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arXiv:2310.07599 · Physical Review A

Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model

Chao-Ze Lu, Gaoyong Sun

Published Apr 10, 2024• 13 citations
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Abstract

We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge-density-wave phase accompanied by a parity-time transition in the first-excited state. The phase transition is characterized by the crossing of the ground-state biorthogonal-order parameter and the sudden change of the first-excited-state entanglement entropy. The gapless phase is verified by the logarithmic scaling of the ground-state entanglement entropy with the central charge $c=1$. Furthermore, we show that all energy spectral clusters would form ellipses in strong nearest-neighbor interactions, for which we establish a universal scaling law. The lengths of the major and minor axes are shown to obey power laws with respect to the nearest-neighbor interaction. The exact expressions are derived for the numbers of energy levels on the outermost elliptic ring of each clusters.

DOI
10.1103/physreva.109.042208

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We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge-density-wave phase accompanied by a parity-time transition in the first-excited state. The phase transition is characterized by the crossing of the ground-state biorthogonal-order parameter and the sudden change of the first-excited-state entanglement entropy. The gapless phase is verified by the logarithmic scaling of the ground-state entanglement entropy with the central charge c=1c=1c=1. Furthermore, we show that all energy spectral clusters would form ellipses in strong nearest-neighbor interactions, for which we establish a universal scaling law. The lengths of the major and minor axes are shown to obey power laws with respect to the nearest-neighbor interaction. The exact expressions are derived for the numbers of energy levels on the outermost elliptic ring of each clusters.
We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two PT\mathcal{PT}PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.
We study quantum phase transitions in a hard-core boson model with nearest-neighbor repulsions in one dimension. As we change the repulsive energy, V , between bosons occupying nearest neighbors, the model exhibits a quantum phase transition from a superfluid (SF) to a charge-density-wave (CDW)-type solid phase at half-filling. By using an exact diagonalization method with a modified Lanczos method, we calculate the ground-state energies up to a precision of O (10 −7 ). From the ground-state energies, we obtain the number of dimers by taking numerical derivatives of the groundstate energies. Because the dissolution of the dimers occurs because of the repulsive energy, V , we find a signature of the quantum phase transition from the behaviors of the correlation energy and those of the number of dimers as a function of V .
The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping (Hatano-Nelson model) under onsite disorder and nearest-neighbor interaction. As opposed to an assertion of previous studies, the entanglement dynamics in this non-Hermitian quantum system is very different from the one in its Hermitian counterpart, especially in the delocalized regime with weak disorder; there the entanglement entropy Sent(t){S}_{\mathrm{ent}}(t)Sent​(t) shows a characteristic nonmonotonic time evolution. We have clarified and quantified the nature of this behavior in the quasiparticle picture. In the asymptotic regime of $t\ensuremath{\rightarrow}\ensuremath{\infty}$, the entanglement entropy Sent(t){S}_{\mathrm{ent}}(t)Sent​(t) in this regime saturates to a much suppressed value, which increases only logarithmically with respect to the size of the subsystem.
We study the one-dimensional hard-core Bose-Hubbard model with three-body interactions. In previous work[1], the two-thirds filling solid with both bond-wave order (BOW) and charge-density wave order (CDW) is found and it undergoes a second order phase transition to the superfluid phase. However, in recent work[2], we found the BOW not independent with CDW order. Thus, by utilizing the density matrix renormalization group, we make use of both entanglement entropy and fidelity susceptibility to detect the phase transition. In two-thirds filling, the extreme point of the entanglement entropy also indicates the superfluid phase transition point. However, the pairwise entanglement entropy drop quickly after additional critical point, such disentangled behaviour demonstrates another melting point to the CDW phase. Thus, a novel intermediate phase between CDW phase and superfluid phase is found. At last, we analyzed the half filling case with entanglement entropy.
We study a model for interacting spinless bosons in one dimension. The bosons are under a hard-core condition, which does not allow two or more bosons in the same site. However, nearestneighbor interactions between bosons ( V ) and hoppings to the nearest empty site ( t ) are allowed. As V increases from a large negative value, the system undergoes a quantum phase transition from a phase-separation (PS) phase to a superfluid (SF) phase because the hopping term overcomes the attractive energy. When V becomes positive and is increased more, the superfluid phase becomes a charge-density-wave (CDW) phase because the repulsive energy blocks the movements of bosons. Via exact diagonalizations, we calculated the ground-state energies, the correlation energies, and the kinetic energies to obtain signatures of the quantum phase transitions. We adopted a fast stateseeking algorithm that enabled us to calculate the ground states and the ground-state energies up to L = 32 more efficiently. Some results are compared with those of quantum Monte Carlo simulations by using stochastic series expansion for the Heisenberg point, and the momentum distribution functions for the three phases are discussed.
The entanglement entropy and quantum fidelity in a hard-core-boson model with nearest- and next-nearest-neighbor interactions are studied numerically. By using exact diagonalization and the density-matrix renormalization group, the effects of interactions on the entanglement entropy and fidelity susceptibility in the model are investigated. We focus our attention on looking for three quantum phase transitions. It is found that the first derivative of the entanglement entropy can indicate all three phase transitions, while the fidelity susceptibility cannot predict the transition from superfluid to bond order in a finite-size system.