Confinement and critical regime in doped frustrated quasi-one dimensional magnets

TL;DR

This paper investigates the effects of impurity doping on the ground state and finite temperature properties of coupled frustrated spin chains, revealing scaling behaviors linked to spin cluster formation using advanced computational methods.

Contribution

It introduces a combined chain-mean field and quantum Monte Carlo approach to model impurity effects in frustrated spin chains, and develops a new Real Space RG method for long-range interactions.

Findings

Scaling behaviors of spin susceptibilities linked to spin cluster formation.

Effective 2D model with anisotropic long-range interactions.

Reproduction of results by a novel Real Space RG method.

Abstract

Ground state and finite temperature properties of a system of coupled frustrated and/or dimerized spin-1/2 chains modeling e.g. the CuGeO$_3$ compound are reviewed. Special emphasis is put on the investigation of the role of impurity doping. A c hain-mean field computation combining exact diagonalisations of the chain hamiltonians together with a mean field treatment of the weak interchain couplings is performed in order to map the microscopic model onto a low-energy effective model. The latter descr ibes a 2-dimensional system of effective spin-1/2 local moments interacting by spacially anisotropic long range spin exchange interactions. An extensive study of this effective model is performed by Stocastic Series Expansion Quantum Monte Carlo for a wide range of temperatures and impurity concentrations. Interesting scaling behaviors of the uniform and staggered spin susceptibilities (above a small ordering Neel temperature due to a residual 3D coupling) can be interpreted in terms of the formation of large clusters of correlated spins carrying a finite magnetization. Such results are reproduced satisfactorily by a new Real Space RG enabling to deal with long range interactions in two-dimensions