Controlling Luttinger Liquid Physics in Spin Ladders under Magnetic Field

We present a $^{14}$N nuclear magnetic resonance study of a single crystal of CuBr$_4$(C$_5$H$_{12}$N)$_2$ (BPCB) consisting of weakly coupled spin-$1/2$ Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate $T_1^{-1}$ at $250$~mK and for (ii) the phase transition to a 3D ordered phase occuring below $110$~mK due to weak inter-ladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and Luttinger liquid model tested in detail over the whole fermion band.\\ M. Klanj\v{s}ek {\em et al.}, Phys. Rev. Lett. {\bf 101} 137207 (2008).