Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians

TL;DR

This paper develops a numerical approach using iDMRG and MPS to characterize topological order in fractional quantum Hall states from microscopic Hamiltonians, enabling calculation of key topological invariants.

Contribution

It introduces a method to compute topological properties directly from microscopic FQH Hamiltonians using infinite cylinder geometries and entanglement spectra.

Findings

Calculated quantum dimensions and topological spins from entanglement spectra.

Determined quasiparticle charges and chiral central charge.

Measured Hall viscosity and modular properties.

Abstract

We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density matrix renormalization group (iDMRG) method based on the matrix-product state (MPS) representation of FQH states on an infinite cylinder. To study localized quasiparticles of a chosen topological charge, we use pairs of degenerate ground states as boundary conditions for the iDMRG. We then show that the wave function obtained on the infinite cylinder geometry can be adapted to a torus of arbitrary modular parameter, which allows us to explicitly calculate the non-Abelian Berry connection associated with the modular T-transformation. As a result, the quantum dimensions, topological spins, quasiparticle charges, chiral central charge, and Hall viscosity of the phase can be obtained using data contained entirely in the entanglement spectrum of an infinite cylinder.