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Entanglement Negativity in Non-Hermitian Su-Schrieffer-Heeger Models

L.S. Lima

Published Jan 1, 2024• 0 citations
Publisher
DOI
10.2139/ssrn.4944475

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Theoretical and Mathematical Physics•May 1, 2026•0 citations
Abstract Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.
Abstract We analytically study zero-energy eigenstates for two non-Hermitian models based on the Su–Schrieffer–Heeger (SSH) chain. The first model is an infinite non-Hermitian SSH chain with nonreciprocal hoppings to a neighboring site and two barriers. We find analytical expressions for the eigenfunctions, including those that describe resonant states. For resonant states, an analogue of the non-Hermitian skin effect is observed. For the second model, a finite non-Hermitian SSH chain with nonreciprocal hoppings with an even or odd number of sites, we also find the eigenfunctions and observe the non-Hermitian skin effect. All results are obtained using the derived Green’s function of the infinite non-Hermitian SSH chain.