Topological invariants of complex energy plane in non-Hermitian systems

• URL: http://arxiv.org/abs/2308.05329v1
• Date: Thu, 10 Aug 2023 04:10:41 GMT
• Title: Topological invariants of complex energy plane in non-Hermitian systems
• Authors: Annan Fan and Shi-Dong Liang
• Abstract summary: Non-Hermitian systems exhibit rich novel physical properties and fundamental issues in condensed matter physics. We propose a generalized local-global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local-global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local-global correspondence and discuss the relationships between the local-global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.

Related papers

• Analytical topological invariants for 2D non-Hermitian phases using Morse theory [0.0]
  We analytically calculate the 2D Zak phase for a 2D non-Hermitian SSH-type Hamiltonian that supports a rich structure and edge currents.<n>Although the band structure breaks down at exceptional points, we show that a specific phase-based topological invariant remains well-defined.
  arXiv  Detail & Related papers  (2026-01-30T18:38:21Z)
• Semiclassical entanglement entropy for spin-field interaction [41.99844472131922]
  We study a general bipartite quantum system consisting of a spin interacting with a bosonic field.<n>Our goal is to develop a semiclassical framework to describe the entanglement dynamics between these two subsystems.
  arXiv  Detail & Related papers  (2026-01-22T14:07:56Z)
• Observation of non-Hermitian topology in cold Rydberg quantum gases [42.41909362660157]
  We experimentally demonstrate non-Hermitian spectra topology in a dissipative Rydberg atomic gas.<n>By increasing the interaction strength, the system evolves from Hermitian to non-Hermitian regime.<n>This work establishes cold Rydberg gases as a versatile platform for exploring the rich interplay between non-Hermitian topology, strong interactions, and dissipative quantum dynamics.
  arXiv  Detail & Related papers  (2025-09-30T13:44:43Z)
• 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-neighbour (between unit cells) Our invariant is invariant under unitary and similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• 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)
• 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)
• Tensor product random matrix theory [39.58317527488534]
  We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
  arXiv  Detail & Related papers  (2024-04-16T21:40:57Z)
• Zero modes of velocity field and topological invariant in quantum torus [0.0]
  We introduce the indexes of the velocity field flow based on the zero modes of the velocity field. We find that these zero modes play the role of effective topological charges or defects linking to Euler characteristic by the Poincar'e-Hopf theorem.
  arXiv  Detail & Related papers  (2024-03-13T04:23:16Z)
• Non-Hermitian topological mobility edges and transport in photonic quantum walks [0.0]
  Mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. The results are illustrated by considering non-Hermitian photonic quantum walks in synthetic mesh lattices.
  arXiv  Detail & Related papers  (2022-05-30T06:27:11Z)
• Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing [58.720142291102135]
  We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
  arXiv  Detail & Related papers  (2022-03-28T14:55:28Z)
• 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)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Detecting non-Bloch topological invariants in quantum dynamics [7.544412038291252]
  Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian systems. We report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks. Our work sheds new light on the experimental investigation of non-Hermitian topology.
  arXiv  Detail & Related papers  (2021-07-30T16:40:30Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• 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)
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence [14.4034719868008]
  We prepare an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. We show that a non-linear ramp may work more efficiently in approaching the topological state. We also compute the edge current in the time evolved state of the system under a semi-periodic boundary condition.
  arXiv  Detail & Related papers  (2020-05-04T13:14:26Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• 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.