On a one-dimensional spin system

Takashi Tonegawa, Makoto Kaburagi, S. Miyashita

U. Brandt, P. Solleder

James D. Johnson

Norikazu Ishimura

An Ising spin system which is situated on a two-dimensional square or a three-dimensional simple cubic lattice is considered. If there is a spin-lattice coupling and the lattice has no translational symmetry, there appears effectively a long range four-spin interaction in which the four spins are on a same axis. The ground state of the spin system is represented by using the ground state of a one-dimensional system where only the interactions along one axis are considered. The devil's staircase which has recently been shown to exist in such a one-dimensional system is wholly reproduced in a system on a two-dimensional square or a three-dimensional simple cubic lattice.

R. W. Gibberd, G.C. Stey

Andrei A. Zvyagin

Spin–charge separation is considered to be one of the key properties that distinguish low-dimensional electron systems from others. Three-dimensional correlated electron systems are described by the Fermi liquid theory. There, low-energy excitations (quasiparticles) are reminiscent of noninteracting electrons: They carry charges −e and spins 1/2. It is believed that for any one-dimensional correlated electron system, low-lying electron excitations carry either only spin and no charge, or only charge without spin. That is why recent experiments looked for such low-lying collective electron excitations, one of which carries only spin, and the other carries only charge. Here we show that despite the fact that for exactly solvable one-dimensional correlated electron models there exist excitations which carry only spin and only charge, in all these models with short-range interactions the low-energy physics is described by low-lying collective excitations, one of which carries both spin and charge.