Geometric and Topological Obstructions to Hermitianization in Quasi-Hermitian Quantum Systems

• URL: http://arxiv.org/abs/2605.05335v2
• Date: Sat, 09 May 2026 15:54:13 GMT
• Title: Geometric and Topological Obstructions to Hermitianization in Quasi-Hermitian Quantum Systems
• Abstract summary: Quasi-Hermitian quantum systems can be mapped to equivalent Hermitian systems via a similarity transformation.<n>We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies.<n>Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems.
• Score: 2.679171884680826
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist.

Related papers

• Observable Geometry for Effective Quantum Circuits [30.806273993716857]
  We study redundancy and effectiveness of Variational Quantum Circuits.<n>Considering unitary transformations acting on Hermitian observables, a stabilizer group decomposition is given.<n>We identify the Hermitian orbit with a quotient space of a symmetric space.
  arXiv  Detail & Related papers  (2026-07-22T14:21:00Z)
• Non-Hermitian topology driven by an identity term: An exactly solvable paradigm [11.093624836836929]
  We show that a momentum-dependent identity term actively deforms the generalized Brillouin zone under non-Hermitian skin pumping.<n>This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection.
  arXiv  Detail & Related papers  (2026-07-09T13:27:07Z)
• A Gauge-Covariant Geometric Framework for Non-Hermitian Quantum Systems [0.0]
  We develop a comprehensive, gauge-covariant geometric framework for non-Hermitian quantum systems.<n>We show that the non-Hermitian geometric curvature originates from the non-commutativity of the stretching components at the operator level.<n>We also examine physical realizations of this model, including the non-Hermitian Su--Schrieffer--Heeger (SSH) and Hatano--Nelson (HN)
  arXiv  Detail & Related papers  (2026-06-14T16:58:04Z)
• Continuum field theory of matchgate tensor network ensembles [36.94429692322632]
  We develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks.<n>As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions.<n>We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term.
  arXiv  Detail & Related papers  (2026-03-06T12:15:35Z)
• Dirac monopole magnets in non-Hermitian systems [10.48168525109442]
  We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions.<n>Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases.<n>These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems.
  arXiv  Detail & Related papers  (2025-08-21T02:47:07Z)
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions [0.0]
  We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems.<n>We show that non-biorthogonal quenches from non-Hermitian to Hermitian Hamiltonians under chiral symmetry exhibit emergent topological characteristics of DQPTs.<n>This work establishes fundamental geometric and topological principles governing quantum criticality in open systems, with implications for quantum sensing and many-body physics in dissipative environments.
  arXiv  Detail & Related papers  (2025-07-21T08:40:46Z)
• 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)
• Observation of non-Hermitian bulk-boundary correspondence in non-chiral non-unitary quantum dynamics of single photons [31.05848822220465]
  In non-Hermitian systems, preserved chiral symmetry is one of the key ingredients, which plays a pivotal role in determining non-Hermitian topology.<n>We theoretically predict and experimentally demonstrate the bulk-boundary correspondence of a one-dimensional (1D) non-Hermitian system with chiral symmetry breaking.
  arXiv  Detail & Related papers  (2025-04-07T09:43:43Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric [6.033106259681307]
  We show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric.
  arXiv  Detail & Related papers  (2021-06-17T16:51:13Z)

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.