Group Theory and Its Applications in Physics

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S = 5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S = 1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 ≫ J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.

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“…where the number of times a given IR labeled by α appears in this decomposition is given by the well known formula [58][59][60] …”

Section: Methodsmentioning

confidence: 99%

Quantum magnetism on the Cairo pentagonal lattice

2012

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“…Though taken in itself, reflection in the xz planeσ v,x is not a symmetry operation (it changes the sign of the field), combining it with time reversalT gives the symmetry operationTσ v,x . The same holds for all vertical mirror planes, and C 2 ⊥ẑ axes, thus the full symmetry group consists of eight unitary and eight non-unitary symmetry operations [2] …”

Section: Magnetic Fieldmentioning

confidence: 96%

“…The notation "g" and "u" in Table I refers to their parity under time reversal. [4] for B = 0 (D 4h notations [2], overline means symmetrization [5]). sym (g) operator sym (u) operator…”

Section: Introductionmentioning

confidence: 99%

Group theory and octupolar order inURu2Si2

2005

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Recent experiments on URu 2 Si 2 show that the low-pressure hidden order is non-magnetic but it breaks time reversal invariance. Restricting our attention to local order parameters of 5f 2 shells, we find that the best candidate for hidden order is staggered order of either T β z or T xyz octupoles.Group theoretical arguments for the effect of symmetry-lowering perturbations (magnetic field, mechanical stress) predict behavior in good overall agreement with observations. We illustrate our general arguments on the example of a five-state crystal field model which differs in several details from models discussed in the literature. The general appearance of the mean field phase diagram agrees with the experimental results. In particular, we find that a) at zero magnetic field, there is a first-order phase boundary between octupolar order and large-moment antiferromagnetism with increasing hydrostatic pressure; b) arbitrarily weak uniaxial pressure induces staggered magnetic moments in the octupolar phase; and c) a new phase with different symmetry appears at large magnetic fields.

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“…Specifically, we will be given operatorsÔ({s i }), with a given symmetry, and write their matrix elements φ ′ α |Ô({s i })|φ α = c φ ′ α |ô(S α )|φ α where c is a constant that depends on S α , and possibly on i, but not on the z-component of the spin (see e.g., Ref. 19). In our calculation, we restrict our attention to the maximum spin manifold S α =S because it turns out that we will need only matrix elements between the quantum p-sublattice singlet states |Φ and |Φ ′ , where S α =S for all α; in any case, when S α <S there is more than one multiplet and the Wigner-Eckart theorem is not enough to specify the matrix elements.…”

Section: A Operator Equivalentsmentioning

confidence: 99%

Effective Hamiltonian and low-lying eigenenergy clustering patterns of four-sublattice antiferromagnets

et al. 2002

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We study the low-lying energy clustering patterns of quantum antiferromagnets with p sublattices (in particular p = 4). We treat each sublattice as a large spin, and using second-order degenerate perturbation theory, we derive the effective (biquadratic) Hamiltonian coupling the p large spins. In order to compare with exact diagonalizations, the Hamiltonian is explicitly written for a finite-size lattice, and it contains information on energies of excited states as well as the ground state. The result is applied to the face-centered-cubic Type I antiferromagnet of spin 1/2, including secondneighbor interactions. A 32-site system is exactly diagonalized, and the energy spectrum of the low-lying singlets follows the analytically predicted clustering pattern.

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Group Theory and Its Applications in Physics

Abstract: The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 333 publications

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Quantum magnetism on the Cairo pentagonal lattice

Quantum magnetism on the Cairo pentagonal lattice

Group theory and octupolar order inURu2Si2

Effective Hamiltonian and low-lying eigenenergy clustering patterns of four-sublattice antiferromagnets

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