Correlation effects in some one dimensional systems

J. M. P. Carmelo, Pedro D Sacramento, D. Bozi +1 more

S. Olszewski, Tomasz Roliński, Marek Cinal +1 more

S. Olszewski, Tomasz Roliński, Marek Cinal +1 more

Benedikt Herwerth, Germán Sierra, J. I. Cirac +1 more

We study states of one- and two-dimensional spin systems that are constructed as correlators within the conformal field theory of a massless, free boson. In one dimension, these are good variational wave functions for $XXZ$ spin chains, and they are similar to lattice Laughlin states in two dimensions. We show that their $zz$ correlations are determined by a modification of the original free-boson theory. An expansion to quadratic order leads to a solvable, effective theory for the correlations in these states. Compared to the massless boson, there is an additional term in this effective theory that explains the behavior of the correlations: a polynomial decay in one dimension and at the edge of a two-dimensional system and an exponential decay in the bulk of a two-dimensional system. We test the validity of our approximation by comparing it to Monte Carlo computations.

Leiming Chen

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2{k}_{F}$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons.

Alexander A. Ovchinnikov, V. Ya. Krivnov