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Jheng-Wei Li1,2, Andreas Gleis1, Jan von Delft1

  • 1Arnold Sommerfeld Center for Theoretical Physics, <a href="https://ror.org/002epp671">Center for NanoScience</a>, and <a href="https://ror.org/04xrcta15">Munich Center for Quantum Science and Technology</a>, <a href="https://ror.org/05591te55">Ludwig-Maximilians-Universität München</a>, 80333 Munich, Germany.

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This summary is machine-generated.

We introduce Controlled Bond Expansion (CBE) to improve quantum dynamics simulations using the time-dependent variational principle (TDVP). This method enhances accuracy by dynamically adjusting matrix product state bond dimensions, reducing projection errors in simulations.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Condensed matter theory

Background:

  • Simulating quantum dynamics is computationally challenging.
  • Standard methods like one-site TDVP for matrix product states face numerical difficulties due to fixed bond dimensions.
  • Projection errors can limit the accuracy of these simulations.

Purpose of the Study:

  • To present a novel approach, Controlled Bond Expansion (CBE), for simulating quantum dynamics.
  • To overcome the limitations of fixed-rank TDVP integrators.
  • To improve the accuracy and efficiency of matrix product state-based quantum dynamics simulations.

Main Methods:

  • Developed a Controlled Bond Expansion (CBE) approach.
  • Integrated CBE with the time-dependent variational principle (TDVP) for matrix product states.
  • Dynamically increased bond dimensions on-the-fly to minimize projection errors.
  • Implemented CBE with minor modifications to standard one-site TDVP algorithms.

Main Results:

  • Demonstrated the performance and accuracy of the CBE-TDVP method.
  • Successfully simulated bipolaron formation in the Peierls-Hubbard model.
  • Investigated spin pumping via adiabatic flux insertion in a chiral spin liquid.
  • Showcased the method's ability to handle complex quantum phenomena.

Conclusions:

  • CBE-TDVP offers an economical and accurate way to simulate quantum dynamics.
  • The method effectively reduces projection errors by adaptively increasing bond dimensions.
  • CBE-TDVP provides a robust framework for studying various quantum phenomena in condensed matter systems.