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

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.