Critical properties of gapped spin-chains and ladders in a magnetic field

Abstract

An interesting feature of spin- chains with a gap is that they undergo a commensurate-incommensurate transition in the presence of an external magnetic field H. The system is in a gapless incommensurate regime for all values of the magnetic field between the lower critical field ${\mathrm{H}}_{\mathrm{c}1\mathrm{}}$ and an upper critical field ${\mathrm{H}}_{\mathrm{c}2\mathrm{}}$, where it is gapless and has power-law correlations. We calculate the critical exponents for such a generic gapped system in the incommensurate regime at the critical field ${\mathrm{H}}_{\mathrm{c}1\mathrm{}}$ and in its vicinity. Our analysis also applies to the spin- ladder. We compute the full dynamical susceptibilities at finite temperature. We use the same to discuss the thermal broadening of various modes and obtain the low-temperature behavior of the nuclear spin relaxation rate ${\mathrm{T}}_1^{\mathrm{-}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.