We investigate the interplay between parity-time-symmetry (PT-symmetry) breaking and localization transitions in non-Hermitian spin chains with an Aubry-André potential and competing Dzyaloshinskii-Moriya (DM) interactions. While prior studies (e.g., [S. Longhi, Phys. Rev. Lett. 122, 237601 (2019)0031-900710.1103/PhysRevLett.122.237601]) suggest a universal alignment of PT transitions and delocalization, our analysis of next-nearest-neighbor DM couplings reveals a critical deviation: the two phenomena decouple in certain parameter regimes, despite coinciding for nearest-neighbor interactions. Through eigenvalue analysis and inverse/normalized participation ratios (IPR/NPR), we identify three distinct phases: (i) extended states (weak potential), (ii) localized states (strong potential), and (iii) an intermediate hybrid phase unique to next-nearest-neighbor DM couplings. To unravel the dynamical fingerprints of these phases, we track the time-dependent density propagation, long-time survival probability, and phase-sensitive Loschmidt echo. The density evolution exhibits ballistic spreading in extended phases versus localized confinement, while the survival probability's decay rate, exponential in localized regimes versus algebraic in extended ones, serves as a clear phase discriminator. Notably, quenches between phases induce distinct dynamical signatures, with the Loschmidt echo sharply reflecting phase boundaries through its decay profile. These results establish dynamical metrics as indispensable tools for characterizing non-Hermitian phase transitions beyond spectral or localization measures.
We investigate the interplay between parity-time-symmetry (PT-symmetry) breaking and localization transitions in non-Hermitian spin chains with an Aubry-André potential and competing Dzyaloshinskii-Moriya (DM) interactions. While prior studies (e.g., [S. Longhi, Phys. Rev. Lett. 122, 237601 (2019)0031-900710.1103/PhysRevLett.122.237601]) suggest a universal alignment of PT transitions and delocalization, our analysis of next-nearest-neighbor DM couplings reveals a critical deviation: the two phenomena decouple in certain parameter regimes, despite coinciding for nearest-neighbor interactions. Through eigenvalue analysis and inverse/normalized participation ratios (IPR/NPR), we identify three distinct phases: (i) extended states (weak potential), (ii) localized states (strong potential), and (iii) an intermediate hybrid phase unique to next-nearest-neighbor DM couplings. To unravel the dynamical fingerprints of these phases, we track the time-dependent density propagation, long-time survival probability, and phase-sensitive Loschmidt echo. The density evolution exhibits ballistic spreading in extended phases versus localized confinement, while the survival probability's decay rate, exponential in localized regimes versus algebraic in extended ones, serves as a clear phase discriminator. Notably, quenches between phases induce distinct dynamical signatures, with the Loschmidt echo sharply reflecting phase boundaries through its decay profile. These results establish dynamical metrics as indispensable tools for characterizing non-Hermitian phase transitions beyond spectral or localization measures.
Localization-delocalization transition and PT-symmetry breaking via second-neighbor coupling in a Heisenberg spin chain
The exploration of non-Hermitian quantum systems, particularly those governed by parity-time ([Formula: see text])-symmetry, has revealed a rich landscape of unconventional phase transitions and localization phenomena. Spin chains with quasiperiodic potentials and competing Heisenberg interactions provide a versatile framework for probing these effects. In this study, we investigate the dynamical and spectral signatures of [Formula: see text]-symmetry breaking and localization-delocalization transitions in spin chains subjected to a non-Hermitian Aubry-André potential and tunable Heisenberg couplings across nearest ([Formula: see text]) and next-nearest neighbors ([Formula: see text]). Our analysis reveals that increasing [Formula: see text] monotonically shifts the critical point [Formula: see text], while [Formula: see text] induces a non-linear response, generating a distinct minimum in [Formula: see text]. Notably, [Formula: see text] leads to the emergence of partially imaginary eigenvalues beyond [Formula: see text], decoupling the onset of [Formula: see text]-symmetry breaking from the localization transition. Using inverse and normalized participation ratios, we identify three distinct phases: extended, localized, and an intermediate hybrid regime characterized by a mobility edge. To capture the dynamical fingerprints of these phases, we employ time-dependent density distribution, long-time survival probability [Formula: see text], analysis. Extended phases exhibit ballistic spreading and algebraic decay, while localized regimes show spatial confinement and exponential decay. These observables serve as robust indicators of non-Hermitian phase transitions, offering insights beyond static spectral measures. Overall, our findings underscore the critical role of dynamical metrics in characterizing phase structure in non-Hermitian spin systems. As interest in non-equilibrium quantum dynamics continues to grow, such models provide a compelling platform for understanding the interplay between [Formula: see text]-symmetry, localization, and quantum coherence in complex many-body systems.
