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Obtaining the two-body density matrix in the density matrix renormalization group method.

Dominika Zgid¹, Marcel Nooijen

¹Department of Chemistry, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada. zgid@scienide.uwaterloo.ca

The Journal of Chemical Physics

|April 17, 2008

Summary

This study introduces a method to efficiently compute the two-body density matrix within Density Matrix Renormalization Group (DMRG) calculations, minimizing computational resources. The approach ensures accurate results by leveraging monotonic convergence in the one-site DMRG algorithm.

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Area of Science:

Computational Physics
Quantum Many-Body Systems

Background:

The Density Matrix Renormalization Group (DMRG) is a powerful algorithm for studying one-dimensional quantum many-body systems.
Calculating the two-body density matrix is crucial for many physical properties but can be computationally expensive.
Existing DMRG methods face challenges with computational cost and potential convergence issues like local minima.

Purpose of the Study:

To develop an efficient method for calculating the two-body density matrix during DMRG computations.
To avoid increasing disk and memory requirements for producing the two-body density matrix.
To address and provide solutions for local minima problems in DMRG calculations.

Main Methods:

The proposed approach calculates different elements of the two-body density matrix at various stages of a DMRG sweep.
It relies on the monotonic convergence property of the one-site DMRG procedure.
Theoretical analysis of the wave function ansatz in DMRG is used to validate the method.

Main Results:

The method allows for the production of the two-body density matrix without additional disk or memory overhead.
The computational cost for obtaining the two-body density matrix is O(M^3k^2 + M^2k^4).
The one-site DMRG algorithm, when used with this method, avoids the N-representability problem.

Conclusions:

The presented approach offers an efficient and resource-friendly way to compute the two-body density matrix in DMRG.
The one-site DMRG procedure's monotonic convergence is key to obtaining accurate density matrices.
Practical strategies are provided to mitigate and avoid local minima in DMRG calculations, ensuring reliable results.