Experimental Quantification of Entanglement Through Heat Capacity

A new experimental realization of heat capacity as an entanglement witness (EW) is reported. Entanglement properties of a low dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin $\frac{1}{2}$ antiferromagnetic system which shows clear signature of quantum phase transition (QPT) at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.