Entanglement Hamiltonians from field theory to the lattice (G. Giudici)
Jul 12, 2018
14:00 - 15:00
Max-Planck-Institut für Quantenoptik
Seminarraum B 2.46
MPQ, Theory Division, hosted by Prof. Norbert Schuch
Given a space bipartition (A, B) of a quantum state, the entanglement Hamiltonian of A is the logarithm of the reduced density matrix obtained after tracing over B.
Despite its relevance in the characterization of entanglement properties of many-body quantum systems on the lattice, exact analytical expressions away from fine tuned points are known only in very few free theories. Oppositely, at the quantum field theory (QFT) level, the entanglement Hamiltonian of a half-space-bipartition has long been known, under the assumption of Lorentz invariance of the QFT.In this talk I will discuss the validity of these field theory predictions on the lattice. I will show that a straightforward discretization of the continuum expression for the entanglement Hamiltonian gives qualitatively and quantitatively accurate results for entanglement spectrum, correlation functions, local and non-local order parameters, and entanglement entropy. This is checked through extensive numerical simulations based on the density-matrix-renormalization-group method, exact diagonalization, and quantum Monte Carlo, on 1- and 2- dimensional lattice models supporting a wide variety of quantum phases and critical points belonging to different universality classes. Our results suggest a generic route for the investigation of lattice entanglement Hamiltonians based on QFT, out of which I outlook some potential applications.