Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Computational Physics

Background:

• Density matrix renormalization group (DMRG) is a powerful algorithm for finding ground states of quantum systems.
• Symmetry sectors are crucial for DMRG efficiency, but traditional methods limit virtual bond space expansion.
• Single-site DMRG lacks bond expansion, while two-site DMRG is computationally expensive.

Purpose of the Study:

• To introduce a novel controlled bond expansion (CBE) algorithm for DMRG.
• To achieve the accuracy and convergence of two-site DMRG at the computational cost of single-site DMRG.
• To investigate the phase diagram of the Kondo-Heisenberg model using the new algorithm.

Main Methods:

• Developed a controlled bond expansion (CBE) algorithm integrated with DMRG (CBE-DMRG).
• The CBE algorithm selectively expands virtual bond spaces by including relevant symmetry sectors.
• The algorithm identifies and incorporates parts of the orthogonal space with significant weight in HΨ.

Main Results:

• CBE-DMRG achieves two-site accuracy and convergence per sweep at single-site computational costs.
• The algorithm is fully variational and does not require mixing parameters.
• Application to the Kondo-Heisenberg model on a width 4 cylinder revealed two distinct phases characterized by different Fermi surface volumes.

Conclusions:

• CBE-DMRG offers a computationally efficient and accurate method for exploring complex quantum systems.
• The algorithm overcomes limitations of traditional DMRG regarding virtual bond space expansion.
• The findings provide new insights into the phase transitions of the Kondo-Heisenberg model.