Band topology of pseudo-Hermitian phases through tensor Berry
connections and quantum metric
- URL: http://arxiv.org/abs/2106.09648v2
- Date: Sat, 6 Nov 2021 10:08:33 GMT
- Title: Band topology of pseudo-Hermitian phases through tensor Berry
connections and quantum metric
- Authors: Yan-Qing Zhu, Wen Zheng, Shi-Liang Zhu, and Giandomenico Palumbo
- Abstract summary: 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.
- Score: 6.033106259681307
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Among non-Hermitian systems, pseudo-Hermitian phases represent a special
class of physical models characterized by real energy spectra and by the
absence of non-Hermitian skin effects. Here, we show that several
pseudo-Hermitian phases in two and three dimensions can be built by employing
$q$-deformed matrices, which are related to the representation of deformed
algebras. Through this algebraic approach we present and study the
pseudo-Hermitian version of well known Hermitian topological phases, raging
from two-dimensional Chern insulators and time-reversal-invariant topological
insulators to three-dimensional Weyl semimetals and chiral topological
insulators. We analyze their topological bulk states through non-Hermitian
generalizations of Abelian and non-Abelian tensor Berry connections and quantum
metric. Although our pseudo-Hermitian models and their Hermitian counterparts
share the same topological invariants, their band geometries are different. We
indeed show that some of our pseudo-Hermitian phases naturally support
nearly-flat topological bands, opening the route to the study of
pseudo-Hermitian strongly-interacting systems. Finally, we provide an
experimental protocol to realize our models and measure the full non-Hermitian
quantum geometric tensor in synthetic matter.
Related papers
- 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-Hermitian Topology in Hermitian Topological Matter [0.0]
We show that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology.
We also find the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators.
Our work uncovers a hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.
arXiv Detail & Related papers (2024-05-16T11:59:15Z) - Topological phases of many-body non-Hermitian systems [0.0]
Many-body fermionic non-Hermitian systems require two sets of topological invariants to describe the topology of energy bands and quantum states respectively.
We identify 10 symmetry classes -- determined by particle-hole, linearized time-reversal, and linearized chiral symmetries.
arXiv Detail & Related papers (2023-11-06T11:39:20Z) - Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides [0.0]
In symmetry-protected topological systems, symmetries are responsible for protecting surface states.
By engineering losses that break the symmetry protecting a topological Hermitian phase, we show that a new genuinely non-Hermitian symmetry emerges.
We classify the systems in terms of the (non-Hermitian) symmetries that are present and calculate the corresponding topological invariants.
arXiv Detail & Related papers (2023-04-12T10:05:02Z) - Hermitian Topologies originating from non-Hermitian braidings [0.0]
We show that the complex energy bands of non-Hermitian systems braid in momentum space even in one dimension.
We derive an elegant identity that equates the linking number between the knots of braiding non-Hermitian bands and the zero-energy loop.
We construct typical topological phases with non-Hermitian braidings, which can be readily realized by artificial crystals.
arXiv Detail & Related papers (2022-12-28T08:08:58Z) - Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
We introduce a class of quantum optical Hamiltonian characterized by three-body couplings.
We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
arXiv Detail & Related papers (2022-04-07T15:39:21Z) - Topological Anderson insulators with different bulk states in
quasiperiodic chains [1.6530012863603747]
We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations.
We show the presence of topological extended, intermediate, and localized phases due to the coexistence of independent topological and localization phase transitions.
arXiv Detail & Related papers (2022-01-04T05:32:43Z) - 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) - Towards a complete classification of non-chiral topological phases in 2D fermion systems [29.799668287091883]
We argue that all non-chiral fermionic topological phases in 2+1D are characterized by a set of tensors $(Nij_k,Fij_k,Fijm,alphabeta_kln,chidelta,n_i,d_i)$.
Several examples with q-type anyon excitations are discussed, including the Fermionic topological phase from Tambara-gami category for $mathbbZ_2N$.
arXiv Detail & Related papers (2021-12-12T03:00:54Z) - 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) - 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)
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.