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Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
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An action-angle representation of spin variables was used to relate the large-S Heisenberg antiferromagnet to the O(3) nonlinear sigma model quantum field theory, with precise equivalence for integral S as discussed by the authors.About:
This article is published in Physics Letters A.The article was published on 1983-02-14. It has received 1855 citations till now. The article focuses on the topics: Sigma model & AKLT model.read more
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Confinement-deconfinement crossover in the lattice C P N − 1 model
Toshiaki Fujimori,Etsuko Itou,Etsuko Itou,Etsuko Itou,Tatsuhiro Misumi,Tatsuhiro Misumi,Muneto Nitta,Norisuke Sakai +7 more
TL;DR: In this article, a lattice Monte Carlo simulation of the sigma model at finite temperature is studied using the σ-Sigma model with small and large circumferences, respectively, where the ratio of the circumference ratio is taken to be sufficiently large to approximate the model.
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First-Principles Simulations of 1 +1 D Quantum Field Theories at θ =π and Spin Chains
TL;DR: In this paper, a lattice study of a 2-flavor U(1) gauge-Higgs model with a topological term at θ =π was presented, and the model was shown to be in the spin-chain universality class.
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A New Phase of the S=1 Bilinear-Biquadratic Chain: -a Trimerized State-
Kiyohide Nomura,Satoshi Takada +1 more
TL;DR: In this article, the S = 1 bilinear-biquadratic model was investigated and it was found that the ground state is extremely degenerate at the pure biquadraatic ferromagnetic point.
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AKLT models on decorated square lattices are gapped
Nicholas Pomata,Tzu-Chieh Wei +1 more
TL;DR: The existence of the nonzero spectral gap of the original two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) models has remained unproven for more than three decades as discussed by the authors.
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Effects of randomness in gapped antiferromagnetic quantum spin chains
TL;DR: In this paper, the effects of bond randomness on spin chains with excitation gaps were studied for the pure case, and they showed that systems with enforced topological structure like the spin 1/2 chain with enforced dimerization and spin 1 chain in the Haldane gapped phase appear very stable against randomness.
References
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Zur Theorie der Metalle
TL;DR: In this article, a Methode angegeben, um die Eigenfunktionen nullter and Eigenwerte erster Naherung (im Sinne des Approximationsverfahrens von London and Heitler) fur ein „eindimensionales Metall“ zu berechnen, bestehend aus einer linearen Kette von sehr vielen Atomen, von denen jedes auser abgeschlossenen Schalen eins-Elektron with Spin besitz
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On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain
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Integrable Hamiltonian systems and interactions through quadratic constraints
TL;DR: In this article, the relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems.
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Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields
TL;DR: In this paper, it is shown that due to interaction the regime of the asymmptotic freedom arises and the continuation to higher dimensions and the applications of the result are briefly discussed.
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What is the spin of a spin wave
L. D. Faddeev,L.A. Takhtajan +1 more
TL;DR: In this paper, it was shown that the spin of a spin wave in the Heisenberg antiferromagnetic chain of spins 1 2 is equal to 1 2 rather than 1 as is generally considered to be true.