Arts & Sciences Events
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Arts & Sciences
[PAST EVENT] HIGH ENERGY THEORY SEMINAR
October 6, 2015
2pm - 3pm
Abstract:
In this talk I will address the effect that boundary conditions and the presence of zero modes have on entanglement. I will focus on a simple case, namely chiral free fermions in 1+1 dimensions, with the spatial dimension being a circle. Dirac (complex) fermions admit generic boundary conditions whereas Majorana (real) fermions have only anti--periodic or periodic boundary conditions. By dividing the spatial region into an entangling region and its complement, and tracing over the degrees of freedom in the complement one obtains the reduced density matrix. The density matrix, and its associated entanglement Hamiltonian are more refined measures of entanglement. Given some entangling region, I will construct the entanglement Hamiltonian, using a combination of Riemann-Hilbert problem and perturbative expansion techniques. As a result I will be able to show how the zero modes manifest themselves as non-local contributions to the entanglement Hamiltonian.
In this talk I will address the effect that boundary conditions and the presence of zero modes have on entanglement. I will focus on a simple case, namely chiral free fermions in 1+1 dimensions, with the spatial dimension being a circle. Dirac (complex) fermions admit generic boundary conditions whereas Majorana (real) fermions have only anti--periodic or periodic boundary conditions. By dividing the spatial region into an entangling region and its complement, and tracing over the degrees of freedom in the complement one obtains the reduced density matrix. The density matrix, and its associated entanglement Hamiltonian are more refined measures of entanglement. Given some entangling region, I will construct the entanglement Hamiltonian, using a combination of Riemann-Hilbert problem and perturbative expansion techniques. As a result I will be able to show how the zero modes manifest themselves as non-local contributions to the entanglement Hamiltonian.