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Time-evolving a matrix product state with long-ranged interactions

Zaletel, Michael P. and Mong, Roger S. K. and Karrasch, Christoph and Moore, Joel E. and Pollmann, Frank (2015) Time-evolving a matrix product state with long-ranged interactions. Physical Review B, 91 (16). Art. No. 165112. ISSN 1098-0121. doi:10.1103/PhysRevB.91.165112.

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We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting, one-dimensional systems, such as Coulombic and dipolar systems, and quasi-two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

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Additional Information:© 2015 American Physical Society. Received 29 July 2014; revised manuscript received 17 February 2015; published 7 April 2015. We are grateful to J. H. Bardarson, E. M. Stoudenmire, and D. Varjas for helpful conversations. The authors wish to acknowledge NSF DMR-1206515 (M.Z. and J.E.M.), the Sherman Fairchild Foundation (R.M.), the Nanostructured Thermoelectrics program of DOE BES (C.K.), and the Simons Foundation (J.E.M.).
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)UNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:16
Classification Code:PACS: 05.30.Jp, 02.70.−c
Record Number:CaltechAUTHORS:20150424-111611043
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56952
Deposited By: Tony Diaz
Deposited On:24 Apr 2015 19:33
Last Modified:10 Nov 2021 21:05

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