Commensurate-incommensurate phase transitions for multichain quantum spin models: exact results

The behavior in an external magnetic field is studied exactly for a wide cl ass of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate ph ase transitions between the gapless phases in the ground state. The conform al limit of these models is studied and it is shown that the low-lying exci tations for the incommensurate phases are not independent, because they are governed by the same magnetic field (chemical potential for excitations). A scenario for the transition from one to two space dimensions for the exac tly integrable multichain quantum spin models is proposed, and it is shown that the incommensurate phases in an external magnetic field disappear in t he limit of an infinite number of coupled spin chains. The similarities in the external field behavior for the quantum multichain spin models and a wi de class of quantum field theories are discussed. The scaling exponents for the appearance of the gap in the spectrum of low-lying excitations of the quantum multichain models due to the relevant perturbations of the integrab le theories are calculated. (C) 2000 American Institute of Physics. [S1063- 777X(00)01002-1].