Tensor network implementation of bulk entanglement spectrum

Journal Article · Mon Aug 25 00:00:00 EDT 2014 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.90.085137· OSTI ID:1505786

Hsieh, Timothy H. ^[1]; Fu, Liang ^[2]; Qi, Xiao -Liang ^[3]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
3. Stanford Univ., Stanford, CA (United States)

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. Here, 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.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
• Grant/Contract Number: SC0010526
• OSTI ID: 1505786
• Alternate ID(s): OSTI ID: 1180311
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 8 Vol. 90; ISSN 1098-0121; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY