Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

Abstract

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of $n_{\mathrm{svd}}$ smaller subcluster vectors using singular value decomposition. For low entanglement entropy $S_{ee}$, (satisfied by short range Hamiltonians), the truncation error is expected to vanish as $\exp (-n_{\mathrm{svd}}^{1/S_{ee}})$. Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

7 pages, 8 figures

References in corpus (7)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Towards measuring Entanglement Entropies in Many Body Systems
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Factorization of shell-model ground-states

Cited by in corpus (3)

• Proton-neutron entanglement in the nuclear shell model
• p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet
• Compression algorithm for discrete light-cone quantization