Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Area of Science:

• Condensed matter physics
• Quantum many-body systems
• Computational physics

Background:

• Frequency-dependent correlations like spectral functions are crucial for interpreting condensed matter experiments.
• The density matrix renormalization group (DMRG) is a powerful framework for studying quantum systems.
• Calculating spectral functions directly in frequency within DMRG typically uses the correction-vector method.

Purpose of the Study:

• To introduce and evaluate the Krylov-space approach as an alternative method for computing the correction vector in DMRG.
• To assess the accuracy and performance of the Krylov-space approach compared to existing methods.
• To investigate the optimal conditions for applying the Krylov-space approach.

Main Methods:

• The study proposes using the Krylov-space approach to compute the correction vector.
• The proposed method is tested on the Heisenberg, t-J, and Hubbard models.
• Performance is benchmarked against the conjugate gradient method and functional minimization.

Main Results:

• The Krylov-space approach demonstrates comparable or superior accuracy to the conjugate gradient method.
• The Krylov-space approach can be more computationally efficient.
• Optimal performance is achieved when a Krylov-space decomposition is also employed for the ground state DMRG calculation.

Conclusions:

• The Krylov-space approach provides a viable and potentially advantageous alternative for calculating spectral functions within DMRG.
• This method offers improved accuracy and efficiency for studying quantum many-body systems.
• Integrating Krylov-space methods for both ground state and excited state calculations enhances overall performance.