U(1)×U(1)symmetry-protected topological order in Gutzwiller wave functions

2014/08/31 by Zheng-Xin Liu, Jia‐Wei Mei, Jia-Wei Mei +2 · 38 citations
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Lattice (music) #Mathematics #Order (exchange) #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #Wave function #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.90.235146

published in Physical Review B 90(23) (American Physical Society) · 11 pages, 9 figures

arxiv created 2014/12/24 · openalex publication_date 2014/12/24 · arxiv updated 2014/12/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Gutzwiller projection is a way to construct many-body wave functions that could carry topological order or symmetry-protected topological (SPT) order. However, an important issue is to determine whether or not a given Gutzwiller-projected wave function (GWF) carries a nontrivial SPT order, and which SPT order is carried by the wave function. In this paper, we numerically study the SPT order in a spin S=1 GWF on the kagome lattice. Using the standard Monte Carlo method, we directly confirm that the GWF has (1) gapped bulk with short-range correlations, (2) a trivial topological order via a nondegenerate ground state, and zero topological entanglement entropy, (3) a nontrivial U(1)\ifmmode×\else\texttimes\fiU(1) SPT order via the Hall conductances of the protecting U(1)\ifmmode×\else\texttimes\fiU(1) symmetry, and (4) a symmetry-protected gapless boundary. This represents numerical evidence of continuous symmetry-protected topological order in two-dimensional bosonic lattice systems.

Citations

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Cited by

• Fractional S-duality, classification of fractional topological insulators, and surface topological order