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Hybrid infinite time-evolving block decimation algorithm for long-range multidimensional quantum many-body systems

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Halimeh,  Jad C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Hashizume, T., Halimeh, J. C., & McCulloch, I. P. (2020). Hybrid infinite time-evolving block decimation algorithm for long-range multidimensional quantum many-body systems. Physical Review B, 102(3): 035115. doi:10.1103/PhysRevB.102.035115.


Cite as: http://hdl.handle.net/21.11116/0000-0007-434D-8
Abstract
In recent years, the infinite time-evolving block decimation (iTEBD) method has been demonstrated to be one of the most efficient and powerful numerical schemes for time evolution in one-dimensional quantum many-body systems. However, a major shortcoming of the method, along with other state-of-the-art algorithms for manybody dynamics, has been their restriction to one spatial dimension. We present an algorithm based on a hybrid extension of iTEBD where finite blocks of a chain are first locally time evolved before an iTEBD-like method combines these processes globally. This in turn permits simulating the dynamics of many-body systems in spatial dimensions d >= 1 where the thermodynamic limit is achieved along one spatial dimension and where long-range interactions can also be included. Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality. We expect the algorithm presented here to be of significant importance to validating and guiding investigations in state-of-the-art ion-trap and ultracold-atom experiments.