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

Michael P. Zaletel, Roger S.K. Mong, Christoph Karrasch, Joel E. Moore, Frank Pollmann

Research output: Contribution to journalArticle

92 Scopus citations

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.

Original languageEnglish (US)
Article number165112
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number16
DOIs
StatePublished - Apr 7 2015

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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