Testing the robustness of topological quantities evaluated from the modular Hamiltonian for a given wavefunction

TL;DR

This paper demonstrates that modular Hamiltonian-based methods can reliably extract topological invariants from lattice models of fractional quantum Hall states, with convergence depending on system size and correlation length.

Contribution

It applies modular Hamiltonian techniques to fractional quantum Hall states, showing their effectiveness and limitations in extracting topological quantities from lattice models.

Findings

Topological quantum numbers converge to expected values in large systems.

Convergence slows as the correlation length increases.

Reliable extraction requires sufficiently large system sizes.

Abstract

Topologically ordered states are characterized by topological quantities like the Hall conductance, topological entanglement entropy, and chiral central charge. Techniques based on the modular Hamiltonian have recently been developed to extract these quantities from a wavefunction. Here, we consider a lattice model of fractional quantum Hall states, a prototypical example of topologically ordered systems, and extract their topological content using the modular Hamiltonian-based methods. We consider the bosonic Laughlin and Moore-Read states and show that the extracted topological quantum numbers converge to their expected results. As expected, the convergence is slower when the correlation length of the state is longer. Generally, our results show that a reliable extraction of topological content through modular methods requires the usage of large systems