Finite-size effects in Heisenberg antiferromagnets

Neuberger, Herbert; Ziman, Timothy

doi:10.1103/physrevb.39.2608

Cited by 200 publications

(208 citation statements)

References 13 publications

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“…The description of the low-energy magnon physics by an effective theory was pioneered by Chakravarty, Halperin, and Nelson in [10]. In analogy to chiral perturbation theory for the pseudo-Goldstone pions in QCD, a systematic low-energy effective field theory for magnons was developed in [11,12,13,14]. The staggered magnetization of an antiferromagnet can be described by a unit-vector field e(x) in the coset space…”

Section: Low-energy Effective Theory For Magnonsmentioning

confidence: 99%

“…The physics of the undoped systems is quantitatively described by magnon chiral perturbation theory [10,11,12,13,14], while the interactions of magnons and holes are described by a low-energy effective theory for hole-doped antiferromagnets [15,16]. Predictions of the effective theory only depend on a small number of low-energy constants which can be determined from either experiments or Monte Carlo data.…”

Section: Introductionmentioning

confidence: 99%

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Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

et al. 2008

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Inspired by the lattice structure of the unhydrated variant of the superconducting material NaxCoO2·yH2O at x = 1 3 , we study the t-J model on a honeycomb lattice by using an efficient loop-cluster algorithm. The low-energy physics of the undoped system and of the single hole sector is described by a systematic low-energy effective field theory. The staggered magnetization per spin f Ms = 0.2688(3), the spin stiffness ρs = 0.102(2)J, the spin wave velocity c = 1.297(16)Ja, and the kinetic mass M ′ of a hole are obtained by fitting the numerical Monte Carlo data to the effective theory predictions.

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Section: Low-energy Effective Theory For Magnonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

et al. 2008

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“…Such scaling equations are explained carefully in the paper by Hasenfratz and Niedermayer [18], and earlier papers on this matter [19,20,21] are cited therein. Oitmaa et al [2] used both series expansions and spin wave methods on the S = 1/2 Heisenberg antiferromagnet on the simple cubic and bcc lattices to obtain estimates of the first term and the second term of equation (7).…”

Section: Generation Of Finite Ferromagnetic Bcc Latticesmentioning

confidence: 99%

“…Now we turn to the magnetization. Oitmaa et al [2], following Neuberger and Ziman [20], determined by effective Lagrangian theory that the second term in the finite lattice scaling equation for the staggered magnetization is proportional to L d−1 . Thus for the Heisenberg antiferromagnet in three dimensions the finite lattice scaling equation for the staggered magnetization is…”

Section: Generation Of Finite Ferromagnetic Bcc Latticesmentioning

confidence: 99%

“…It is also known that A s 6 does increase substantially as s increases, and our Table 2 shows the accelerating increase of A s 6 from s = 0 to s = 3/2. According to Oitmaa et al [2] and others [18], [19], [20], on the bcc lattice −A 4 = βv/2 where the geometric shape factor β = 2.1104607 and v is the spin wave velocity. Using the average estimate of A 4 we obtain v = 2.15(2).…”

Section: Generation Of Finite Ferromagnetic Bcc Latticesmentioning

confidence: 99%

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Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

et al. 2001

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In this paper finite bcc lattices are defined by a triple of vectors in two different ways -upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for Sz = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates.

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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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Finite-size effects in Heisenberg antiferromagnets

Cited by 200 publications

References 13 publications

Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

Loop-cluster simulation of the zero- and one-hole sectors of thet−Jmodel on the honeycomb lattice

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

Frustrated Quantum Magnets

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