Tensor network implementation of bulk entanglement spectrum
Name
PhysRevB.90.085137.pdf
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190.59 KB
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Author(s)
Fu, Liang
Qi, Xiao-Liang
Hsieh, Timothy Hwa-wei
Date Issued
August 2014
Journal
Physical Review B
Publisher
American Physical Society
Citation
Hsieh, Timothy H., Liang Fu, and Xiao-Liang Qi. “Tensor Network Implementation of Bulk Entanglement Spectrum.” Phys. Rev. B 90, no. 8 (August 2014). © 2014 American Physical Society
Version
Final published version
Abstract
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in T. Hsieh and L. Fu (arXiv:1305.1949). This involved computing the bulk entanglement spectrum (BES) of the ground state upon tracing out an extensive subsystem. This work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d + 1 dimensions, which can be studied using Monte Carlo or tensor renormalization-group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the Affleck-Kennedy-Lieb-Tasaki (AKLT) wave function (and its generalizations) remarkably contains critical six-vertex (and, in general, eight-vertex) models within it.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.90.085137
