Solvable non-Hermitian skin effects and real-space exceptional points: Non-Hermitian generalized Bloch theorem

• URL: http://arxiv.org/abs/2302.13309v3
• Date: Sun, 30 Apr 2023 12:37:15 GMT
• Title: Solvable non-Hermitian skin effects and real-space exceptional points: Non-Hermitian generalized Bloch theorem
• Authors: Xintong Zhang, Xiaoxiao Song, Shubo Zhang, Tengfei Zhang, Yuanjie Liao, Xinyi Cai, Jing Li
• Abstract summary: Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects. We have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates. Our approach is widely applicable for one-dimensional non-Hermitian tight-binding models.
• Score: 3.572447654851124
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta's theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su-Schrieffer-Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

Related papers

• Geometric origin of self-intersection points in non-Hermitian energy spectra [1.985724084078542]
  Unlike Hermitian systems, non-Hermitian energy spectra can form closed loops in the complex energy plane. We rigorously demonstrate that these self-intersection points result from the intersection of the auxiliary generalized Brillouin zone and the Brillouin zone in one-band systems.
  arXiv  Detail & Related papers  (2025-02-07T08:42:34Z)
• 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. These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated. 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)
• Non-chiral non-Bloch invariants and topological phase diagram in non-unitary quantum dynamics without chiral symmetry [26.179241616332387]
  We identify the non-Bloch topological phase diagram of a one-dimensional (1D) non-Hermitian system without chiral symmetry. We find that such topological invariants can distinguish topologically distinct gapped phases. Our work provides a useful platform to study the interplay among topology, symmetries and the non-Hermiticity.
  arXiv  Detail & Related papers  (2024-07-26T03:29:30Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Locality and Exceptional Points in Pseudo-Hermitian Physics [0.0]
  Pseudo-Hermitian operators generalize the concept of Hermiticity. This thesis is devoted to the study of locality in quasi-Hermitian theory. Chiral symmetry and representation theory are used to derive large classes of pseudo-Hermitian operators.
  arXiv  Detail & Related papers  (2023-06-06T22:19:05Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Krylov complexity in quantum field theory, and beyond [44.99833362998488]
  We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
  arXiv  Detail & Related papers  (2022-12-29T19:00:00Z)
• Pontryagin-Optimal Control of a non-Hermitian Qubit [0.0]
  We study the control of a single non-Hermitian qubit. We show how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit conditioned on no emission.
  arXiv  Detail & Related papers  (2022-08-04T20:51:29Z)
• Non-Hermitian Topology and Exceptional-Point Geometries [15.538614667230366]
  Non-Hermitian theory is a theoretical framework that excels at describing open systems. Non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories.
  arXiv  Detail & Related papers  (2022-04-19T12:41:31Z)
• Exponential Tail Local Rademacher Complexity Risk Bounds Without the Bernstein Condition [30.401770841788718]
  The local Rademacher toolbox is one of the most successful general-purpose toolboxes. Applying the Bernstein theory to problems where optimal performance is only achievable via non-probable settings yields an exponential-tail excess risk. Our results apply to improper prediction regimes not covered by the toolbox.
  arXiv  Detail & Related papers  (2022-02-23T12:27:53Z)
• Hermitian zero modes protected by nonnormality: Application of pseudospectra [0.0]
  We develop a theory of zero modes with quantum anomaly for general Hermitian lattice systems. We relate exact zero modes and quasi-zero modes of a Hermitian system to spectra and pseudospectra of a non-Hermitian system. Our theory reveals the presence of nonnormality-protected zero modes, as well as the usefulness of the nonnormality and pseudospectra as tools for topological and/or non-Hermitian physics.
  arXiv  Detail & Related papers  (2020-05-04T17:58:52Z)

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.