Lanczos-boosted numerical linked-cluster expansion for quantum lattice models

Area of Science:

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

Background:

• Numerical linked-cluster expansions (NLCE) are powerful for calculating finite-temperature properties of quantum lattice models.
• Exact solutions of small clusters are typically required, with full diagonalization being a computational bottleneck.

Purpose of the Study:

• To investigate the efficacy of partial diagonalization via the Lanczos algorithm within NLCE.
• To address the computational limitations of full diagonalization in NLCE for large clusters.

Main Methods:

• Applied partial diagonalization using the Lanczos algorithm to the largest clusters in NLCE.
• Tested the approach on the frustrated Heisenberg model (checkerboard lattice) and the Fermi-Hubbard model (square lattice).

Main Results:

• Partial diagonalization proved as effective as full diagonalization for NLCE.
• The Lanczos-based approach significantly mitigated time and memory constraints.
• Achieved performance surpassing state-of-the-art methods in parallel computing environments.

Conclusions:

• Partial diagonalization with the Lanczos algorithm is a viable and efficient alternative for NLCE.
• This method enhances the scalability and performance of quantum lattice model simulations.
• The approach offers a promising direction for advancing computational studies in condensed matter physics.