Quantum Entanglement in Non-Hermitian Hubbard Model

L.S. Lima

Said Harir, A. Zouhair, Zoubair Boulahia +2 more

Weitao Chen, Liangtao Peng, Hantao Lu +1 more

Dramatically different from the Hermitian systems, the conventional bulk-boundary correspondence (BBC) is broken in the non-Hermitian systems. In this paper, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of the bulk-boundary correspondence, which eventually disappears at some critical value of interaction.

X. Z. Zhang, L. Jin, Z. Song

We study interchain pair tunneling dynamics based on an exact two-particle solution for a two-leg ladder. We show that the Hermitian Hamiltonian shares a common two-particle eigenstate with a corresponding non-Hermitian Hubbard Hamiltonian in which the non-Hermiticity arises from an on-site interaction of imaginary strength. Our results provide that the dynamic processes of two-particle collision and cross-leg tunneling are well described by the effective non-Hermitian Hubbard Hamiltonian based on the eigenstate equivalence. We also find that any common eigenstate is always associated with the emergence of a spectral singularity in the non-Hermitian Hubbard model. This result is valid for both Bose and Fermi systems and provides a clear physical implication of the non-Hermitian Hubbard model.

Arun K. Pati

Akoramurthy B, Surendiran B, Xiaochun Cheng

We introduce the Biorthogonal Variational Quantum Eigensolver (B-VQE), a quantum algorithm for simulating non-Hermitian many-body systems on noisy intermediate-scale quantum (NISQ) hardware. Non-Hermitian quantum matter exhibits exceptional points, parity-time symmetry breaking, and non-Hermitian skin effects, yet existing quantum algorithms often rely on costly post-selection procedures and are not designed to capture biorthogonal eigenstates. B-VQE employs independent variational circuits to represent the left and right eigenstates of a non-Hermitian Hamiltonian and optimizes a biorthogonal objective function that directly tracks non-Hermitian phase transitions. The framework incorporates an Exceptional-Point Detector (EPD) that identifies exceptional points through a hardware-native coalescence metric and a Non-Hermitian Quantum Geometric Tensor (NH-QGT) readout that distinguishes state-topological and band-topological signatures in interacting many-body systems. To overcome the exponential overhead associated with conventional non-Hermitian simulation, we develop an importance-sampling mitigation strategy that removes the need for ancilla-based post-selection while retaining polynomial computational scaling. We validate the approach on three representative models: a non-Hermitian Hubbard chain, a non-Hermitian XXZ spin chain, and a two-dimensional non-Hermitian (t)-(J) model. B-VQE achieves relative energy errors below (5\times10^{-3}) and locates exceptional points with high accuracy on noise-free simulations while resolving phase boundaries associated with localization, quantum scars, and skin-effect physics. These results establish B-VQE as a scalable NISQ methodology for constructing non-Hermitian many-body phase diagrams and exploring topological and critical phenomena in open quantum systems.