Non-Hermitian many-body localization in asymmetric chains with long-range interaction

TL;DR

This paper addresses how non-Hermitian spectra relate to many-body localization in a clean 1D chain with power-law long-range interactions and asymmetric hopping. The authors use exact diagonalization and finite-size scaling to identify static real-to-complex spectral transitions and ergodic-MBL transitions via $f_{\rm Im}$ and $S_{L/2}$ across varying $V$ and $\alpha$, revealing non-monotonic but non-overlapping phase boundaries. They further corroborate these static findings with dynamical measurements of $S(t)$ and $\mathcal{I}(t)$ and explore open-boundary behavior where the spectrum remains real and only MBL persists, while highlighting a many-body non-Hermitian skin effect that shifts localization. An experimental route in cold-atom systems is proposed, strengthening the relevance of these results for non-Hermitian quantum dynamics and potential sensing applications.

Abstract

Understanding the relationship between many-body localization and spectra in non-Hermitian many-body systems is crucial. In a one-dimensional clean, long-range interaction-induced non-Hermitian many-body localization system, we have discovered the coexistence of static and dynamic spectral real-complex phase transitions, along with many-body ergodic-localized phase transitions. The phase diagrams of these two types of transitions show similar non-monotonic boundary trends but do not overlap, highlighting properties distinct from conventional disorder-induced non-Hermitian many-body localization. We also propose a potential experimental realization of this model in cold-atom systems. Our findings provide valuable insights for further understanding the relationship between non-Hermitian many-body localization and non-Hermitian spectra in long-range interacting systems.

Figures (11)

• Figure 1: Schematic of findings. (a) and (b) illustrate phase diagrams of the spectral RC phase transition and ergodic-MBL phase transition, where the white dashed lines represent phase boundaries. Blue and red regions represent the real-spectrum phase (MBL phase) and complex-spectrum phase (ergodic phase), respectively. The gray area indicates regions where no phase transitions occur. In (c), we consider NN asymmetric hopping hard-core boson systems with long-range interactions, where exhibit asymmetric hopping $Je^{-g}$ and $Je^{g}$, the strength of long-range interaction $V$ and long-range interaction exponent $\alpha$.
• Figure 2: (a)-(d) Eigenenergy spectra for varying the strength of long-range interaction $V$ from $0$ to $80$ under the exponent of long-range interaction $\alpha=0.2, 1, 5, 20$ at $L=12$ under PBC. Insets show the cases for $V=0$ and $V=80$, respectively. The colorbar represents the strength of long-range interaction $V$.
• Figure 3: Spectral RC phase transition. (a)-(f) present results from Eq. (\ref{['eq:main']}) for the exponents $\alpha = 0.2, 0.5, 1, 3, 5, 20$ for lattice sizes $L=12, 14, 16$. Crossovers are observed in all cases, with the crossover shifting to larger $V$ values for $\alpha = 20$.
• Figure 4: Ergodicity-MBL phase transitions. (a)-(f) Illustrate the relationship between the system size-independence of average half-chain entanglement entropy $\bar{S}_{L/2}/L$ of selected right eigenstates within a central range of the real part of the spectrum (specifically those within $\pm 4\%$ of the middle), and the strength long-range interaction $V$ under different exponent $\alpha=0.2, 0.5, 1, 3, 5, 20$, across different system sizes $L=12, 14, 16$.
• Figure 5: The ratio of real to complex eigenspectrum $f_{\rm Im}$ and the system size-independence of average half-chain entanglement entropy $\bar{S}_{L/2}/L$ in the NN interaction limit and all-to-all limit. (a) and (b) show the NN interaction limit case, while (c) and (d) represent the all-to-all limit case. No phase transitions are observed in either scenario.