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Classical simulation of infinite-size quantum lattice systems in two spatial dimensions

J. Jordan·R. Orus·G. Vidal·F. Verstraete·J. I. Cirac
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Abstract

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac, cond-mat/0407066] and the infinite {\em time-evolving block decimation} algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analysing its second order quantum phase transition.

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J. Jordan, R. Orus, G. Vidal, F. Verstraete, J. I. Cirac. 2008-10-02. Classical simulation of infinite-size quantum lattice systems in two spatial dimensions. https://doi.org/10.1103/physrevlett.101.250602

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