$q$th-root non-Hermitian Floquet topological insulators

• URL: http://arxiv.org/abs/2203.09838v3
• Date: Mon, 15 Aug 2022 02:54:41 GMT
• Title: $q$th-root non-Hermitian Floquet topological insulators
• Authors: Longwen Zhou, Raditya Weda Bomantara, and Shenlin Wu
• Abstract summary: We show the presence of multiple edge and corner modes at fractional quasienergies $pm(0,1,...2n)pi/2n$ and $pm(0,1,...,3n)pi/3n$. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $\pm(0,1,...2^{n})\pi/2^{n}$ and $\pm(0,1,...,3^{n})\pi/3^{n}$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

Related papers

• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Dynamical characterization of $Z_{2}$ Floquet topological phases via quantum quenches [4.927579219242575]
  We develop the first full and unified dynamical characterization theory for the $Z_2$ Floquet topological phases. By measuring the minimal information of Floquet bands via the stroboscopic time-averaged spin polarizations, we show that the topological spin texture patterns emerging on certain discrete momenta of Brillouin zone. Our work provides a highly feasible way to detect the $Z_2$ Floquet topology and completes the dynamical characterization for the full classes of Floquet topological phases.
  arXiv  Detail & Related papers  (2023-10-31T19:43:08Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Extracting higher central charge from a single wave function [0.19999259391104385]
  A quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond $c_-$ to gapping out the edge. We show that the higher central charge can be characterized by the expectation value of the textitpartial rotation operator acting on the wavefunction of the topologically ordered state. This allows us to extract the higher central charge from a single wavefunction, which can be evaluated on a quantum computer.
  arXiv  Detail & Related papers  (2023-03-08T19:00:02Z)
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies [14.084478426185266]
  We show how to define a quantized many-body charge polarization $vecmathscrP$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. We derive colored Hofstadter butterflies, corresponding to the quantized value of $vecmathscrP$, which further refine the colored butterflies from the Chern number and discrete shift.
  arXiv  Detail & Related papers  (2022-11-16T19:00:00Z)
• Ground state degeneracy on torus in a family of $\mathbb{Z}_N$ toric code [2.7286395031146062]
  Topologically ordered phases in $2+1$ dimensions are characterized by three mutually-related features. The most remarkable feature of the topologically ordered phases is that the ground state may be unique. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.
  arXiv  Detail & Related papers  (2022-11-01T06:34:53Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
  We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
  arXiv  Detail & Related papers  (2022-05-30T18:01:34Z)
• 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)
• Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions [0.0]
  We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two dimensions. According to our classification, there is a one-to-one between these Floquet phases and rational functions $pi(z)$. We also show that $tildepi(z)$ is directly related to the time-averaged $U(1)$ current that flows in a particular geometry.
  arXiv  Detail & Related papers  (2020-10-05T18:07:57Z)
• 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.