. Rev. D 50, 3987 (1994)
15. Holzhey, C., Larsen, F., Wilczek, F.: Geometric and renormalized entropy in conformal field theory. Nucl. Phys. B 424, 443 (1994)
16. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, London (1985)
17. Jakšić, V., Pillet, C.-A.: Mathematical theory of non-equilibrium quantum statistical mechanics. J. Stat. Phys. 108, 787 (2002)
18. Jin, B.-Q., Korepin, V.E.: Quantum spin chain, Toeplitz determinants, and Fisher-Hartwig conjecture. J. Stat. Phys. 116, 79 (2004)
19. Jordan, P., Wigner, E.: Pauli's equivalence prohibition. Z. Phys. 47, 631 (1928)
20. Latorre, J.I., Rico, E., Vidal, G.: Ground state entanglement in quantum spin chains. Quantum Inf. Comput. 4, 48 (2004)
21. Ruelle, D.: Natural nonequilibrium states in quantum statistical mechanics. J. Stat. Phys. 98, 57 (2000)
22. Sachdev, S.: Quantum phase transitions. Cambridge University Press, London (1999)
23. 3: evidence for the thermal transport via spinons. Phys. Rev. B 62, R6108 (2000)
24. 3. Phys. Rev. B 64, 054412 (2001)
25. Srednicki, M.: Entropy and area. Phys. Rev. Lett. 71 666 (1993)
26. Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 60, 227902 (2003)
27. Zotos, X.: Finite temperature Drude weight of the one-dimensional spin-1/2 Heisenberg model. Phys. Rev. Lett. 82, 1764 (1999)
28. Zotos, X., Naef, F., Prelověk, P.: Transport and conservation laws. Phys. Rev. B 55, 11029 (1997)