Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions

Author(s): J. Jordan, R. Orús, G. Vidal, F. Verstraete, J. I. Cirac

Journal: Physical Review Letters

Volume: 101

Page(s): 250602

Year: 2008

DOI Number: 10.1103/PhysRevLett.101.250602

Link: Link to publication


We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite 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 analyzing its second order quantum phase transition.


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