Wei-Norman approach for non-Hermitian driven spin-$S$ systems and its application to defect freezing

• URL: http://arxiv.org/abs/2607.04075v1
• Date: Sun, 05 Jul 2026 01:56:32 GMT
• Title: Wei-Norman approach for non-Hermitian driven spin-$S$ systems and its application to defect freezing
• Abstract summary: We show that for a spin-$S$ subject to a general non-Hermitian time-dependent singularity elements of the evolution operator can be expressed in closed analytical forms.<n>As an application, we investigate a specific nonequilibrium non-Hermitian phenomenon known as defect freezing.
• Score: 5.266721048634643
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the theoretical study of nonequilibrium non-Hermitian systems, obtaining exact analytical solutions for their nonadiabatic dynamics is highly desirable yet often challenging. In this work, we identify a class of non-Hermitian quantum systems where this difficulty can be substantially reduced. Employing the Wei-Norman approach, we show that for a spin-$S$ subject to a general non-Hermitian time-dependent drive, the matrix elements of the evolution operator can be expressed in closed analytical forms (via Jacobi polynomials) in terms of the corresponding spin-$1/2$ model. This approach is straightforward and accessible to nonspecialists in Lie algebra. As an application, we investigate a specific nonequilibrium non-Hermitian phenomenon known as defect freezing, i.e., the existence of excitations in the adiabatic limit, in spin-$S$ extensions of the $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger model under linear quenches. We derive exact analytical expressions for the momentum-resolved excitation probabilities and the total excitation densities. Our results reveal that defect freezing occurs exclusively in momentum sectors that traverse the $\mathcal{PT}$-symmetry-broken region -- and thus pass through a pair of higher-order exceptional points (EPs) -- during the quench; notably, the excitation density exhibits a singularity at a critical value of the non-Hermiticity parameter. This work enriches the analytical toolkit for nonadiabatic dynamics in multi-level non-Hermitian systems and provides quantitative, testable predictions for defect freezing across higher-order EPs, possibly accessible on platforms such as electric circuit networks and photonic lattices.

Related papers

• Monitored free fermions under periodic driving [42.078441758883635]
  We investigate periodically driven free-fermionic systems subjected to monitoring of the local particle density.<n>We use the nonlinear sigma-model (NLSM) to explain the long-wavelength physics of the time-dependent Hamiltonian.<n>Our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems.
  arXiv  Detail & Related papers  (2026-08-22T08:10:12Z)
• Non-equilibrium thermodynamics of collapse models in the strongly non-Gaussian regime [0.0]
  We show that a dissipative Disi-Penrose (dDP) model induces complex, non-Gaussian phase-space dynamics.<n>We rigorously establish the thermodynamic consistency of this friction mechanism across both weakly and strongly non-Gaussian regimes.<n>Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state.
  arXiv  Detail & Related papers  (2026-06-04T15:04:07Z)
• Graph Symmetry Organizes Exceptional Dynamics in Open Quantum Systems [0.0]
  We introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator.<n>We further introduce a numerical diagnostic - the exceptional-point strength $mathcalE$ - based on eigenvector conditioning.<n>More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems.
  arXiv  Detail & Related papers  (2026-03-11T11:14:07Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves [39.92721695835137]
  A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve.<n>The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions.
  arXiv  Detail & Related papers  (2026-01-10T18:54:24Z)
• Identifiable learning of dissipative dynamics [25.409059056398124]
  We introduce I-OnsagerNet, a neural framework that learns dissipative dynamics directly from trajectories.<n>I-OnsagerNet extends the Onsager principle to guarantee that the learned potential is obtained from the stationary density.<n>Our approach enables us to calculate the entropy production and to quantify irreversibility, offering a principled way to detect and quantify deviations from equilibrium.
  arXiv  Detail & Related papers  (2025-10-28T07:57:14Z)
• Bound polariton states in the Dicke-Ising model [41.94295877935867]
  We present a study of hybrid light-matter excitations in cavity QED materials.<n>We derive the exact excitations of the system in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-06-17T18:00:01Z)
• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• Symmetry-resolved entanglement in critical non-Hermitian systems [0.0]
  We study the symmetry-resolved entanglement in the ground state of the non-Hermitian Su-Schrieffer-Heeger chain at the critical point. By combining bosonization techniques in the field theory and exact lattice numerical calculations, we analytically derive the charged moments of $rho_A$ and $|rho_A|$.
  arXiv  Detail & Related papers  (2023-03-09T13:14:26Z)
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems [1.2289361708127877]
  We study the dynamics of an exactly solvable non-Hermitian system, hosting both $mathcalPT$-symmetric and $mathcalPT$-broken modes. In contrast to Hermitian systems, our study reveals that PT -broken time evolution leads to defect freezing and hence the violation of adiabaticity.
  arXiv  Detail & Related papers  (2023-01-05T19:00:00Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Lindbladian dissipation of strongly-correlated quantum matter [0.9290757451344674]
  The Sachdev-Ye-Kitaev Lindbladian is a paradigmatic solvable model of dissipative many-body quantum chaos. Analytical progress is possible by developing a mean-field theory for the Liouvillian time evolution on the Keldysh contour.
  arXiv  Detail & Related papers  (2021-12-22T18:17:52Z)
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
  Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
  arXiv  Detail & Related papers  (2021-07-27T07:11:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.