Weyl-type topological phase transitions in fractional quantum Hall like systems

Abstract

We develop a method to characterize topological phase transitions for strongly correlated Hamiltonians defined on two-dimensional lattices based on the many-body Berry curvature. Our goal is to identify a class of quantum critical points between topologically nontrivial phases with fractionally quantized Hall (FQH) conductivity and topologically trivial gapped phases through the discontinuities of the many-body Berry curvature in the so-called flux Brillouin zone (fBZ), the latter being defined by imposing all possible twisted boundary conditions. For this purpose, we study the finite-size signatures of several quantum phase transitions between fractional Chern insulators and charge-ordered phases for two-dimensional lattices by evaluating the many-body Berry curvature numerically using exact diagonalization. We observe degeneracy points (nodes) of many-body energy levels at high-symmetry points in the fBZ, accompanied by diverging Berry curvature. We find a correspondence between the number and order of these nodal points, and the change of the topological invariants of the many-body ground states across the transition, in close analogy with Weyl nodes in non-interacting band structures. This motivates us to apply a scaling procedure, originally developed for non-interacting systems, for the Berry curvature at the nodal points. This procedure offers a useful tool for the classification of topological phase transitions in interacting systems harboring FQH-like topological order.

References in corpus (27)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Maximally localized Wannier functions: Theory and applications
• Topological quantum chemistry
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Scaling of geometric phases close to quantum phase transition in the XY chain
• Geometric phases and criticality in spin chain systems
• Zoology of Fractional Chern Insulators
• First order character and observable signatures of topological quantum phase transitions
• Hierarchy of fractional Chern insulators and competing compressible states
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Topological Phase Transitions for Interacting Finite Systems
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect
• Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons
• Fractional Chern insulators with strong interactions far exceeding bandgaps
• Scaling Theory of Topological Phase Transitions
• Combined topological and Landau order from strong correlations in Chern bands
• Scaling Theory of ${\mathbb{Z}}_2$ Topological Invariants
• Degeneracy of Many-body Quantum States in an Optical Lattice with a Uniform Magnetic Field

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