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Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

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Reducing memory cost of exact diagonalization using singular value decomposition.

Marvin Weinstein¹, Assa Auerbach, V Ravi Chandra

¹SLAC National Accelerator Laboratory, Stanford, California 94025, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This summary is machine-generated.

A new Lanczos algorithm reduces memory for lattice Hamiltonian diagonalization. This method uses singular value decomposition (SVD) for efficient computation, even for complex quantum systems.

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Area of Science:

Quantum Many-Body Physics
Computational Physics
Condensed Matter Theory

Background:

Diagonalizing lattice Hamiltonians is computationally intensive, often requiring significant memory.
Variational methods are limited by the choice of ansatz, restricting applicability.
Efficient numerical techniques are crucial for studying complex quantum systems.

Purpose of the Study:

To develop a memory-efficient algorithm for diagonalizing lattice Hamiltonians.
To overcome limitations of variational methods in quantum many-body studies.
To enable the study of larger and more complex lattice systems.

Main Methods:

A modified Lanczos algorithm incorporating singular value decomposition (SVD).
Partitioning the lattice into subclusters for vector projection.
Truncation of vectors based on entanglement entropy (S(ee)) and SVD dimensions (n(svd)).

Main Results:

Dramatically reduced memory requirements for Hamiltonian diagonalization.
Successful convergence testing on Heisenberg models for Kagomé clusters (24, 30, 36 sites).
Demonstrated feasibility with less than 15 GB of dynamical memory without exploiting lattice symmetries.

Conclusions:

The Lanczos-SVD algorithm offers a powerful, memory-efficient approach for quantum many-body problems.
The method shows promise for systems with low entanglement entropy, characteristic of short-range Hamiltonians.
Potential for generalization to multiple partitioning schemes and comparison with existing techniques.