Berlin 2015 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 65: Low-Dimensional Systems: 1D – Theory
TT 65.2: Talk
Wednesday, March 18, 2015, 15:30–15:45, H 0104
Efficient time-evolution for long-ranged one-dimensional Hamiltonians — •Frank Pollmann1, Mike Zaletel2, Roger S. K. Mong3, Christoph Karrasch2, and Joel E. Moore2 — 1Max-Planck-Institut f"ur Physik komplexer Systeme, 01187 Dresden, Germany — 2University of California, Berkeley, California 94720, USA — 3California Institute of Technology, Pasadena, California 91125, USA
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. 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.