Title: Tensor network implementation of bulk entanglement spectrum

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. 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)more » models within it.« less

Authors:

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

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+ Show Author Affiliations

1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2. Stanford Univ., Stanford, CA (United States)

Publication Date:

Mon Aug 25 00:00:00 EDT 2014

Research Org.:

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

OSTI Identifier:

1505786

Alternate Identifier(s):

OSTI ID: 1180311

Grant/Contract Number:  

SC0010526

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:

Journal Volume: 90; Journal Issue: 8; Journal ID: ISSN 1098-0121

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY