Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level

• URL: http://arxiv.org/abs/2308.03548v2
• Date: Sat, 9 Dec 2023 12:33:36 GMT
• Title: Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Authors: Arkadiusz Bochniak and Gerardo Ortiz
• Abstract summary: We develop a hierarchical scheme that generates bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling factor. Most importantly, it reveals a fusion mechanism for quasielectrons and magnetoexcitons that generalizes ideas about particle fractionalization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Starting from Halperin multilayer systems we develop a hierarchical scheme that generates, bosonic and fermionic, single-layer quantum Hall states (or vacua) of arbitrary filling factor. Our scheme allows for the insertion of quasiparticle excitations with either Abelian or non-Abelian statistics and quantum numbers that depend on the nature of the original vacuum. Most importantly, it reveals a fusion mechanism for quasielectrons and magnetoexcitons that generalizes ideas about particle fractionalization introduced in A. Bochniak, Z. Nussinov, A. Seidel, and G. Ortiz, Commun. Phys. 5, 171 (2022) for the case of Laughlin fluids. In addition, in the second quantization representation, we uncover the inherent topological quantum order characterizing these vacua. In particular, we illustrate the methodology by constructing generalized composite (generalized Read) operators for the non-Abelian Pfaffian and Hafnian quantum fluid states.

Related papers

• Many-Body Quantum Geometric Dipole [0.0]
  Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. We demonstrate in this work that this property can be formulated in a generic way, which does not require wavefunctions expressed in terms of single particle-hole states. Our study demonstrates that the QGD is an intrinsic property of collective modes which is valid beyond approximations one might make for their wavefunctions.
  arXiv  Detail & Related papers  (2024-06-17T21:01:03Z)
• A Universal Kinematical Group for Quantum Mechanics [0.0]
  In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms.
  arXiv  Detail & Related papers  (2024-04-28T18:46:24Z)
• Realization of a fractional quantum Hall state with ultracold atoms [0.0]
  Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice.
  arXiv  Detail & Related papers  (2022-10-19T22:48:43Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Disorder-Assisted Assembly of Strongly Correlated Fluids of Light [0.08388591755871733]
  We construct low-entropy quantum fluids of light in a Bose Hubbard circuit. We first benchmark this lattice melting technique by building and characterizing arbitrary single-particle-in-a-box states. This work opens new possibilities for preparation of topological and otherwise exotic phases of synthetic matter.
  arXiv  Detail & Related papers  (2022-07-01T17:56:15Z)
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe [0.0]
  We identify several gapped phases near the first Mott lobe at strong interactions. They are connected by a particle-hole symmetry to a variety of quantum Hall states stabilized at low fillings. We characterize phases of both particle and hole type and identify signatures compatible with Laughlin, Moore-Read, and Bosonic Quantum Hall states.
  arXiv  Detail & Related papers  (2021-11-22T19:00:01Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• 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)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
  Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
  arXiv  Detail & Related papers  (2020-04-07T15:00:41Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.