Occupation-Dependent Particle Separation in One-Dimensional Non-Hermitian Lattices

Yi Qin and Linhu Li

Phys. Rev. Lett. 132, 096501 – Published 27 February 2024

Abstract

We unveil an exotic phenomenon arising from the intricate interplay between non-Hermiticity and many-body physics, namely, an occupation-dependent particle separation for hardcore bosons in a one-dimensional lattice driven by unidirectional non-Hermitian pumping. Taking hardcore bosons as an example, we find that a pair of particles occupying the same unit cell exhibit an opposite non-Hermitian pumping direction to that of unpaired ones occupying different unit cells. By turning on an intracell interaction, many-body eigenstates split in their real energies, forming separable clusters in the complex energy plane with either left-, right-, or bipolar-types of non-Hermitian skin effect (NHSE). The dependency of skin accumulating directions on particle occupation is further justified with local sublattice correlation and entanglement entropy of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests as uni- or bidirectional pumping for many-body initial states, allowing for spatially separating paired and unpaired particles. Our results unveil the possibility of designing and exploring novel non-Hermitian phases originated from particle nonconservation in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial configurations.

Received 24 July 2023
Revised 28 November 2023
Accepted 2 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.096501

Physics Subject Headings (PhySH)

Edge states Fermions

Dynamical systems Non-Hermitian systems Quantum many-body systems

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Yi Qin and Linhu Li ^*

Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, and School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai 519082, China

^*lilh56@mail.sysu.edu.cn

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Issue

Vol. 132, Iss. 9 — 1 March 2024

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Images

Figure 1
Schematic of a 1D ladder lattice with two sublattices in a unit cell, each represents a Hatano-Nelson model, and NHSE in its single-particle level. (a) The hopping amplitude to the left (right) direction is $J_{A, B}^{-}$ ( $J_{A, B}^{+}$ ). The intracell hopping strength and interaction are $J_{p}$ and $V$ , respectively. Blue arrows indicate the skin accumulation directions for paired and unpaired particles. (b) Density distribution for all single-particle eigenstates (pink) and their average (black) for different $J_{p}$ . Other parameters are $J_{A}^{+} = 0.45$ , $J_{A}^{-} = 1.24$ , $J_{B}^{+} = - 0.82$ , $J_{B}^{-} = - 1.22$ , $L = 30$ .
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Figure 2
Energy spectrum and skin accumulations for $N = 2$ and $N = 3$ . For both cases, gray and colored dots indicate energy spectra under PBCs and OBCs, respectively, with the color map representing the mean position of each eigenstate, $\bar{x} = ⟨ \hat{x} ⟩$ . (a)–(c) Energy spectra for $N = 2$ for different values of $J_{p}$ and $V$ , with insets showing the density profiles of all eigenstates in all clusters (pink) and their average (black). (d) Density distributions of all eigenstates (pink) and their average (black) of each cluster in (c) (labeled by roman numerals). Three primary eigenstate clusters with right-NHSE are seen to be induced by the intracell hopping $J_{p}$ , and a secondary one with left NHSE is separated from them when turning on the interaction $V$ . Note that the secondary cluster (III) corresponds to a much smaller sub-Hilbert space of paired particles, whose effective Hamiltonian has real OBC eigenvalues [88]. (e) Phase diagram of $Q_{L}$ , the number of left-NHSE modes, for $N = 2$ . (f)–(j) The same quantities as in (a)–(e) for our system with $N = 3$ particles, which hosts four primary clusters with right NHSE, and two secondary clusters exhibiting bipolar-type of skin localization. $L = 10$ is chosen for all panels, other parameters are the same as in Fig. 1.
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Figure 3
Sublattice correlation $C_{n}$ and entanglement entropy $S_{n} = S_{num} + S_{con}$ , i.e., the sum of particle number entropy and configuration entropy. (a) Real part of the eigenenergy for each eigenstate, (b) sublattice correlation of each eigenstate, and (c) sublattice entanglement entropy, for the system with $N = 2$ particles. (d)–(f) The same quantities for $N = 3$ with two emerged secondary clusters. In both cases, emerged secondary clusters with $C_{n} \approx 1$ have smaller $S_{n}$ compared to that of primary clusters with $C_{n} \approx 0$ , serving a signature to distinguish states with double and single occupations. Parameters are $L = 10$ , $V = 20$ , and $J_{p} = 20$ , with the same $J_{A, B}^{\pm}$ as in Fig. 1.
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Figure 4
Dynamics evolution for initial states with different configurations. (a)–(d) the density profiles of the evolved state $| ψ (t) ⟩$ , for different initial states $| ψ (0) ⟩$ given by (a) $| (A B)_{5} ⟩$ , (b) $| (A B)_{4} A_{5} ⟩$ , (c) $| B_{4} B_{5} ⟩$ , and (d) $| B_{3} B_{4} B_{5} ⟩$ , with $J_{p} = 20$ , $V = 5$ and $L = 8$ . Paired and unpaired particles are seen to move to opposite directions. (e) The velocity of density peak for (a)–(d) versus interaction $V$ . Red squares (blue crosses) refer to the left-moving peak of $N = 2$ ( $N = 3$ ) with doubly occupied initial state. Blue rhombuses (black circles) refer to the right-moving peak of $N = 2$ ( $N = 3$ ) with singly occupied initial state. Blue stars refer to the right-moving peak of $N = 3$ with doubly occupied initial state. As can be seen, the velocity is almost unchanged for singly occupied initial states of $| B_{4} B_{5} ⟩$ and $| B_{3} B_{4} B_{5} ⟩$ [or the unpair particle in $| (A B)_{4} A_{5} ⟩$ ] with different $V$ , as these states are immune to the intracell interaction. Other parameters no mentioned here are the same as in Fig. 1.
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