Thermodynamics of the Spin Luttinger Liquid in a Model Ladder Material

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound $({\mathrm{C}}_5{\mathrm{H}}_{12}\mathrm{N}{)}_2{\mathrm{CuBr}}_4$ is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modeling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the entire phase diagram.