No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Connected components of irreducible maps and 1D quantum phases
Bachmann, S. , Michalakis, S. , Nachtergaele, B. , and Sims, R. , “Automorphic equivalence within gapped phases of quantum lattice systems,” Commun. Math. Phys. 309(3), 835–871 (2012).
, J. I.
, and Schuch
, “Robustness in projected entangled pair states
,” e-print arXiv:1306.4003
Fannes, M. , Nachtergaele, B. , and Werner, R. , “Finitely correlated states on quantum spin chains,” Commun. Math. Phys. 144(3), 443–490 (1992).
Kato, T. , Perturbation Theory for Linear Operators (Springer: Classics in Mathematics, 1980).
Lax, T. , “Linear algebra,” in Pure and Applied Mathematics (Wiley, 1996).
Nachtergaele, B. , “The spectral gap for some quantum spin chains with discrete symmetry breaking,” Commun. Math. Phys. 175, 565–606 (1996).
Ortega, J. , Numerical Analysis: A Second Course (SIAM: Classics in Applied Mathematics, 1972).
Perez-Garcia, D. , Verstaete, F. , Wolf, M. M. , and Cirac, J. I. , “Matrix product state representations,” Quantum Inf. Comput. 7, 401–430 (2007).
Sanz, M. , Péres-García, D. , Wolf, M. M. , and Cirac, J. I. , “A quantum version of Wielandt’s inequality,” IEEE Trans. Inf. Theory 56, 4668 (2010).
The size of [K, L] and Λ depends on b and . Moderate upper bounds are provided in Ref. 20.
Wolf, M. M. , Ortiz, G. , Verstraete, F. , and Cirac, J. I. , “Quantum phase transitions in matrix product systems,” Phys. Rev. Lett. 97(11), 110403 (2006).
Article metrics loading...
We investigate elementary topological properties of sets of completely positive (CP) maps that arise in quantum Perron-Frobenius theory. We prove that the set of primitive CP maps of fixed Kraus rank is path-connected and we provide a complete classification of the connected components of irreducible CP maps at given Kraus rank and fixed peripheral spectrum in terms of a multiplicity index. These findings are then applied to analyse 1D quantum phases by studying equivalence classes of translational invariant matrix product states that correspond to the connected components of the respective CP maps. Our results extend the previously obtained picture in that they do not require blocking of physical sites, they lead to analytic paths, and they allow us to decompose into ergodic components and to study the breaking of translational symmetry.
Full text loading...
Most read this month