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

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.

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Hashizume, Tomohiro1, Author
Halimeh, Jad C.2, Author           
McCulloch, Ian P.1, Author
Affiliations:
1external, ou_persistent22              
2Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: Phase transitions and critical phenomena
 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.

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 Dates: 2020-07-072020-07-15
 Publication Status: Issued
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Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 102 (3) Sequence Number: 035115 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008