Hsieh, T. (2014). Bulk Entanglement Spectrum: From Topological States to Quantum Criticality. Perimeter Institute. https://pirsa.org/14100075

MLA

Hsieh, Timothy. Bulk Entanglement Spectrum: From Topological States to Quantum Criticality. Perimeter Institute, Oct. 14, 2014, https://pirsa.org/14100075

BibTex

@misc{ pirsa_PIRSA:14100075,
doi = {10.48660/14100075},
url = {https://pirsa.org/14100075},
author = {Hsieh, Timothy},
keywords = {Condensed Matter},
language = {en},
title = {Bulk Entanglement Spectrum: From Topological States to Quantum Criticality},
publisher = {Perimeter Institute},
year = {2014},
month = {oct},
note = {PIRSA:14100075 see, \url{https://pirsa.org}}
}

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 (BES) 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. We also implement BES using tensor networks, derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase, and demonstrate that the AKLT wavefunction (and its generalizations) remarkably contains critical six-vertex (and in general eight-vertex) models within it.