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

TL;DR

This paper introduces a method to identify and classify topological phase transitions in strongly correlated two-dimensional lattice systems by analyzing the many-body Berry curvature and its discontinuities, revealing Weyl-like nodes.

Contribution

The authors develop a novel approach using many-body Berry curvature and scaling techniques to characterize topological phase transitions in fractional quantum Hall-like systems.

Findings

Identified degeneracy points with diverging Berry curvature at high-symmetry points.

Established a correspondence between nodal points and changes in topological invariants.

Applied a scaling procedure to classify topological phase transitions in interacting 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.