Plateau transitions of spin pump and bulk-edge correspondence

Abstract

Sequential plateau transitions of quantum spin chains ($S$=1,3/2,2 and 3) are demonstrated by a spin pump using dimerization and staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as a time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With open boundary condition, discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk edge correspondence. It requires extra level crossings in the pump as a super-selection rule that is consistent with the Valence Bond Solid (VBS) picture.

11 pages, 6 figures

References in corpus (9)

• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Implementation of Spin Hamiltonians in Optical Lattices
• Spin pumping and measurement of spin currents in optical superlattices
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Designing spin-1 lattice models using polar molecules
• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist
• Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice

Cited by in corpus (5)

• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle