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Physical review. B, Condensed matter

Exactly soluble quantum spin models on a double layer: The net spin model

Hua Lin, J. L. Shen, H. Y. Shik

Published Nov 4, 2002• 24 citations
Publisher

Abstract

We study a set of exactly soluble spin models in one and two dimensions for any spin S. Its ground state, the excitation spectrum, and quantum phase transition points, as well as dimensional crossover are determined.
DOI
10.1103/physrevb.66.184402

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4. The Ground States of One and Two Dimensional Quantum Spin Systems with Spin Polarons

邦夫 石田

Bussei Kenkyu•Sep 20, 1989•0 citations
We study a set of exactly soluble spin models in one and two dimensions for any spin SSS. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
We study a set of exactly soluble spin models in one and two dimensions for any spin SSS. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
We study a set of exactly soluble spin models in one and two dimensions for any spin SSS. Its ground state, the excitation spectrum, quantum phase transition points, as well as dimensional crossover are determined.
We introduce a class of gapped three-dimensional models, dubbed "cage-net fracton models," which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility.Starting from layers of two-dimensional string-net models, whose spectrum includes non-Abelian anyons, we condense extended one-dimensional "flux strings" built out of pointlike excitations.Flux-string condensation generalizes the concept of anyon condensation familiar from conventional topological order and allows us to establish properties of the fracton-ordered (equivalently, flux-string-condensed) phase, such as its groundstate wave function and spectrum of excitations.Through the examples of doubled-Ising and SUð2Þ k cagenet models, we demonstrate the existence of strictly immobile Abelian fractons and of non-Abelian particles restricted to move only along one dimension.In the doubled-Ising cage-net model, we show that these restricted-mobility non-Abelian excitations are a fundamentally three-dimensional phenomenon, as they cannot be understood as bound states among two-dimensional non-Abelian anyons and Abelian particles.We further show that the ground-state wave function of such phases can be understood as a fluctuating network of extended objects-cages-and strings, which we dub a cage-net condensate.Besides having implications for topological quantum computation in three dimensions, our work may also point the way towards more general insights into quantum phases of matter with fracton order.