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

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 ${\mathrm{H}}_{\mathrm{c}1}$ and an upper critical field ${\mathrm{H}}_{\mathrm{c}2}$, 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 ${\mathrm{H}}_{\mathrm{c}1}$ 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 ${\mathrm{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. We discuss the results obtained here for the special cases of the dimerized chain, frustrated chain, and the spin- ladder.

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