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Computing excited eigenstates using inexact Lanczos methods and tree tensor network states.

Madhumita Rano1, Henrik R Larsson1

  • 1Department of Chemistry and Biochemistry, University of California, Merced, California 95343, USA.

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Summary
This summary is machine-generated.

This study introduces a new method combining the inexact Lanczos method with tree tensor network states (TTNSs) to efficiently compute excited eigenstates in quantum many-body systems.

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Area of Science:

  • Computational physics
  • Quantum mechanics
  • Quantum many-body systems

Background:

  • Tensor network states are standard for ground states but struggle with excited states.
  • Accurate computation of excited eigenstates is crucial for understanding quantum many-body dynamics.

Purpose of the Study:

  • To develop an efficient method for computing excited eigenstates in quantum many-body systems.
  • To address the challenge of obtaining accurate excited states using tensor network methods.

Main Methods:

  • Combines the inexact Lanczos method with tree tensor network states (TTNSs).
  • Applies the TTNS inexact Lanczos method to challenging quantum vibrational state computations.

Main Results:

  • Successfully computed excited vibrational states for acetonitrile, the Zundel ion, and the Eigen ion.
  • Demonstrated the method's capability on systems with high dimensionality and complex correlations.

Conclusions:

  • The TTNS inexact Lanczos method provides an efficient approach for calculating excited eigenstates.
  • This method is broadly applicable to various quantum many-body systems.