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Updated: Jan 19, 2026

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

Krishnakumar Bhattaram1,2, Ehsan Khatami2

  • 1Lynbrook High School, 1280 Johnson Ave., San José, California 95129, USA.

Physical Review. E
|September 11, 2019
PubMed
Summary

Numerical linked-cluster expansions can now calculate quantum model properties more efficiently. Partial diagonalization using the Lanczos algorithm offers a faster alternative to full diagonalization for complex lattice models.

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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.