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We analyze measurements of the magnetization, differential susceptibility andspecific heat of quasi-one dimensional insulatorCu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$ (CuPzN) subjected to magnetic fields. We showthat the thermodynamic properties are defined by quantum spin liquid formedwith spinons, with the magnetic field tuning the insulator CuPzN towardsquantum critical point related to fermion condensation quantum phase transition(FCQPT) at which the spinon effective mass diverges kinematically. We show thatthe FCQPT concept permits to reveal and explain the scaling behavior ofthermodynamic characteristics. For the first time, we construct the schematic$T-H$ (temperature---magnetic field) phase diagram of CuPzN, that containsLandau-Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling thatof heavy-fermion compounds.

Quasi-one-dimensional quantum spin liquid in the $\rm {Cu(C_4H_4N_2)(NO_3)_2}$ insulator