Long range order in the ground state of two-dimensional antiferromagnets

Neves, E. Jordão; Perez, J. Fernando

doi:10.1016/0375-9601(86)90571-2

Cited by 139 publications

(83 citation statements)

References 14 publications

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“…This theorem does not give any indications for the T = 0 behavior of 2-dimensional magnets which are the central point of these lectures. (Rigorous proofs of order exist for spin 1 and larger [15,16,17]. )…”

Section: Ferromagnetic Sublattices "Quantum Fluctuations" and Dimer mentioning

confidence: 99%

Frustrated Quantum Magnets

Lhuillier

Misguich

2002

High Magnetic Fields

140

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A description of different phases of two dimensional magnetic insulators is given.The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Néel phases. Order by disorder selection is illustrated. All these phases break SU (2) symmetry and are gapless phases with ∆S z = 1 magnon excitations.Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful ∆S = 0, or1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.

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Section: Ferromagnetic Sublattices "Quantum Fluctuations" and Dimer mentioning

confidence: 99%

Frustrated Quantum Magnets

Lhuillier

Misguich

2002

High Magnetic Fields

140

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“…We make use of the stochastic series expansion quantum Monte Carlo (SSE-QMC) method based on the operator-loop algorithm [10], which allows us to faithfully monitor the T 0 physics by a -doubling approach [8] on L L lattices with L up to 36 sites. The results are typically averaged over at least 200 disorder realizations.In the clean limit p 0, and at zero magnetic field h 0, the SU(2) symmetric version of this model for D 0 is known exactly to show Néel LRO [11]. The presence of finite single-ion anisotropy (D > 0) reduces the symmetry to U(1), and antiferromagnetic ordering takes place in the xy plane.…”

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confidence: 94%

Mott Glass in Site-DilutedS=1Antiferromagnets with Single-Ion Anisotropy

Roscilde

Haas

2007

Phys. Rev. Lett.

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The interplay between site dilution and quantum fluctuations in S=1 Heisenberg antiferromagnets on the square lattice is investigated using quantum Monte Carlo simulations. Quantum fluctuations are tuned by a single-ion anisotropy D. In the clean limit, a sufficiently large D>Dc=5.65(2)J forces each spin into its mS=0 state, and thus destabilizes antiferromagnetic order. In the presence of site dilution, quantum fluctuations are found to destroy Néel order before the percolation threshold of the lattice is reached, if D exceeds a critical value D*=2.3(2)J. This mechanism opens up an extended quantum-disordered Mott-glass phase on the percolated lattice, characterized by a gapless spectrum and vanishing uniform susceptibility.

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“…The correlation length ξ S=1 ≈ 6 [18]. In 2D, we know from the rigorous result [15,16] that the ground state has an LRO, thus it is gapless and ξ S=1 = ∞. Hence, there should be a QPT at some critical J c y from a disordered to and ordered ground state.…”

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confidence: 99%

Mott transition in quasi-one-dimensional systems

Moukouri

Eidelstein

2011

Phys. Rev. B

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We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter ty from an insulator to a metal. Therefore, if ty is fixed in the metallic phase, increasing the interaction U leads to a metal-to-insulator transition at a finite critical U . This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting induced antiferromagnetic insulator for any U > 0.The metal-insulator transition (MIT), also called the Mott transition [1], is certainly one of the most difficult challenge facing condensed matter theorists. Hubbard [2], in a pioneering work, introduced a simple one-band Hamiltonian which has only two parameters, t for the kinetic energy of the electrons and U for the local electronelectron interactions. This model is at half-filling the model of reference for the MIT. In D = 1, Lieb and Wu [3] obtained an exact solution by using the Bethe ansatz. The ground state is an insulator for any U/W > 0, where W is the band width. Thus, the MIT occurs at the critical value (U/W ) c = 0. In infinite dimensions, the dynamical mean-field theory (DMFT) [4,5] predicts a critical point at (U/W ) c ≈ 1.The discovery of layered materials, where the motion of electrons driving the low energy physics is mostly confined in the layers, has raised great interest into the twodimensional (2D) Hubbard model. The physics at large U/W > ∼ 1 is now understood, the charge excitations are gapped, the spin excitation are described by the Heisenberg Hamiltonian which has long-range order (LRO) at T = 0. But for U/W < ∼ 1, the physics is still unclear. Our current knowledge about the weak-coupling regime is mostly drawn from the Hartree-Fock approximation and from quantum Monte Carlo (QMC) simulations [6,7]. The QMC results agree qualitatively with the HartreeFock prediction that the ground state is a Slater insulator for any U/W > 0. However, in most recent studies such as in Ref. [7], even though considerable progress has been achieved in reaching larger systems, in the weak U regime where the eventual gap is small, reliable extrapolations of the QMC data remain difficult to achieve. It would thus be preferable to apply finite size scaling for data analysis instead of relying on extrapolations.More recently, extensions of the DMFT which include non-local fluctuations, the dynamical cluster approximation (DCA) [8] or the cellular DMFT [9,10], have been applied to the 2D Hubbard model. The focus in these studies have mostly been to discuss the nature of the MIT within the paramagnetic solution of the DMFT equations. A systematic comparison of the possible ordered or disordered ground states as function of the cluster sizes is still lacking. Therefore, the issue as to whether or not quantum fluctuations destroy the Hartree-Fock solution in the half-filled 2D Hubbard model in the small U regime remains open.In this letter, we show that insight into this problem...

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Long range order in the ground state of two-dimensional antiferromagnets

Cited by 139 publications

References 14 publications

Frustrated Quantum Magnets

Frustrated Quantum Magnets

Mott Glass in Site-DilutedS=1Antiferromagnets with Single-Ion Anisotropy

Mott transition in quasi-one-dimensional systems

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