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Chinese Journal of Physics

Entanglement entropy in the ground state of supersymmetric fermion lattice models

M. A. Jafarizadeh, F. Eghbalifam, S. Nami

Published Mar 21, 2022• 2 citations
Publisher
DOI
10.1016/j.cjph.2021.09.020

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Abstract We investigate the entanglement entropy in the ground state of the supersymmetric fermion lattice model. The Hamiltonian of this model is block diagonal in the basis of a fixed number of particles, so we compute the entanglement entropy for the blocks of the Hamiltonian separately. We explain the way of calculating the correlation matrix and the entanglement entropy for the ground state of supersymmetric Hamiltonian on diverse graphs. Then we show that the entanglement entropy exhibits the volume law scaling in various choices of the number of fermions in regular graphs. Also, we give the analytical formula for the entanglement entropy in one scalable set of strongly regular graphs in terms of their parameters, and we prove that the entanglement entropy satisfies a volume law.
We study the structure of entanglement in a supersymmetric lattice model of fermions on certain types of decorated graphs with quenched disorder. In particular, we construct models with controllable ground-state degeneracy protected by supersymmetry and the choice of Hilbert space. We show that in certain special limits, these degenerate ground states are associated with local impurities and that there exists a basis of the ground-state manifold in which every basis element satisfies a boundary law for entanglement entropy. On the other hand, by considering incoherent mixtures or coherent superpositions of these localized ground states, we can find regions that violate the boundary law for entanglement entropy over a wide range of length scales. More generally, we discuss various criteria for constructing violations of the boundary law for entanglement entropy and discuss possible relations of our work to recent holographic studies.
We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1+1)-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Rényi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of (1+1)-dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Our results confirm the widely believed conjecture that the critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.