Critical properties and Bose-Einstein condensation in dimer spin systems

We analyze the spin relaxation time $1∕T_1$ for a system made of weakly coupled one-dimensional ladders. This system allows us to probe the dimensional crossover between a Luttinger liquid and a Bose-Einstein condensate of magnons. We obtain the temperature dependence of $1∕T_1$ in the various dimensional regimes, and discuss the experimental consequences.

Figure 1

(Color online) Summary of the temperature dependence of $1∕T_1$. $T_c\left(h\right)$ represents the BEC condensation temperature. ${\Delta }_0$ is the gap in the absence of magnetic field. The temperature dependence is indicated for the various regimes (see text).

Figure 2

Skeleton self-energy graphs at second order. The dotted line represents the interaction and the straight line the magnon propagator. The magnon propagator is computed with the first-order self-energy. Because of the low-density limit close to the quantum critical point this expansion is well behaved.