Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States

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.