Exact mobility rings in non-Hermitian quasiperiodically decorated Lieb lattices

• URL: http://arxiv.org/abs/2608.16719v1
• Date: Mon, 17 Aug 2026 15:35:21 GMT
• Title: Exact mobility rings in non-Hermitian quasiperiodically decorated Lieb lattices
• Abstract summary: The mobility ring (MR) is fundamental to understanding the Anderson transition in non-Hermitian (NH) disordered systems.<n>Here, we analytically derive the Lyapunov exponents and obtain exact expressions for the MRs.<n>We reveal distinct evolutionary behaviors of the MRs driven by the quasiperiodic potential strength.
• Score: 5.437499298223565
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The mobility ring (MR), a critical boundary in the complex energy plane separating extended and localized states, is fundamental to understanding the Anderson transition in non-Hermitian (NH) disordered systems. While MRs have been extensively studied in one-dimensional (1D) NH quasiperiodic models, rigorous analytical frameworks beyond 1D remain critically scarce. Here, we investigate a class of two-dimensional (2D) quasiperiodically decorated Lieb lattices (QDLLs) featuring complex incommensurate potentials selectively applied to the lattice vertices. By exactly mapping these 2D structures onto NH generalized Aubry-Andr{é}-Harper (AAH) models and leveraging extended-localized transition point, we analytically derive the Lyapunov exponents and obtain exact expressions for the MRs. These exact theoretical boundaries are strongly corroborated by numerical computations of wavefunction fractal dimensions and real-space probability distributions. Furthermore, we reveal distinct evolutionary behaviors of the MRs driven by the quasiperiodic potential strength: systems characterized by $κ=2$ possess a single MR, whereas systems with $κ=3$ undergo a dynamic sequential evolution from a single integrated ring into two independent rings. We hope that our exact results of MRs in 2D will benefit the study of Anderson localizations and MRs in high-dimensional NH systems.

Related papers

• Solvable relaxation in discrete unitary systems: Ruelle-Pollicott resonances and CMV matrices [0.0]
  Leading eigenvalues of the truncated propagator, known as Ruelle-Pollicott (RP) resonances, are an elegant way of addressing the dynamics of unitary many-body systems.<n>We study unitary propagators in their canonical form, known in the mathematical literature as the CMV matrices.
  arXiv  Detail & Related papers  (2026-08-28T17:52:00Z)
• A first-principles linear response theory for open quantum systems and its application to Orbach and direct magnetic relaxation in Ln-based coordination polymers [39.146761527401424]
  Single-Molecule Magnets (SMMs) exhibit slow magnetic relaxation as a result of axial magnetic anisotropy inhibiting spin-phonon transitions.<n>We numerically implement a first-principles linear-response theory for open quantum systems that provides access to the complex a.c. magnetic susceptibility.
  arXiv  Detail & Related papers  (2026-03-19T10:19:50Z)
• Riemannian Langevin Dynamics: Strong Convergence of Geometric Euler-Maruyama Scheme [51.56484100374058]
  Low-dimensional structure in real-world data plays an important role in the success of generative models.<n>We prove convergence theory of numerical schemes for manifold-valued differential equations.
  arXiv  Detail & Related papers  (2026-03-04T01:29:35Z)
• Plug-and-Play Diffusion Meets ADMM: Dual-Variable Coupling for Robust Medical Image Reconstruction [45.25461515976432]
  Plug-and-Play diffusion prior (DP) frameworks have emerged as a powerful paradigm for imaging reconstruction.<n>We present a novel approach to resolving bias-hallucination trade-off, achieving state-of-the-art gradients with significantly accelerated convergence.
  arXiv  Detail & Related papers  (2026-02-26T16:58:43Z)
• EMGauss: Continuous Slice-to-3D Reconstruction via Dynamic Gaussian Modeling in Volume Electron Microscopy [41.838228673736076]
  We present EMGauss, a general framework for 3D reconstruction from planar scanned 2D slices with applications in Volume electron microscopy.<n>Our key innovation is to reframe slice-to-3D reconstruction as a 3D dynamic scene rendering problem based on Gaussian splatting.<n>Compared with diffusion- and GAN-based reconstruction methods, EMGauss substantially improves quality, enables continuous slice synthesis, and eliminates the need for large-scale pretraining.
  arXiv  Detail & Related papers  (2025-12-07T06:39:57Z)
• Universal semiclassical dynamics in disordered two-dimensional systems [0.0]
  We analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/xi_W$, where in 2D the time-scale $xi_W$ follows a stretched-exponential dependence on disorder strength.
  arXiv  Detail & Related papers  (2024-09-19T17:59:00Z)
• Robust extended states in Anderson model on partially disordered random regular graphs [44.99833362998488]
  It is shown that the mobility edge in the spectrum survives in a certain range of parameters $(d,beta)$ at infinitely large uniformly distributed disorder. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Universal features of entanglement entropy in the honeycomb Hubbard model [44.99833362998488]
  This paper introduces a new method to compute the R'enyi entanglement entropy in auxiliary-field quantum Monte Carlo simulations. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions.
  arXiv  Detail & Related papers  (2022-11-08T15:52:16Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands [7.4705069914791045]
  The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. Here we propose a class of 2D-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of a (extended) Lieb lattice. By mapping these models to the 2D Aubry-Andr'e model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials.
  arXiv  Detail & Related papers  (2022-09-29T12:58:56Z)
• Evolution of entanglement entropy in strongly correlated bosons in an optical lattice [0.0]
  We investigate the time evolution of the second-order R'enyi entropy (RE) for bosons in a one-dimensional optical lattice. We show that the RE is proportional to the population of doublon-holon pairs that span the boundary of the subsystem.
  arXiv  Detail & Related papers  (2022-09-27T12:48:01Z)
• Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in a doped polyacetylene [1.8986796884429729]
  Spin-dependent charge transfer decay in an alkali atom doped polyacetylene is studied in terms of the complex spectral analysis. Nonhermitian effective Hamiltonian has been derived from the total system hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-29T08:30:25Z)

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.