Solving Gapped Hamiltonians Locally

Details Solving Gapped Hamiltonians Locally Solving Gapped Hamiltonians Locally

2005-08-23

arxiv.org/abs/cond-mat/0508554v2

Phys. Rev. B 73, 085115 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

13 pages, 2 figures; minor changes to references, additional discussion of numerics

Scientific paper

10.1103/PhysRevB.73.085115

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that the ground state of any such Hamiltonian is close to a generalized matrix product state. The range of the given operators needed to obtain a good approximation to the ground state is proportional to the square of the logarithm of the system size times a characteristic "factorization length". Applications to many-body quantum simulation are discussed. We also consider density matrices of systems at non-zero temperature.

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