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

Michael P. Zaletel, Roger S. K. Mong, Christoph Karrasch, Joel E. Moore, and Frank Pollmann
Phys. Rev. B 91, 165112 – Published 7 April 2015

Abstract

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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  • Received 29 July 2014
  • Revised 17 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.165112

©2015 American Physical Society

Authors & Affiliations

Michael P. Zaletel1,2, Roger S. K. Mong3, Christoph Karrasch1,4, Joel E. Moore1,4, and Frank Pollmann5

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, Stanford University, Stanford, California 94305, USA
  • 3Walter Burke Institute for Theoretical Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
  • 4Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 5Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany

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Issue

Vol. 91, Iss. 16 — 15 April 2015

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