ZN Berry Phases in Symmetry Protected Topological Phases

2017/09/05 by Toshikaze Kariyado, Takahiro Morimoto, Yasuhiro Hatsugai · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Berry #Berry connection and curvature #Brillouin zone #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Geometric phase #Mathematical physics #Mathematics #Phase (matter) #Physics #Quantization (signal processing) #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.120.247202

published as Phys. Rev. Lett. 120, 247202 (2018)

arxiv created 2017/09/05 · openalex created_date 2017/09/15 · openalex publication_date 2018/06/15 · arxiv updated 2018/06/20 · openalex updated_date 2026/08/06

Abstract

We show that the Z_N Berry phase (Berry phase quantized into 2π/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small system size. The Z_N Berry phase is defined in a N-1-dimensional parameter space of local gauge twists, which we call the "synthetic Brillouin zone," and an appropriate choice of an integration path consistent with the symmetry of the system ensures exact quantization of the Berry phase. We demonstrate the usefulness of the Z_N Berry phase by studying two 1D models of bosons, SU(3) and SU(4) Affleck-Kennedy-Lieb-Tasaki models, where topological phase transitions are captured by Z₃ and Z₄ Berry phases, respectively. We find that the exact quantization of the Z_N Berry phase at the topological transitions arises from a gapless band structure (e.g., Dirac cones or nodal lines) in the synthetic Brillouin zone.

Citations

• Detection of symmetry-protected topological phases in one dimension
• Degeneracy and consistency condition for Berry phases: Gap closing under a local gauge twist
• Periodic table for topological insulators and superconductors
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Spin many-body phases in standard and topological waveguide QED simulators
• Observation of symmetry-protected zero modes in topolectrical circuits