[Prof. Gil Young Cho] Many-Body Invariants for Chern and Chiral Hinge …

Caption: (a) Classification of phases of Chern insulator and (b) Hinge insulator based on their many-body invariants. (c) Many-body invariants of Chern insulator and (d) Hinge insulator can be computed from the slope of the line connecting two points, which correspond to two ground states.

[Prof. Gil Young Cho] Many-Body Invariants for Chern and Chiral Hinge Insulators

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​We construct new many-body invariants for 2D Chern and 3D chiral hinge insulators characterizing quantized pumping of bulk dipole and quadrupole moments. The many-body invariants are written entirely in terms of many-body ground state wave functions on a torus geometry with twisted boundary conditions and a set of unitary operators. We present a number of supporting arguments for the invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. Therefore, the invariants explicitly encircle several different pillars of theoretical descriptions of topological phases. Furthermore, our many-body invariants are written in forms which can be directly
employed in various numerics including the exact diagonalization and the density-matrix renormalization group simulations. We finally confirm our invariants by numerical computations including an infinite density-matrix renormalization group on quasi-one-dimensional systems. 

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