Aspects of Confinement in Low Dimensions

We briefly review some examples of confinement which arise in condensed matter physics. We focus on two instructive cases: the off-critical Ising model in a magnetic field, and an array of weakly coupled (extended) Hubbard chains in the Wigner crystal phase. In the appropriate regime, the elementary excitations in these 1+1 and quasi-one-dimensional systems are confined into `mesons'. Although the models are generically non-integrable, quantum mechanics and form factor techniques yield valuable information.Comment: Contribution to Ian Kogan memorial volume, World Scientifi

Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc

The q-state Potts field theory with $2\le q\le 4$ in the low-temperature phase is considered in presence of a weak magnetic field h. In absence of the magnetic field, the theory is integrable, but not free at q>2: its elementary excitations - the kinks - interact at small distances, and their interaction can be characterized by the factorizable scattering matrix which was found by Chim and Zamolodchikov. The magnetic field induces the long-range attraction between kinks causing their confinement into the bound-states. We calculate the masses of the two-kink bound states in the leading order in |h| -> 0 expressing them in terms of the scattering matrix of kinks at h=0.Comment: 20 pages, no figures, v2: one section and references adde

On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6

In a recent paper Coldea et al (2010 Science {\bf 327} 177) report observation of the weak confinement of kinks in the Ising spin chain ferromagnet CoNb2O6 at low temperatures. To interpret the entire spectra of magnetic excitations measured via neutron scattering, they introduce a phenomenological model, which takes into account only the two-kink configurations of the spin chain. We present the exact solution of this model. The explicit expressions for the two-kink bound-state energy spectra and for the relative intensities of neutron scattering on these magnetic modes are obtained in terms of the Bessel function.Comment: 18 pages, 9 figures; v2: figures 1,3,4 replaced, few misprints correcte

SU(N) Evolution of a Frustrated Spin Ladder

Recent studies indicate that the weakly coupled spin-1/2 Heisenberg antiferromagnet with next nearest neighbor frustration supports massive spinons when suitably tuned. The straightforward SU(N) generalization of the low energy ladder Hamiltonian yields two independent SU(N) Thirring models with N-1 multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low-energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the N=2 and N>2 cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the N=infinity limit of the four chain magnet is not a trivial free theory.Comment: 10 pages, RevTex, 5 figures; SU(N) approach clarifie

Towards a Field Theory of the Plateau Transition

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the Integer Quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL($2,{\Bbb C}$)/SU(2) WZNW model (at the usual Ka{\v c}--Moody point and with the level $6 \leq k \leq 8$). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.Comment: typos corrected, a revised versio