Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands

• URL: http://arxiv.org/abs/2407.12559v1
• Date: Wed, 17 Jul 2024 13:44:39 GMT
• Title: Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Authors: K. B. Yogendra, G. Baskaran, Tanmoy Das,
• Abstract summary: Fractional excitations offer vast potential for both fundamental physics and quantum technologies. Here, we investigate the evolution of low-energy Majorana dispersions across various crystalline phases of the pi-flux in the Kitaev spin model on a honeycomb lattice. We identify conditions under which this superexchange interaction acts as a Z2 gauge field, governing the tight-binding hopping of Majorana Wannier orbitals.
• Score: 0.19116784879310028
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fractional excitations offer vast potential for both fundamental physics and quantum technologies. However, their dynamics under the influence of gauge fields pose a significant challenge to conventional models. Here, we investigate the evolution of low-energy Majorana dispersions across various crystalline phases of the \pi-flux in the Kitaev spin model on a honeycomb lattice. We develop an effective tight-binding description for these low-energy Majorana fermions, introducing a gauge potential through a superexchange-like interaction that systematically eliminates the high-energy spectrum. We identify conditions under which this superexchange interaction acts as a Z2 gauge field, governing the tight-binding hopping of Majorana Wannier orbitals. Our study reveals an intriguing phase transition between two non-trivial topological phases characterized by gapless flat-band (extensive) degeneracy. To further explore flat band physics, we introduce a mean-field theory describing a gauge-invariant Majorana density-wave order within these bands. The resulting split Chern bands facilitate the partial filling of Chern bands, effectively leading to fractional Chern states. Our work, encompassing both the gauge-mediated tight-binding model and the mean-field theory, opens doors for future exploration of $U(1)$, $SU(N)$ gauge-mediated tight-binding approach to other fractional or entangled Wannier excitations.

Related papers

• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling [7.493142873994949]
  We propose a minimal braiding setup in a linear array of quantum dots consisting of two minimal Kitaev chains coupled through an ancillary, normal quantum dot. We find that the errors caused by either of these effects can be efficiently mitigated by optimal control of the ancillary quantum dot that mediates the exchange of the non-Abelian anyons.
  arXiv  Detail & Related papers  (2025-01-27T13:53:14Z)
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States [39.58317527488534]
  We investigate the impact of introducing a local cavity within the center of a topological chain. This cavity induces a scissor-like effect that bisects the chain, liberating Majorana zero modes (MZMs) within the bulk. By leveraging the symmetry properties of fermion modes within a two-site cavity, we propose a novel method for generating MZM-polariton Schr"odinger cat states.
  arXiv  Detail & Related papers  (2024-09-06T18:00:00Z)
• Emergent Majorana metal from a chiral spin liquid [50.56734933757366]
  We propose a novel mechanism to explain the emergence of an intermediate gapless spin liquid phase (IGP) in the antiferromagnetic Kitaev model. We show that the Majorana spectral function captures the dynamical spin and dimer correlations obtained by the infinite Projectedangled Pair States (iPEPS) an Entsatz.
  arXiv  Detail & Related papers  (2024-05-20T18:00:01Z)
• Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory [39.58317527488534]
  Superconductivity and charge density waves are observed in close vicinity in strongly correlated materials. We investigate the nature of such an intertwined state of matter stabilized in the phase diagram of the elementary $t$-$tprime$-$U$ Hubbard model. We provide conclusive evidence that the macroscopic wave functions of the superconducting fragments are well-described by soliton solutions of a Ginzburg-Landau equation.
  arXiv  Detail & Related papers  (2023-07-21T18:00:07Z)
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids [0.0]
  A common construction of $mathbbZ$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links. A common construction of $mathbbZ$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links.
  arXiv  Detail & Related papers  (2023-06-15T18:00:01Z)
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms [1.8749305679160366]
  Rydberg atom arrays offer promising platforms for quantum simulation of correlated quantum matter. This work proposes a novel stripe-lattice model with Raman superarray of Rydberg atoms to realize bosonic fractional quantum anomalous Hall phase.
  arXiv  Detail & Related papers  (2023-02-25T15:48:36Z)
• Tuning long-range fermion-mediated interactions in cold-atom quantum simulators [68.8204255655161]
  Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow to further control the range and shape of the mediated interactions.
  arXiv  Detail & Related papers  (2022-03-31T13:32:12Z)
• Probing Majorana Modes via Local Spin Dynamics [0.0]
  We study Majorana modes in a quantum spin chain with bond-dependent exchange interactions. Here, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model.
  arXiv  Detail & Related papers  (2021-12-30T12:40:53Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Bloch-Landau-Zener dynamics induced by a synthetic field in a photonic quantum walk [52.77024349608834]
  We realize a photonic quantum walk in the presence of a synthetic gauge field. We investigate intriguing system dynamics characterized by the interplay between Bloch oscillations and Landau-Zener transitions.
  arXiv  Detail & Related papers  (2020-11-11T16:35:41Z)

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.