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Verfasst von:Wall, Michael L. [VerfasserIn]   i
 Carr, Lincoln D. [VerfasserIn]   i
Titel:Out-of-equilibrium dynamics with matrix product states
Verf.angabe:M. L. Wall and Lincoln D. Carr
E-Jahr:2012
Jahr:18 December 2012
Umfang:39 S.
Teil:volume:14
 year:2012
 extent:39
Fussnoten:Gesehen am 15.06.2018
Titel Quelle:Enthalten in: New journal of physics
Ort Quelle:[Bad Honnef] : Dt. Physikalische Ges., 1999
Jahr Quelle:2012
Band/Heft Quelle:14(2012) Artikel-Nummer 125015, 39 Seiten
ISSN Quelle:1367-2630
Abstract:Theoretical understanding of strongly correlated systems in one spatial dimension has been greatly advanced by the density-matrix renormalization group (DMRG) algorithm, which is a variational approach using a class of entanglement-restricted states called matrix product states (MPSs). However, DMRG suffers from inherent accuracy restrictions when multiple states are involved due to multi-state targeting and also the approximate representation of the Hamiltonian and other operators. By formulating the variational approach of DMRG explicitly for MPSs one can avoid errors inherent in the multi-state targeting approach. Furthermore, by using the matrix product operator (MPO) formalism, one can exactly represent the Hamiltonian and other operators relevant for the calculation. The MPO approach allows one-dimensional (1D) Hamiltonians to be templated using a small set of finite state automaton rules without reference to the particular microscopic degrees of freedom. We present two algorithms which take advantage of these properties: eMPS to find excited states of 1D Hamiltonians and tMPS for the time evolution of a generic time-dependent 1D Hamiltonian. We properly account for time-ordering of the propagator such that the error does not depend on the rate of change of the Hamiltonian. Our algorithms are applicable to microscopic degrees of freedom of any variety, and do not require Hamiltonian-specialized implementation. We benchmark our algorithms with a case study of the Ising model, where the critical point is located using entanglement measures. We then study the dynamics of this model under a time-dependent quench of the transverse field through the critical point. Finally, we present studies of a dipolar, or long-range Ising model, again using entanglement measures to find the critical point and study the dynamics of a time-dependent quench through the critical point.
DOI:doi:10.1088/1367-2630/14/12/125015
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kostenfrei: Volltext ; Verlag: http://dx.doi.org/10.1088/1367-2630/14/12/125015
 kostenfrei: Volltext: http://stacks.iop.org/1367-2630/14/i=12/a=125015
 DOI: https://doi.org/10.1088/1367-2630/14/12/125015
Datenträger:Online-Ressource
Sprache:eng
K10plus-PPN:1576799921
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