Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice
Source abstract
Abstract
We introduce a simple algorithm providing a compressed representation (∈ℝNorbits×Norbits×ℕNorbits) of an irreducible Hamiltonian matrix (number of magnons M constrained, dimension: Nspins!M!(Nspins−M)!>Norbits) of the spin-1/2 Heisenberg antiferromagnet on the L×L non-periodic lattice, not looking for a good basis. As L increases, the ratio of the matrix dimension to Norbits converges to 8 (order of the symmetry group of square) for the exact ground state computation. The sparsity of the Hamiltonian is retained in the compressed representation. Thus, the computational time and memory consumptions are reduced in proportion to the ratio.
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Research context
OpenAlex topics: Quantum many-body systems · Physics of Superconductivity and Magnetism · Model Reduction and Neural Networks
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Affiliations
Ulsan National Institute of Science and Technology (UNIST) 1 School of Natural Science, , Ulsan 44919, Korea
Kumoh National Institute of Technology 2 Department of Software Engineering & Department of Applied Mathematics, , Gumi 39177, Korea
Ulsan National Institute of Science and Technology (UNIST) 3 School of Electrical and Computer Engineering & School of Natural Science, , Ulsan 44919, Korea
Funding
National Research Foundation of Korea
References (20)
Show source-provided references
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