Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Theory

Background:

• Standard density matrix renormalization group theory (DMRG) is computationally intensive due to iterative diagonalization.
• Accurate simulation of large quantum systems requires efficient theoretical methods.

Purpose of the Study:

• To develop a more efficient alternative to standard DMRG.
• To improve the computational performance of quantum system simulations without significant accuracy loss.

Main Methods:

• Propose inner space perturbation theory (isPT) to replace iterative diagonalization in DMRG.
• Partition retained eigenstates into active and secondary spaces.
• Utilize one-step Davidson iteration for computing wave functions and energies.

Main Results:

• isPT offers a balance between computational efficiency and accuracy.
• The method captures more entanglement within the same computational time.
• Numerical examples on polyacenes and periacene demonstrate significant efficiency gains with minimal accuracy loss.
• Perturbation calculations showed convergence in all tested examples.

Conclusions:

• isPT provides a computationally advantageous approach for quantum system simulations.
• The method retains the accuracy of DMRG while reducing computational cost.
• isPT is a promising technique for studying complex quantum systems.