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

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