Computational Study of the Spectral Behaviour of Different Isospectrally Patterned Lattices

• URL: http://arxiv.org/abs/2507.08351v2
• Date: Thu, 24 Jul 2025 07:44:27 GMT
• Title: Computational Study of the Spectral Behaviour of Different Isospectrally Patterned Lattices
• Authors: Peter Schmelcher,
• Abstract summary: lattice Hamiltonian of IPL consist of coupled cells which possess all the same set of eigenvalues.<n>We show that localized states appear in near-degenerate pairs and this near-degeneracy is lifted upon entering the delocalization regime.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We perform a computational spectral analysis of different isospectrally patterned lattices (IPL). Having been introduced very recently, the lattice Hamiltonian of IPL consist of coupled cells which possess all the same set of eigenvalues. The latter is achieved in a controllable manner by parametrizing the cells via the phases of the involved orthogonal (or unitary) transformations. This opens the doorway of systematically designing lattice Hamiltonians with unique properties by choosing correspondingly varying phases across the lattice. Here we focus on two-dimensional cells and explore symmetric as well as asymmetric IPL w.r.t. a given center. A tunable fraction of localized vs. delocalized eigenstates belonging to the three subdomains of the corresponding energy bands is demonstrated and analyzed with different measures of localization. In the asymmetric case the center of localization can be shifted arbitrarily by shifting the underlying phase grid. Introducing a complete phase revolution leads for low and high energies to two well-separated branches of localized states which finally merge with increasing energy into the branch of delocalized states. Remarkably, the localized states appear in near-degenerate pairs and this near-degeneracy is lifted upon entering the delocalization regime. A corresponding generalization to several phase revolutions is provided showing a characteristic nodal pattern among the near-degenerate eigenstates.

Related papers

• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [41.94295877935867]
  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)
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases [5.131854158904627]
  We study an analogous situation for three-dimensional fracton phases by means of tensor network states (isoTNS) with finite bond dimension.<n>We find a family of exact wavefunctions for which the symmetry fractionalization under an anti-unitary symmetry on both types of excitations is directly visible.<n>Based on the isoTNS description of the wavefunction, we determine a linear-depth quantum circuit to sequentially realize these states on a quantum processor.
  arXiv  Detail & Related papers  (2025-01-30T19:00:02Z)
• Isospectrally Patterned Lattices [0.0]
  We introduce and explore patterned lattices consisting of coupled isospectral cells that vary across the lattice.<n>The isospectrality of the cells is encapsulated in the phase that characterizes each cell and can be designed at will such that the lattice exhibits a certain phase gradient.
  arXiv  Detail & Related papers  (2024-06-26T15:28:58Z)
• Localization with non-Hermitian off-diagonal disorder [0.0]
  We discuss a non-Hermitian system governed by random nearest-neighbour tunnellings.<n>A physical situation of completely real eigenspectrum arises owing to the Hamiltonian's tridiagonal matrix structure.<n>The off-diagonal disorder leads the non-Hermitian system to a delocalization-localization crossover in finite systems.
  arXiv  Detail & Related papers  (2023-10-20T18:02:01Z)
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation [0.0]
  We study the phase diagram and anyon condensation transitions of a $mathbbZ$ topological order perturbed by Ising interactions in the Toric Code. The interplay between the global Ising symmetry and the lattice space group symmetries results in a non-trivial symmetry fractionalization class for the anyons. We provide numerical evidence for the occurrence of two symmetry breaking patterns predicted by the specific symmetry fractionalization class of the anyons in the explored phase diagram.
  arXiv  Detail & Related papers  (2022-04-07T18:00:00Z)
• Resonant energy scales and local observables in the many-body localised phase [0.0]
  We formulate a theory for resonances in the many-body localised phase of disordered quantum spin chains in terms of local observables. Key result is to show that there are universal correlations between the matrix elements of local observables and the many-body level spectrum.
  arXiv  Detail & Related papers  (2022-02-21T19:00:07Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators [68.8204255655161]
  We present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.
  arXiv  Detail & Related papers  (2021-02-18T16:19:52Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.