Abstract By dealing with an elastic medium with a disclination, we search for the influence of the disclination topology on a geometric quantum phase yielded by the interaction of a nonuniform magnetic field with the permanent electric dipole moment of a neutral particle. This magnetic field is produced by a nonuniform electric current density. Further, we explore the non-Abelian nature of the geometric quantum phase in search of quantum holonomies for this neutral particle system and discuss a possible application to the geometric quantum computation.Abstract By dealing with an elastic medium with a disclination, we search for the influence of the disclination topology on a geometric quantum phase yielded by the interaction of a nonuniform magnetic field with the permanent electric dipole moment of a neutral particle. This magnetic field is produced by a nonuniform electric current density. Further, we explore the non-Abelian nature of the geometric quantum phase in search of quantum holonomies for this neutral particle system and discuss a possible application to the geometric quantum computation.

Quantum Information ProcessingJun 20, 20260 citations

A unified theory of quantum holonomies

Atushi Tanaka, Taksu Cheon

arXiv:0902.2878Annals of PhysicsMar 26, 20098 citations

Crystalline responses for rotation-invariant higher-order topological insulators

Julian May-Mann, Taylor L. Hughes

Two-dimensional higher-order topological insulators can display a number of exotic phenomena, such as half-integer charges localized at both corners and disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with ${C}_{4}$ rotation symmetry, and present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners). We extend this analysis to interacting systems, and predict the response of fractional quadrupole insulators, which exhibit charge $e/2(2k+1)$ bound to corners and disclinations.Two-dimensional higher-order topological insulators can display a number of exotic phenomena, such as half-integer charges localized at both corners and disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with ${C}_{4}$ rotation symmetry, and present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners). We extend this analysis to interacting systems, and predict the response of fractional quadrupole insulators, which exhibit charge $e/2(2k+1)$ bound to corners and disclinations.

arXiv:2108.00008Physical review. B./Physical review. BDec 28, 202220 citations

{C}_{4}

rotation symmetry, and present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners). We extend this analysis to interacting systems, and predict the response of fractional quadrupole insulators, which exhibit charge

e/2(2k+1)

bound to corners and disclinations.