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

Abstract

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.

5 pages + 3 pages appendices, 4 figures

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• Full counting statistics in the Haldane-Shastry chain
• Simulating generic spin-boson models with matrix product states
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
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• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
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• Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
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• Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions
• Cooling schemes for two-component fermions in layered optical lattices
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• Dynamic structure factor from real time evolution and exact correction vectors with matrix product states
• Many-body localization in a tilted potential in two dimensions
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction