Publication: Matrix product state representations
Loading...
Official URL
Full text at PDC
Publication Date
2007-07
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Rinton Press
Citations
Exportar
Abstract
This work gives a detailed investigation of matrix product state (TOPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.
Description
UCM subjects
Unesco subjects
Keywords
Citation
M. Fannes, B. Nachtergaele and R. F. Werner, Commun. Math. Phys. 144, 443-490 (1992)
A. Klümper, A. Schadschneider, J. Zittartz, J. Phys. A 24, L955 (1991); Z. Phys. B 87, 281(1992).
I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki, Commun. Math. Phys. 115, 477 (1988)
M. Fannes, B. Nachtergaele and R. F. Werner, Lett. Math. Phys. 25, 249-258 (1992)
M. Hastings, Phys. Rev. B 73, 085115 (2006).
B. Nachtergaele, Commun. Math. Phys., 175, 565 (1996).
G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)
D. E. Evans and E. Hoegh-Krohn, J. London Math. Soc. 17, 345-355 (1978)
F. Verstraete, J.I. Cirac, J.I. Latorre, E. Rico and M.M.Wolf, Phys.Rev.Lett. 94, 140601 (2005)
C. King, quant-ph/0412046;
I. Devetak, P.W. Shor, quant-ph/0311131;
M.M. Wolf, D. Pérez-García, Phys. Rev. A 75, 012303 (2007).
R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.
S. Knabe, J. Stat. Phys. 52, 627 (1988).
C. Schoen, E. Solano, F. Verstraete, J. I. Cirac, M. M. Wolf, Phys. Rev. Lett. 95, 110503 (2005).
C. Schoen, K. Hammerer, M.M. Wolf, J.I. Cirac, E. Solano , Phys. Rev. A 75, 032311 (2007).
Y. Delgado, L. Lamata, J. Leon, D. Salgado, E. Solano, Phys. Rev. Lett. 98, 150502 (2007).
N. Schuch, M.M. Wolf, F. Verstraete, J.I. Cirac, arXiv:0705.0292 (2007).
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
S. White, Phys. Rev. Lett. 69, 2863 (1992)
S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995); S. Rommer and S. Ostlund, Phys. Rev. B 55, 2164 (1997)
F. Verstraete, A.Weichselbaum, U. Schollwöck, J. I. Cirac, Jan von Delft, cond-mat/0504305.
F. Verstraete, D. Porras and I. Cirac, Phys. Rev. Lett. 93, 227205 (2004).
L. Bombelli, R.K. Koul, J. Lee, R.D. Sorkin, Phys. Rev. D 34, 373 (1986).
M. Srednicki, Phys. Rev. Lett. 71, 66 (1993);
R. Bousso, Rev. Mod. Phys. 74, 825 (2002).
G. Vidal, J. I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003);
B.Q. Jin, V. Korepin, J.Stat.Phys. 116, 79 (2004);
P. Calabrese, J. Cardy, J.Stat.Mech. P06002 (2004);
M.B. Plenio J. Eisert, J. Dreissig, M. Cramer, Phys. Rev. Lett. 94, 060503 (2005).
M.M. Wolf, Phys. Rev. Lett. 96, 010404 (2006);
D. Gioev and I. Klich, Phys. Rev. Lett. 96, 100503 (2006)
F. Verstraete, M.M. Wolf, D. Perez-Garcia, J.I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)
M.M. Wolf, F. Verstraete, M.B. Hastings, J.I. Cirac, arXiv:0704.3906 (2007).
M.M. Wolf, G. Ortiz, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 97, 110403 (2006).
P. Calabrese and J. Cardy, J. Stat. Mech. (2004) P06002.
B.-Q. Jin and V.E. Korepin, J. Stat. Phys. 116, 79 (2004).
M. B. Hastings, Phys. Rev. Lett. 93, 140402 (2004); M.B. Hastings, T. Koma, Commun. Math. Phys. 265, 781 (2006); B. Nachtergaele, R. Sims, Commun. Math. Phys.,265,119 (2006).
P. Hayden, D. Leung, P. W. Shor, A. Winter, Commun. Math. Phys. 250, 371 (2004).
F. Verstraete and I. Cirac, Phys. Rev. B 73, 094423 (2006)
U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005).
A. Ben-Tal and A.Nemirovski, Mathematics of Operational Research 23, 769 (1998).
J. Eisert, Phys. Rev. Lett. 97, 260501 (2006).
R. Jozsa, quant-ph/0603163 (2006); G. Vidal, Phys. Rev. Lett. 91, 147902 (2003); D. Aharonov, Z. Landau, J. Makowsky, quant-ph/0611156.
N. Yoran, A. Short, quant-ph/0601178 (2006); M. Van den Nest, W. Dür, G. Vidal, H. J. Briegel, Phys. Rev. A 75, 012337 (2007); I. Markov, Y. Shi, quant-ph/0511069 (2005).
N. Schuch, M.M. Wolf, F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 98, 140506 (2007).
F. Verstraete, J.I. Cirac,Phys. Rev. A 70,060302(R) (2004).
D. Gross, J.Eisert, arXiv:quant-ph/0609149 (2006).