Interaction effects between impurities in low-dimensional spin-(1/2) antiferromagnets

Abstract

PACS. 75.10.Jm -Quantized Spin Models. PACS. 75.30.Hx -Magnetic impurity interactions.Abstract. -We are considering the interplay between several non-magnetic impurities in the spin-1/2 Heisenberg antiferromagnet in chains, ladders and planes by introducing static vacancies in numerical quantum Monte Carlo simulations. The effective potential between two and more impurities is accurately determined, which gives a direct measure of the quantum correlations in the systems. Large effective interaction potentials are an indication of strong quantum correlations in the system and reflect the detailed nature of the valence bond ground states. In two-dimensions (2D) the interactions are smaller, but can still be analyzed in terms of valence bonds.Introduction. -The interplay between impurities in antiferromagnetic backgrounds has become an important topic ever since the discovery of high-temperature superconductivity. The interaction energy between mobile holes has been examined with a variety of numerical and analytical methods for t-J and Hubbard models in order to get a better insight into the pairing mechanism in the HiT c compounds [1][2][3][4]. Equally interesting is the effect of static impurities [5][6][7][8][9] which for example are known to induce spin-1/2 degrees in ladders, that interact to form gapless excitations in otherwise gapped systems [10,11]. For static vacancies one of the first studies was performed by Bulut et al. with linear spin-wave approximation and numerics on small lattices [5], establishing a nearest neighbor attraction and an interesting enhancement of the local quantum correlations.We are now considering several static holes (vacancies) in low dimensional antiferromagnets like chains, ladders and planes on larger lattices, in order to calculate their impurity and interaction energies in the limit of zero temperature. The energies are changed because nearest neighbor correlations S i · S j are altered around the vacancies which in turn visualize the quantum correlations on the lattice. Therefore the interaction energy between two or more impurities gives direct information on the quantum correlations by showing the underlying local valence bond order as will be explained for a variety of configurations in the antiferromagnetic spin-1/2 Heisenberg model H = J i,j S i · S j where i, j denotes nearest neighbor sites on chain, ladder and square lattices.In order to determine impurity contributions to the total energy and the effective potentials between vacancies we have to sum up all bond strengths in the system and subtract the

Even-odd effect in short antiferromagnetic Heisenberg chains

“…In particular, one would expect the spatial derivative term in Eq. (17) to become more important once the total spin is excited since the additional net spin needs to be distributed along the chain. A discussion of this point with regards to the spin density will be given in Sec.…”

“…The model for an infinite chain or one-dimensional antiferromagnetic Heisenberg chain (AFHC) has attracted enormous interest, especially after Haldane's conjecture of a fundamental difference between integer and half-integer spin chains, which is by now well established. [12][13][14] Finite but long chains have also received significant attention, but mainly for connecting numerical results to the thermodynamic limit via scaling 15 or for understanding boundary, 16 impurity, 17 and doping effects. 18 On the other hand, very little has been done for short chains with s > 1 2 , in which the Haldane gap is always smaller than the finite-size excitation energy, and the difference between integer and half-integer spins is thus expected to become irrelevant.…”

Magnetic responses of randomly depleted spin ladders

“…In the case of the power-law distribution (32) for which the exponent α = 2zξ is the one of the couplings distribution and J max = J 0 (see below Eq. (60) while, at low-T , a Sommerfeld-like expansion, in which the constant three appearing the denominator of (56) has to be carefully taken into account, yields a power-law:…”

“…(64), naturally yields lowtemperature corrections from a Sommerfeld expansion, valid provided T H, which reads m(H, T ) = m(H, 0) + π 2 6 P (H)T 2 + · · · , where P (H) is the derivative of the coupling distribution. For instance, in the case of the continuous distribution (32) and taking the approximation z * 1/(2ξ), the temperature corrections depend on doping and magnetic field through…”

Tunable nanomagnetism in moderately cold fermions on optical lattices

“…More recently, various extensions to correlated hosts have been considered, e.g., in the context of high-T c superconductivity. 4 The impact of localized defects on the spin physics of insulating systems (i.e., for a strongly correlated host) in two dimensions has been modelled via vacancies in the Heisenberg model [34][35][36][37] and via sites with extra external couplings; 37 we will relate our work to some of these studies in the following.…”