Universal aspects of bulk density of states in non-Hermitian lattices

• URL: http://arxiv.org/abs/2608.14508v1
• Date: Fri, 14 Aug 2026 17:22:43 GMT
• Title: Universal aspects of bulk density of states in non-Hermitian lattices
• Abstract summary: We show that non-Hermitian systems lack a unique bulk DOS.<n>We identify the Brown measure as a canonical and convenient representative of the bulk DOS.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Hermitian lattice Hamiltonians generally exhibit strong boundary sensitivity, with periodic and open boundary conditions producing distinct density of states (DOS) in the complex-energy plane. This has led to the view that extended non-Hermitian systems lack a unique bulk DOS, with different prescriptions representing inequivalent bulk physics. Here, we show that this apparent ambiguity is largely illusory. For any finite-range tight-binding Hamiltonian, we establish a universal bulk structure: all DOS definitions arising as thermodynamic limits of finite systems share identical multipole moments and generate identical bulk dynamics at finite times and for observables measured far from boundaries. This universality is intimately tied to the thermodynamic Green's functions, which we show to be independent of the boundary condition for large enough complex frequencies. Among all equivalent descriptions, we identify the Brown measure - obtained via Hermitization and resolvent analysis - as a canonical and convenient representative of the bulk DOS, defined directly from the infinite-volume Hamiltonian. We further show that point-gap topology imposes additional universal constraints: boundary-dependent Green's functions are forced to coincide throughout topologically trivial point gaps. This, in particular, provides a systematic criterion, valid in arbitrary dimension, for determining where and how eigenvalues of different boundary truncations can accumulate in the complex plane, and precisely delineates the regime in which the DOS ambiguity retains physical significance.

Related papers

• Point-gap topology in amorphous non-Hermitian quantum systems [13.150867305443107]
  We introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit.<n>Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems.
  arXiv  Detail & Related papers  (2026-08-09T13:09:36Z)
• Resolution of Infrared Entanglement Divergences via the Extended Uncertainty Principle [0.0]
  We show that the IR divergence is intimately tied to the unbounded spatial delocalization of zero-modes.<n>In this work, we demonstrate that this infinite growth is naturally resolved by invoking the Extended Uncertainty Principle (EUP)<n>We extend this regularizing mechanism to many-body systems by evaluating the entanglement entropy and entanglement spectrum of a one-dimensional harmonic chain and a massless scalar field.
  arXiv  Detail & Related papers  (2026-07-31T13:48:43Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• The Large-Scale Structure of Entanglement in Quantum Many-body Systems [44.99833362998488]
  We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems.<n>In particular, we show that every gapped phase of matter, even the trivial one, in $Dgeq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement.
  arXiv  Detail & Related papers  (2025-03-05T19:01:05Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Exact universal bounds on quantum dynamics and fast scrambling [0.0]
  We show that the spectral form factor sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times. We use this result to constrain the scrambling of information in interacting many-body systems.
  arXiv  Detail & Related papers  (2022-12-28T18:47:20Z)
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems [0.0]
  The spectral and dynamical properties of dissipative quantum systems are investigated from a topological point of view. We find anomalous skin modes with exponential amplification even though the quantum system is purely dissipative.
  arXiv  Detail & Related papers  (2020-10-28T10:15:40Z)
• Entropy scaling law and the quantum marginal problem [0.0]
  Quantum many-body states that frequently appear in physics often obey an entropy scaling law. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. We derive a closed-form expression for the maximum entropy density compatible with those marginals.
  arXiv  Detail & Related papers  (2020-10-14T22:30:37Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.