Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface

• URL: http://arxiv.org/abs/2104.13314v4
• Date: Fri, 23 Jul 2021 16:34:02 GMT
• Title: Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
• Authors: Kazuki Ikeda, Shoto Aoki, Yoshiyuki Matsuki
• Abstract summary: We explore the hyperbolic band theory under a magnetic field for the first time. We construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood. We also show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann surface. Our methods and results can be confirmed experimentally by circuit quantum electrodynamics (cQED), which enables us to create novel materials in a hyperbolic space. To investigate the band structures, we construct directly the hyperbolic magnetic Bloch states and find that they form Dirac cones on a coordinate neighborhood, by which they can be regarded as a global quantum gravity solution detectable in a laboratory. Besides this is the first explicit example of a massless Dirac state on a higher genus surface. Moreover we show that the energy spectrum exhibits an unusual fractal structure refracting the negative curvature, when plotted as a function of a magnetic flux.

Related papers

• Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields [54.010858975226945]
  We study the dynamics of EVBs in magnetic fields using exact solutions of the relativistic paraxial equation in magnetic fields. We provide a unified description of different regimes under generalized Gouy rotation, linking the Gouy phase to EVB rotation angles. This work offers new insights into the dynamics of EVBs in magnetic fields and suggests practical applications in beam manipulation and beam optics of vortex particles.
  arXiv  Detail & Related papers  (2024-07-03T03:29:56Z)
• Matter relative to quantum hypersurfaces [44.99833362998488]
  We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
  arXiv  Detail & Related papers  (2023-08-24T16:39:00Z)
• Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory [58.720142291102135]
  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)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Topological Matter and Fractional Entangled Quantum Geometry through Light [0.0]
  We show that global topological properties are encoded from the poles of the surface allowing a correspondence between smooth fields, metric and quantum distance with the square of the topological number. We develop the theory, "quantum topometry" in space and time, and present applications on transport from a Newtonian approach.
  arXiv  Detail & Related papers  (2022-09-30T11:17:24Z)
• Toward Quantization of Inhomogeneous Field Theory [0.0]
  We show the classical equivalence between an inhomogeneous scalar field theory and a scalar field theory on curved spacetime background. We propose how to quantize a specific field theory with broken Poincar'e symmetry inspired by standard field theoretic approaches.
  arXiv  Detail & Related papers  (2022-06-27T11:53:59Z)
• Hyperbolic band theory through Higgs bundles [0.0]
  Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation. A corresponding hyperbolic band theory has emerged, extending 2-dimensional Euclidean band theory in a natural way to higher-genus configuration spaces. Higgs bundles enjoy natural interpretations in the context of band theory.
  arXiv  Detail & Related papers  (2022-01-30T00:25:38Z)
• Algebra of Hyperbolic Band Theory under Magnetic Field [0.0]
  We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface.
  arXiv  Detail & Related papers  (2021-07-22T11:30:36Z)
• Crystallography of Hyperbolic Lattices [0.0]
  We derive, for the first time, a list of example hyperbolic $p,q$ lattices and their hyperbolic Bravais lattices. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices.
  arXiv  Detail & Related papers  (2021-05-03T18:00:07Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• 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)

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.