Non-Abelian Hopf-Euler insulators

• URL: http://arxiv.org/abs/2405.17305v3
• Date: Tue, 20 Aug 2024 17:59:47 GMT
• Title: Non-Abelian Hopf-Euler insulators
• Authors: Wojciech J. Jankowski, Arthur S. Morris, Zory Davoyan, Adrien Bouhon, F. Nur Ünal, Robert-Jan Slager,
• Abstract summary: A class of non-Abelian topological insulators in three dimensions carry a single bulk Hopf index protected by insulator ($mathcalPT$) inversion symmetry. Such systems naturally realize nodal structures in the three-dimensional Brillou zonein, providing a physical manifestation of the linking number described by the Hopf invariant. Our findings pave the way for novel experimental realizations of real-space quantum-geometry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped ``flag'' phase, which displays a three-band multi-gap Pontryagin invariant. Unlike the previously reported $\mathcal{PT}$-symmetric four-band real Hopf insulator, which hosts a $\mathbb{Z} \oplus \mathbb{Z}$ invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum-geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms.

Related papers

• From orthogonal link to phase vortex in generalized dynamical Hopf insulators [5.111942603132791]
  We unravel the quenched two-dimensional (2D) two-band Chern insulators under a parallel quench protocol. We find that whether the dynamical Hopf invariant exists or not, the links in (2+1)D space always keep their standard shape even for topological initial states.
  arXiv  Detail & Related papers  (2023-09-04T04:03:46Z)
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index [0.0]
  We study naturally arising multi-gap linked nodal rings, topologically characterized by split-biquaternion charges. We analyze the edge states corresponding to this Pontryagin index as well as their subject to the gap-closing disorder.
  arXiv  Detail & Related papers  (2023-08-29T18:21:48Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• 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)
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators [5.6888061544906545]
  We present a near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. We focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional way.
  arXiv  Detail & Related papers  (2021-05-21T18:00:00Z)
• Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices [2.1532925122722744]
  Bogoliubov excitations of Bose-Einstein condensates in optical lattices may possess band topology in analogous to topological insulators in class AII of fermions. This work is a universal formalism to study all kinds of symmetry-protected topological bosonic Bogoliubov bands.
  arXiv  Detail & Related papers  (2020-10-09T03:15:28Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Topological Euler class as a dynamical observable in optical lattices [0.0]
  We show that the invariant $(xi)$ falls outside conventional symmetry-eigenvalue indicated phases. We theoretically demonstrate that quenching with non-trivial Euler Hamiltonian results in stable monopole-antimonopole pairs. Our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.
  arXiv  Detail & Related papers  (2020-05-06T18:00:03Z)
• 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.