One-dimensional non-Hermitian quasicrystals with parity and time-reversal (PT) symmetry can simultaneously exhibit localization-delocalization transition, topological phase transition, and PT-symmetry-breaking transition. This motivates this work to investigate how the absence of PT symmetry impacts topological metal-insulator transitions in non-Hermitian quasicrystals. We propose a non-Hermitian quasiperiodic model that generally does not preserve PT symmetry and demonstrate that, in most parameter regions, such a system supports triple phase transitions that encompass localization, topology, and degeneracy-breaking. The system may also exhibit a particular type of localization-delocalization transition analogous to the Hermitian case, namely, without activating topological phase transitions or degeneracy-breaking transitions. Our work extends the topological metal-insulator transitions previously studied in PT-symmetric systems to a more general class of non-Hermitian setting, and further reveals that non-Hermitian systems can host distinct types of localization behavior.
Non-Hermitian quantum mechanics with parity-time (PT) symmetry offers a powerful framework for exploring the complex interplay of dissipation and coherent interactions in open quantum systems. While PT-symmetry breaking has been studied in various physical systems, its observation on a quantum many-body level remains elusive. Here, we experimentally realize a non-Hermitian XY model in a strongly-interacting Rydberg-atom array. By measuring the Loschmidt Echo of a fully polarized state, we observe distinct dynamical signatures of a PT-symmetry-breaking phase transition. Dipole interactions are found to play a crucial role, not only determining the transition point but also triggering a non-Hermitian many-body blockade effect that protects the Loschmidt Echo from decay with a non-monotonic dependence on the system size. Our results reveal intricate interaction-induced effects on PT-symmetry breaking and open the door for exploring non-Hermitian many-body dynamics beyond single-particle and mean-field paradigms.
We investigate non-Hermitian quantum phase transitions driven by staggered imaginary Dzyaloshinskii--Moriya (DM) interactions in a transverse-field XY chain. By virtue of a staggered nonunitary transformation, we exactly diagonalize the Hamiltonian. For D<1, this procedure maps the non-Hermitian model onto a standard Hermitian XY chain, allowing analytical derivation of the full phase boundaries. The parameter line D=1 forms an exceptional boundary with coalesced quasiparticle eigenvalues and eigenvectors, while the entire D>1 regime falls into the RT-symmetry-broken phase containing two distinct z-ferromagnetic phases. We examine common quantum-information probes and show that conventional measures, such as entanglement entropy, quantum discord, and quantum coherence, fail to capture the RT symmetry-breaking transition. To address this deficiency, we propose a novel coherence measure QCmaxLR based on RT symmetry and complex-conjugate eigenpair correlations. Embedding intrinsic non-Hermitian information of left and right eigenstates, QCmaxLR reliably identifies the RT symmetry-breaking transition and accurately resolves all magnetic phase boundaries.
The critical phase of a non-Hermitian quasicrystal can support stronger transport than its surrounding delocalized phase. We demonstrate this anomalous behavior in the one-dimensional nonreciprocal Aubry-André-Harper model through a combined study of dynamical quantum phase transitions (DQPTs) and wavepacket diffusion. Using a parity-sorted energy-spectrum classification that directly encodes the generalized PT symmetry, we find that DQPTs in this system are energy-resolved, in contrast to the energy-independent DQPTs of Hermitian quasicrystals. The energy-resolved features are most pronounced when the initial and final Hamiltonians belong to different phases (localized or extended), and they are tied to the even-odd index structure of the spectrum, which we exploit to organize the quench-dynamical landscape. For wavepacket dynamics after a single-site quench, the diffusion exponent β, extracted from the long-time power-law scaling of the root-mean-square displacement σ(τ), partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic (β=1), the critical phase is normally diffusive (β=0.5), and the localized phase yields β→0. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous β=1 at criticality to the self-similar multifractal structure of the critical eigenstates, whose nodal positions are organized by the golden ratio. A finite-size scaling ansatz built on the wave-front propagation yields σ(τ)∝τ. The parity-resolved DQPTs and the β-phase diagram establish two complementary dynamical diagnostics of nonreciprocal quasicrystals, in which nonreciprocity promotes transport at the critical point and suppresses it in the delocalized phase.
We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility χ and the eigenstate fractal dimension d(1) [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent z, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of z=3.