Typical realizations of Heisenberg chains are transition metal oxides (TMO) where charge excitations have a gap (for example the usual Heisenberg model describes the magnetic properties of the Hubbard or t-J model in the insulating Mott phase, i.e. at half-filling). In such a situation the effective low-energy degrees of freedom are the magnetic modes. The frustration induced by doping of such system is known to lead to a variety of new interesting phenomena, in particular anomalous transport properties, various types of ordered states etc.
In one spatial dimension a change of the electron density by doping of a spin-1/2 Heisenberg chain leads to models with gapless spin and charge excitations. Usually these are in the universality class of Tomonaga-Luttinger liquids exhibiting spectacular phenomena such as spin charge separation, anomalous critical exponents and more.
Broad interest has been attracted recently by the properties of doped Heisenberg spin systems with spin S larger than 1/2. Nickeloxides (S=1) and manganates (S=2) with Perovskite lattice structure have been synthesized and show a variety of phases when the concentration of charge carriers or the external magnetic field is varied.
Considering generalizations of the so-called supersymmetric t-J model we have succeeded to construct a family of systems which should contain all the states relevant for a theoretical description of these substances at low energies. In addition to the (antiferromagnetic) exchange interaction of the spins these models allow for propagating modes which are spin-(S-1/2) "holes" moving in the spin-S background of the undoped system. In one spatial dimension these models are exactly solvable by means of the Bethe Ansatz which allows detailed studies of the phase diagram of these systems.
Without an external magnetic field these models have three gapless modes. One of them is connected to the charge excitations while the other two are associated with the magnetic degrees of freedom. As a function of doping the latter show a smooth transition from a product of a level-2S WZW model and a minimal one to a level-(2S-1) WZW model and a c=1 theory.
Application of these findings to analyze experiments on the materials mentioned above are under way.
Holger Frahm, Markus P. Pfannmüller and Alexei M. Tsvelik:
Doping of a spin-1 chain: an integrable model
(Phys. Rev. Lett.
81 (1998) 2116-2119)
Holger Frahm
Doped Heisenberg chains: Spin-S generalizations of the
supersymmetric t-J model
(Nucl. Phys.
B559 [FS] (1999) 613-636)
Holger Frahm and Constantin Sobiella
Doping-induced magnetization plateaus
(Phys. Rev.
Lett. 83 (1999) 5579-5582)
Holger Frahm and Nikita A. Slavnov:
Magnetic properties of doped Heisenberg chains
(Nucl. Phys. B 575
[FS] (2000) 485-503)