Simulating typical entanglement with many-body Hamiltonian dynamics

Details Simulating typical entanglement with many-body Hamiltonian dynamics Simulating typical entanglement with many-body Hamiltonian dynamics

2011-08-02

arxiv.org/abs/1108.0485v2

Phys. Rev. A 84, 052321 (2011)

Physics

Quantum Physics

Revised, 11 pages, 7 figures

Scientific paper

10.1103/PhysRevA.84.052321

We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.

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