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      Exact ground states with deconfined gapless excitations for the 3 leg spin-1/2 tube

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          Abstract

          We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators - one on the triangles, and the other on the square plaquettes on the side of the tube - that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i) for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii) for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii) between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phase.

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          Most cited references11

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          Excitation Spectrum of a Dimerized Next-Neighbor Antiferromagnetic Chain

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            Magnetization Plateaux in N-Leg Spin Ladders

            In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ-chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of N weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number N of cylindrically coupled chains numerically. For N = 3 we explicitly observe a spin-gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit N to infinity.
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              Spin Driven Jahn-Teller Distortion in a Pyrochlore system

              The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, pyrochlore lattice, is investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin-singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ZnV\(_2\)O\(_4\) and MgV\(_2\)O\(_4\).
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                Author and article information

                Journal
                27 July 2011
                2012-01-06
                Article
                10.1103/PhysRevLett.108.017205
                1107.5501
                6b7a04a4-e658-4f6a-82fd-cf072b856354

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Phys. Rev. Lett. 108, 017205 (2012)
                5 pages, 5 figures, paper revised, references added
                cond-mat.str-el

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