Journal
PHYSICAL REVIEW B
Volume 91, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.91.045138
Keywords
-
Funding
- EU
- DFG
- Alexander von Humboldt foundation
- Adolph C. and Mary Sprague Miller Institute for Basic Research in Science
- University of California Berkeley
Ask authors/readers for more resources
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 (D), temperature (beta(-1)), and system size (N). First, we introduce a compression method in which the bond dimension scales as D = e(O(log22 (N/epsilon))) if beta < O (log(2) N). Second, building on the work of Hastings [M.B. Hastings, Phys. Rev. B 73, 085115 (2006)], we derive a polynomial scaling relation, D = (N/epsilon)(O(beta)). 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 D = N-O(log2 N) whenever the density of states only grows polynomially in the system size. All results hold for any spatial dimension of the lattice.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available