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- W133033975 abstract "We show how the area law for the entanglement entropy may be violated by free fermions on a lattice and look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets $A$ and $bar{A}$ is given, the states with maximal entanglement entropy (volume law) may be factored into Bell-pairs (BP) formed by two states with support on $A$ and $bar{A}$. We then exhibit, for translational invariant fermionic systems on a lattice, an Hamiltonian whose ground state is such to yield an exact volume law. As expected, the corresponding Fermi surface has a fractal topology. We also provide some examples of fermionic models for which the ground state may have an entanglement entropy $S_A$ between the area and the volume law, building an explicit example of a one-dimensional free fermion model where $S_A (L) propto L^beta$ with $beta$ being intermediate between $beta = 0$ (area law) and $beta = 1$ (BP-state inducing volume law). For this model, the dispersion relation has a zig-zag structure leading to a fractal Fermi surface whose counting box dimension equals, for large lattices, $beta$. Our analysis clearly relates the violation of the area law for the entanglement entropy of the ground state to the emergence of a non-trivial topology of the Fermi surface." @default.
- W133033975 created "2016-06-24" @default.
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- W133033975 date "2014-05-14" @default.
- W133033975 modified "2023-09-24" @default.
- W133033975 title "Bell-Paired States Inducing Volume Law for Entanglement Entropy in Fermionic Lattices" @default.
- W133033975 hasPublicationYear "2014" @default.
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