Entanglement negativity in free lattice models

Po-Yao Chang, Xueda Wen, Shinsei Ryu

L.S. Lima

L.S. Lima

L.S. Lima

Viktor Eisler, Zoltán Zimborás

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.

Malen Arias, Marina Huerta, Andrei Rotaru +1 more

We study the entanglement negativity for the free, scalar chiral current in two spacetime dimensions, which is a simple model violating the Haag duality in regions with nontrivial topology. For the ground state of the system, both on the line and on the circle, we consider the setups given by two intervals, either adjacent or disjoint. We find analytic expressions for the moments of the partial transpose of the reduced density matrix and the logarithmic negativity. In the limit of small separation distance, this expression yields the same subleading topological contribution occurring in the mutual information. In the limit of large separation distance between the two intervals, the exponential decay of the logarithmic negativity is obtained from its analytic expression. The analytic formulas are checked against exact numerical results from a bosonic lattice model, finding a perfect agreement. We observe that, since the chiral current generates the neutral subalgebra of the full chiral Dirac fermion theory, this analysis highlights how symmetries produce nontrivial features in the entanglement structure that are analogue to those ones already observed in the mutual information for regions with nontrivial topology.