Algorithms for entanglement renormalization

2007/07/31 by G. Evenbly, G. Vidal · 1 voice · 3 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.other #quant-ph

paper · pdf · doi:10.1103/physrevb.79.144108

published as Phys. Rev. B 79, 144108 (2009) · 23 pages, 28 figures

arxiv created 2009/04/13 · arxiv updated 2015/05/12

Abstract

We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this optimization is logarithmic in the linear system size. Specialized algorithms for the treatment of infinite systems are also described. Benchmark simulation results are presented for a variety of 1D systems, namely Ising, Potts, XX and Heisenberg models. The potential to compute expected values of local observables, energy gaps and correlators is investigated.

Cited by

• Operator Learning for efficient Quantum Computation
• Clifford disentanglers for entanglement reduction in molecular electronic structure simulations
• Low T-count preparation of nuclear eigenstates with tensor networks

Discussions

• In the paper you cited ( https://arxiv.org/abs/1311.4531 ), they use a snake-like or zigzag mapping to flatten a 2D lattice into a 1D chain, and this mapping introduces effective longer-range interact [stackexchange, 1 points]

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