Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains

Nijs, Marcel den; Rommelse, Koos

doi:10.1103/physrevb.40.4709

Cited by 827 publications

(256 citation statements)

References 43 publications

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“…The unique ground state of H All the above facts were proved in [3], see also [5,9,11,15,17,19,24] for various refinements.…”

Section: Proof Of Theoremmentioning

confidence: 79%

Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

Yarotsky

2005

Commun. Math. Phys.

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Abstract. We consider ground states in relatively bounded quantum perturbations of classical lattice models. We prove general results about such perturbations (existence of the spectral gap, exponential decay of truncated correlations, analyticity of the ground state), and also prove that in particular the AKLT model belongs to this class if viewed at large enough scale. This immediately implies a general perturbation theory about this model.

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“…The unique ground state of H All the above facts were proved in [3], see also [5,9,11,15,17,19,24] for various refinements.…”

Section: Proof Of Theoremmentioning

confidence: 79%

Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

Yarotsky

2005

Commun. Math. Phys.

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“…The antiferromagnetic isotropic spin-1 model introduced by Affleck, Kennedy, Lieb and Tasaki (AKLT model) [3], whose ground state can be exactly calculated, has been a useful toy model to validate Haldane's prediction of the massive behavior for integer spin chains. Moreover, it lead to a deeper understanding for integer spin chains such as the discovery of the special type of long-range order [4,5]. The AKLT model has been generalized to higher-spin models, anisotropic models, etc [6,7,8,9,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Spin-spin correlation functions of the q-valence-bond-solid state of an integer spin model

Arita

Motegi

2011

Journal of Mathematical Physics

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We consider the valence-bond-solid ground state of the q-deformed higher-spin AKLT model (q-VBS state) with q real. We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of the q-VBS state. We compute the longitudinal and transverse spinspin correlation functions, and determine the correlation amplitudes and correlation lengths.

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“…35͒ of an isolated Haldane chain. 36,37 Starting from the Haldane chain limit ͑J 1x = J 2 =0͒ it has been predicted by the Monte Carlo simulations 38 as well as analytically 39 that an infinitesimal coupling J 1x leads to the destruction of the topological string order 40 of the Haldane chain. However, due to the protection by the finite energy gap of the spin-1 Haldane chain all other ground-state properties as well as the thermodynamics are only minimally affected by a small interchain coupling J 1x and a finite, albeit small [41][42][43][44] coupling is necessary to establish magnetic longrange order.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the frustrated spatially-anisotropicS=1antiferromagnet on a square lattice

et al. 2009

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We study the S = 1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings J 1x and J 1y frustrated by a next-nearest-neighbor coupling J 2 numerically using the density-matrix renormalization-group ͑DMRG͒ method and analytically employing the Schwinger-Boson mean-field theory ͑SBMFT͒. Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the Néel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuationinduced first-order transition between the Néel state and a stripe antiferromagnet for 1 / 3 Յ J 1x / J 1y Յ 1 and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum-disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic J 1 -J 2 model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for S = 1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.

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Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains

Cited by 827 publications

References 43 publications

Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

Ground States in Relatively Bounded Quantum Perturbations of Classical Lattice Systems

Spin-spin correlation functions of the q-valence-bond-solid state of an integer spin model

Phase diagram of the frustrated spatially-anisotropicS=1antiferromagnet on a square lattice

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