D. V. Khveshchenko

Spin-gap fixed points in the double-chain problem.

Applying the bosonization procedure to weakly coupled Hubbard chains we discuss the fixed points of the renormalization group flow where all spin excitations are gapful and a singlet pairing becomes the dominant instability.

Singlet pairing in the double-chain t - J model

Applying the bosonization procedure to constrained fermions in the framework of the one-dimensional t-J model, we discuss a scenario of singlet superconductivity in a lightly doped double chain where all spin excitations remain gapful.

RAMAN SCATTERING AND ANOMALOUS CURRENT ALGEBRA IN MOTT INSULATORS

Recent experiments on inelastic light scattering in a number of insulating cuprates [1] revealed a new excitation appearing in the case of crossed polarizations just below the optical absorption threshold. This observation suggests that there exists a local exciton-like state with an odd parity with respect to a spatial reflection. We present the theory of high energy large shift Raman scattering in Mott insulators and interpret the experiment [1] as an evidence of a chiral bound state of a hole and a doubly occupied site with a topological magnetic excitation. A formation of these composites is a crucial feature of various topological mechanisms of superconductivity. We show that inelastic light scattering provides an instrument for direct measurements of a local chirality and anomalous terms in the electronic current algebra.

Charge-spin separation in 2D Fermi systems: Singular interactions as modified commutators, and solution of the 2D Hubbard model in the bosonized approximation.

The general two-dimensional fermion system with repulsive interactions (typified by the Hubbard model) is bosonized, taking into account the finite on-shell forward-scattering phase shift derived in earlier papers. By taking this phase shift into account in the bosonic commutation relations, a consistent picture emerges showing the charge-spin separation and anomalous exponents of the Luttinger liquid.

ON EXACT BOSONIZATION OF THE CALOGERO-SUTHERLAND MODEL

We elaborate on an algebraic method of a momentum space bosonization of exactly solvable one-dimensional models in the framework of the Calogero-Sutherland model. The approach provides an exact representation of the local field operator of the Calogero-Sutherland model in terms of quasiparticle eigenstate’s creation-annihilation operators and furnishes a simple method to compute exact correlation functions.We demonstrate that the exact form-factors of the Calogero-Sutherland model which were recently found in Ref.[10] in confirmation of the congectures earlier made by Haldane (Ref.[9]) can be reproduced in the framework of some bosonization procedure in momentum space. This observation implies a possibility of an exact bosonization of this model describing one-dimensional anyons.

GAUGE THEORY OF ANTIFERROMAGNETISM IN TWO DIMENSIONS FOR LARGE RANK SYMMETRY GROUP

We examine long wavelength fluctuations in two-dimensional magnetic systems with the symmetry group of a large rank N. The mean field solution is obtained and the existence of the parity-violating ground state is established. On the basis of the 1/N expansion, an effective gauge theory containing the Chern-Simons term is derived, which allows one to obtain a spectrum, spin and statistics of long wavelength excitations.

Physical realization of the parity anomaly and quantum Hall effect

Abstract We present the lattice version of the anomalous Dirac operator in (2+1) dimensions. This version is associated with a group of magnetic translations rather than translations. This group naturally provided homologically nontrivial fiber bundles, the first Chern class of which is directly related with the number of zero modes and spectral asymmetry of the Dirac operator. The results are in agreement with the lattice fermions doubling phenomenon. The relation of the parity anomaly in (2+1) and the Hall effect is elucidated.

BOSONIZATION OF CURRENT-CURRENT INTERACTIONS

We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of

ON CALCULATION OF ENERGY OF PLANAR LATTICE FERMIONS IN A MAGNETIC FIELD

W_\infty

PARITY VIOLATION AND SUPERCONDUCTIVITY IN DOPED MOTT INSULATORS

on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.