Controlling energy spectra and skin effect via boundary conditions in non-Hermitian lattices

• URL: http://arxiv.org/abs/2602.16780v1
• Date: Wed, 18 Feb 2026 19:00:02 GMT
• Title: Controlling energy spectra and skin effect via boundary conditions in non-Hermitian lattices
• Authors: S Rahul, Pasquale Marra,
• Abstract summary: Non-Hermitian systems exhibit unique spectral properties, including the non-Hermitian skin effect and exceptional points.<n>We analyze the Hatano-Nelson model with generalized boundary conditions induced by complex hopping amplitudes at the boundary.<n> tuning the boundary hopping amplitudes precisely controls the non-Hermitian skin effect.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian systems exhibit unique spectral properties, including the non-Hermitian skin effect and exceptional points, often influenced by boundary conditions. The modulation of these phenomena by generalized boundary conditions remains unexplored and not understood. Here, we analyze the Hatano-Nelson model with generalized boundary conditions induced by complex hopping amplitudes at the boundary. Using similarity transformations, we determine the conditions yielding real energy spectra and skin effect, and identify the emergence of exceptional points where spectra transition from real to complex. We demonstrate that tuning the boundary hopping amplitudes precisely controls the non-Hermitian skin effect, i.e., the localization of eigenmodes at the lattice edges. These findings reveal the sensitivity of spectral and localization properties to boundary conditions, providing a framework for engineering quantum lattice models with tailored spectral and localization features, with potential applications in quantum devices.

Related papers

• Unveiling non-Hermitian band structures with non-Bloch supercells [23.45255537572689]
  Non-Hermitian systems exhibit complex band structures where both energy and momentum have imaginary parts.<n>We introduce a non-Bloch supercell framework designed to overcome this challenge by decoupling Bloch phase control from the imaginary part of momentum.
  arXiv  Detail & Related papers  (2025-10-23T03:18:23Z)
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [39.146761527401424]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• 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)
• Enantiosensitive positions of exceptional points in open chiral systems [39.58317527488534]
  We show that exceptional points can be enantiosenstive, enabling a new type of control over topological and chiral properties of non-Hermitian open chiral systems.<n>Our results combine high enantiosensitivity with topological robustness in chiral discrimination and separation, paving the way for new approaches in the control of non-Hermitian and chiral phenomena.
  arXiv  Detail & Related papers  (2025-02-26T09:20:08Z)
• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems.<n>These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated.<n>We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Real-space detection and manipulation of topological edge modes with ultracold atoms [56.34005280792013]
  We demonstrate an experimental protocol for realizing chiral edge modes in optical lattices. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes. We study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.
  arXiv  Detail & Related papers  (2023-04-04T17:36:30Z)
• Anomalous second-order skin modes in Floquet non-Hermitian systems [6.001217436402815]
  The non-Hermitian skin effect under open boundary conditions is widely believed to originate from the intrinsic spectral topology under periodic boundary conditions. We show that the Floquet Hamiltonian exhibits a second-order skin effect that is robust against perturbations and disorder under open boundary conditions.
  arXiv  Detail & Related papers  (2023-03-20T16:44:33Z)
• Boundary conditions for the quantum Hall effect [0.0]
  We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip. We find that the latter introduce a new kind of states with no classical analogues, and add a finer structure to the quantization pattern of the Hall conductivity. Our model also predicts the breakdown of the quantum Hall effect at high values of the applied electric field.
  arXiv  Detail & Related papers  (2022-09-17T12:37:40Z)
• Real spectra and phase transition of skin effect in nonreciprocal systems [0.0]
  We study the one-dimensional nonreciprocal lattices with real nearest neighboring hopping and find that the energy spectra under open boundary conditions can be entirely real or imaginary. We further investigate the spectral properties and the non-Hermitian skin effect in the one-dimensional mosaic lattices with real nonreciprocal hopping introduced at equally spaced sites.
  arXiv  Detail & Related papers  (2022-03-16T13:38:08Z)
• Non-Hermitian skin effect as an impurity problem [0.0]
  A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Here we devise a general procedure to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions.
  arXiv  Detail & Related papers  (2021-05-03T22:32:04Z)
• 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)

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.