Effective Hamiltonians and dilution effects in Kagome and related anti-ferromagnets

Abstract

What is the zero-temperature ordering pattern of a Heisenberg anti-ferromagnet with large spin length S (and possibly small dilution), on the Kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular that the classical ground states become nonfrustrated, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most satisfactory is the Moessner-Chalker constraint enumeration. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime. PACS Nos.: 75. 10N, 75.50Ee, 75.40, 75.25+z Résumé : Quel est à T = 0 l'ordonnance d'un système antiferromagnétique de Heisenberg avec une grande longueur de spin S (et possiblement une faible dilution) construit sur un réseau de Kagomé ou sur d'autres réseaux conçus à partir de triangles ou de tétraèdres réunis par les sommets ? Je présente d'abors un résumé de l'utilisation de hamiltoniens efficaces pour résoudre la dégénérescence importante du fondamental, menant à une ordonnance à longue portée du type habituel. Je discute ensuite les effets de la dilution, en particulier que les états fondamentaux classiques deviennent non frustrés, en ce que chaque simplex de spin est satisfait de façon optimale. Des trois explications de ce phénomène, la plus satisfaisante est l'enumeration des contraintes de Moessner-Chalker. L'énergie du point zéro quantique peut compétitionner avec l'énergie classique d'échange dans un système dilué, créant la frustration et un état de verre de spin. Je pense que le régime au delà de 97% d'occupation est qualitativement différent du régime à plus forte dilution.[Traduit par la Rédaction]

Fractionalized Z2 Classical Heisenberg Spin Liquids

“…The first Heisenberg spin liquid to be identified unambiguously, the antiferromagnet on the pyrochlore lattice [7,12] is a U (1) spin liquid exhibiting pinch-points in its structure factor indicating algebraically decaying correlations [7,[12][13][14][15], as well as fractionalisation of its microscopic degrees of freedom: disorder in the form of dilution creates new, weakly-interacting, magnetic degrees of freedom which possess a half of the microscopic magnetic moments of the Heisenberg model [16,17].…”

Deformed triangular lattice antiferromagnets in a magnetic field: Role of spatial anisotropy and Dzyaloshinskii-Moriya interactions

“…9 This biquadratic interaction represents an effective Hamiltonian that is generated by quantum and/or thermal fluctuations. 43 We have incorporated such a biquadratic spin interaction and optimized its (fielddependent) coupling constant such that we reproduce the leading 1/S energy differences between several important states in the classical ground-state manifold. In this way, we find that quantum zero-point energy can be semiquantitatively described by the following classical biquadratic Hamiltonian with negative coupling constant:…”

Effective Hamiltonians for large-Spyrochlore antiferromagnets

“…Instead, our approach is to express E ′ as an effective Hamiltonian H eff [12], for a generic classical ground state, often via crude approximations that have no controlled small parameter, yet result in an elegant form. For any H eff , we seek (i) its (approximate) analytic form (ii) its energy scale, (iii) which spin pattern gives the minimum E harm , and (iv) how large is the remaining degeneracy.…”

“…The effective Hamiltonian has value beyond the possibility (as here) that it leads us to unexpected ground states. First, we can model the T > 0 behavior using a Boltzmann ensemble exp(−βH eff ) [12]. Second, starting from H eff , more complete models may be built by the addition of anisotropies, quantum tunneling [13], or dilution [12].…”

“…First, we can model the T > 0 behavior using a Boltzmann ensemble exp(−βH eff ) [12]. Second, starting from H eff , more complete models may be built by the addition of anisotropies, quantum tunneling [13], or dilution [12]. Apart from analytics, we also pursued the brute-force approach of fitting H eff to a database of numerically evaluated energies; minimizing the resulting H eff may well lead us to a new ground state not represented in the database.…”