Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State

TL;DR

This paper shows that the ground state of a topological phase contains critical information about its transition to a trivial phase, revealed through a novel bulk entanglement spectrum analysis.

Contribution

It introduces a method to detect topological phase transitions from a single wavefunction by analyzing the bulk entanglement spectrum with a specific partition.

Findings

Bulk entanglement spectrum mimics excitation spectrum of a bulk Hamiltonian.

Method applies to integer quantum Hall states.

Reveals criticality within topological states without tuning Hamiltonian parameters.

Abstract

A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum has a low-lying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to probe a topological phase transition from a single wavefunction by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between topological phase transition and entanglement criticality is rigorously established for integer quantum Hall states.