Fully symmetrized valence-bond based technique for solving exchange Hamiltonians of molecular magnets

Sahoo, Shaon; Raghunathan, Rajamani; Ramasesha, S.; Sen, Diptiman

doi:10.1103/physrevb.78.054408

Cited by 20 publications

(42 citation statements)

References 34 publications

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“…The N 2 BPS as well as non-BPS extremal black holes under certain condition share the common feature that the moduli near the horizon are stabilized due to the attractor mechanism [7,15]. Recently various aspects on the non-BPS black holes were studied, see [16] and references therein.…”

Section: Introductionmentioning

confidence: 99%

N=8attractors

2006

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We derive and solve the black hole attractor conditions of N 8 supergravity by finding the critical points of the corresponding black hole potential. This is achieved by a simple generalization of the special geometry symplectic structure to all extended supergravities with N > 2. There are two classes of solutions for regular black holes, one for 1=8 BPS ones and one for the non-BPS. We discuss the solutions of the moduli at the horizon for BPS attractors using N 2 language. An interpretation of some of these results in N 2, STU black hole context helps to clarify the general features of the black hole attractors.

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Section: Introductionmentioning

confidence: 99%

N=8attractors

2006

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“…9 Firstly, we need to construct the C matrix, whose ith row contains the coefficients of the constant M S functions appearing in the ith VB basis function. This is a pretty fast step as the constant M S states are an ordered sequence of integers and a VB state with n lines is a linear combination of 2n constant M S functions.…”

Section: Hybrid Methods Based On Vb Basis and Constant Ms Basismentioning

confidence: 99%

“…This symmetry can break the M S = 0 space into even and odd total spin subspaces. 9 Since in most cases, the lowest excited state usually has a spin which is one different from that of the ground state, this symmetry makes it easy to obtain the spin gaps accurately.…”

Section: Solving Exchange Hamiltonianmentioning

confidence: 99%

“…Furthermore, in case of molecular magnets containing magnetic ions with spin greater than half, the exchange operator between such high spin centers also generates 'illegal' VB diagrams as it involves non-nearest neighbour exchange interactions between constituent elementary spins. 9,14,15 In view of these difficulties, a fully symmetrized VB approach to solving Heisenberg exchange Hamiltonian particularly in the context of molecular magnets is not feasible.…”

Section: Symmetrized Vb Approachmentioning

confidence: 99%

“…Complete factorization of the Hilbert space of the Hamiltonian using both spin and spatial symmetries has been the focus of many studies. 9 However, exploitation of spatial and spin symmetries has been possible only for Abelian point groups. Here we present a general technique which is a hybrid method based on Valence-bond basis and the basis of z-component of the total spin, which is applicable to all types of point groups and is easy to implement on computer.…”

Section: Solving Exchange Hamiltonianmentioning

confidence: 99%

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Computing magnetic anisotropy constants of single molecule magnets

et al. 2009

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We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, D M and E M for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant M S -valence bond (VB) technique of solving spin Hamiltonians employing full spatial and spin symmetry adaptation and we illustrate this technique by solving the exchange Hamiltonian of the Cu 6 Fe 8 system. Treating the anisotropy Hamiltonian as perturbation, we compute the D M and E M values for various eigenstates of the exchange Hamiltonian. Since, the dipolar contribution to the magnetic anisotropy is negligibly small, we calculate the molecular anisotropy from the single-ion anisotropies of the metal centers. We have studied the variation of D M and E M by rotating the single-ion anisotropies in the case of Mn 12 Ac and Fe 8 SMMs in ground and few low-lying excited states of the exchange Hamiltonian. In both the systems, we find that the molecular anisotropy changes drastically when the single-ion anisotropies are rotated. While in Mn 12 Ac SMM D M values depend strongly on the spin of the eigenstate, it is almost independent of the spin of the eigenstate in Fe 8 SMM. We also find that the D M value is almost insensitive to the orientation of the anisotropy of the core Mn(IV) ions. The dependence of D M on the energy gap between the ground and the excited states in both the systems has also been studied by using different sets of exchange constants.

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Supersymmetric black holes in string theory

Mohaupt

2007

Fortschritte der Physik

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We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2 supergravity, special geometry, the black hole attractor equations and the underlying variational principle. Special attention is payed to the crucial role of higher derivative corrections. Finally we discuss black hole partition functions and their relation to the topological string, mainly from the supergravity perspective. We try to summarize the state of art and discuss various open questions and problems.Comment: 43 pages, based on a talk given at the midterm meeting of the RTN project `Constituents, Fundamental Forces and Symmetries of the Universe' in Naples, October 9-13, 200

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Fully symmetrized valence-bond based technique for solving exchange Hamiltonians of molecular magnets

Cited by 20 publications

References 34 publications

N=8attractors

N=8attractors

Computing magnetic anisotropy constants of single molecule magnets

Supersymmetric black holes in string theory

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