Inference from Matrix Products: A Heuristic Spin Glass Algorithm

Details Inference from Matrix Products: A Heuristic Spin Glass Algorithm Inference from Matrix Products: A Heuristic Spin Glass Algorithm

2008-07-18

arxiv.org/abs/0807.3008v3

Phys. Rev. Lett. 101, 167206 (2008).

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure, minor typos fixed

Scientific paper

10.1103/PhysRevLett.101.167206

We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate "boundary Hamiltonian" whose accuracy depends on a parameter $k$. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a $k$ which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.

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