Commensurate-Incommensurate Phase Transitions for Multi-Chain Quantum Spin Models: Exact Results

The behavior in an external magnetic field is studied exactly for a wide class of multi-chain quantum spin models. It is shown that the magnetic field together with the inter-chain couplings cause the commensurate-incommensurate phase transitions between the gapless phases in the groundstate. The conformal limit of these models is studied and it is shown that the low-lying excitations 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 exactly integrable multi-chain quantum spin models is proposed and it is shown that the incommensured phases in an external magnetic field disappear in the limit of an infinite number of the coupled spin chains. The similarities in the external field behavior for the quantum multi-chain spin models and a wide class of quantum field theories are discussed. The scaling exponents for the appearence of the gap in the spectrum of the low-lying excitations of the quantum multi-chain models due to the relevant perturbations of the integrable theories are calculated. PACS numbers: 75.10.Jm,11.10.Kk