Time-evolving a matrix product state with long-ranged interactions
By M. Zaletel, Roger S. K. Mong, C. Karrasch, J. Moore, Frank Pollmann. 2014
252 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/149f452f34395454b8ec0485925f53bac7b25fbd
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Time-evolution methods for matrix-product states (2019, methodology): “, four operators Û ′(δ1,2,3,4) are required for a third-order error [40].”