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Quantum Spin Chains

Quantum spin chains have for a number of years been a test bed for understanding fundamental physical properties of many-body quantum systems. Studies of spin chains have provided examples of novel ground states, fractional excitations, quantum disorder and critical behavior. The new knowledge obtained from studying these systems is used to explain, predict and tune phenomena both on the fundamental level and those employed in technological applications such as magnetic recording media, CMR read-heads, magnetic sensors, spin-based electronics, etc. Recent experiments on doped layered curates and nickelates have also indicated close connection between quantum magnetism of doped two-dimensional (2D) Mott insulators, including high-temperature superconductors, and the physics of quantum spin chains and ladders. In fact, one approach to understanding the two-dimensional quantum antiferromagnetics (AFM) realized in Mott insulating state of layered metal oxides is based on studying dimensional cross-over in an array of one-dimensional Mott insulators, or coupled spin chains. This approach takes advantage of significant theoretical breakthroughs that have occurred in this field in the past decade. Two main research directions pursued by our group are

Covalency, itinerancy, dimensional cross-over and spinons in S=1/2 chains

Among the most important recent theoretical developments is that of  quantum field theory methods yielding exact analytical expressions for two- and four-spinon contributions to the dynamical structure factor of S=1/2 Heisenberg chain. Not only these results can be used for extending theoretical predictions to 2D via examination of dimensional crossover in arrays of coupled S=1/2 chains, they can also be accurately matched against results of neutron scattering experiments probing quantum spin dynamics in real 1D Mott-insulating materials, such as  Sr2CuO3 and SrCuO2,  allowing to establish how well it is described by the model spin Hamiltonian. In particular, this opens a possibility for quantitative experimental examination of the influence of charge transfer (covalency) and charge excitation (itinerancy) on spin dynamics of 1D Mott insulating copper oxides, while similar studies in 2D systems are hindered by the absence of equally accurate predictions of the dynamical spin response.

Haldane spin gap in S=1 chains: doping and dimensional cross-over effects

Properties of 1D quantum antiferromagnet change dramatically when its spin increases from 1/2  to 1. In fact, as was first established by Haldane, integer and half-integer spin chains belong to different universality classes, of which spin-1/2 and spin-1 chains are the ultimate quantum representatives. Spin-1/2 chains are Luttinger liquids with critical ground state and gapless continuum spectrum composed of fractional spinon excitations, while AFM S=1 Haldane chains have robust singlet ground state and coherent magnon excitations separated from it by a finite gap. These magnon quasiparticles become unstable and yield to a continuum at high energies when their pair decays become cinematically allowed. When doped, S=1 AFM chain develops peculiar spin-density polarons, whose structure reflects hidden order existing in the Haldane state and which can be probed by magnetic neutron scattering.  A finite interchain coupling J'c is required for suppressing spin gap and inducing Neel order in an array of Haldane chains. Hence, regime of dimensional crossover realized in model S=1 AFM chain materials, such as CsNiCl3 and RbNiCl3, differs dramatically from the S=1/2 case. How these two dynamical and crossover regimes converge with increasing spin to the limiting classical-spin case S>>1 is still an open question. 

More information on these topics and an overview of our recent results can be obtained by visiting presentations and selected publications pages.

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Last Modified: Friday, 21-Mar-2008 18:19:00 EDT