Monday, July 8, 2013

1307.1486 (Tarun Grover)

Quantum Entanglement of Interacting Fermions in Monte Carlo    [PDF]

Tarun Grover
Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as, the Renyi entropies of the ground state wavefunction? This is an important question because entanglement plays a crucial role in exposing subtle quantum phenomena, such as, fractionalization and topological order. Even though progress has been made in addressing this question for interacting Hamiltonians of bosons and spin-systems, as yet there exist no corresponding methods for interacting fermions. Here we show that the entanglement structure of interacting fermionic Hamiltonians has a particularly simple form -- the interacting reduced density matrix can be written as a sum of the reduced density matrices of certain free fermionic systems. This decomposition allows us to calculate the Renyi entropies for Hamiltonians which can be simulated via Determinantal Monte Carlo, while employing the efficient techniques hitherto available only for free fermion systems. Furthermore, one can develop a systematic expansion for the interacting entanglement Hamiltonian itself, which is again calculable within the Monte Carlo. This method works for the ground state, as well as for the thermally averaged reduced density matrix. We discuss potential applications, and possible implications for the scaling laws of the entanglement entropy.
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