Abstract
We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with projected entangled pair states (PEPS) as a function of the bond dimension (), temperature (), and system size (). First, we introduce a compression method in which the bond dimension scales as if . Second, building on the work of Hastings [M. B. Hastings, Phys. Rev. B 73, 085115 (2006)], we derive a polynomial scaling relation, . This implies that the manifold of PEPS forms an efficient representation of Gibbs states of local quantum Hamiltonians. From those bounds it also follows that ground states can be approximated with whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.
- Received 29 September 2014
- Revised 23 December 2014
DOI:https://doi.org/10.1103/PhysRevB.91.045138
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