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
- 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.