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We use an alternative approach to study the quantum phase transition in acoupled cavity lattice at finite temperature. As an illustrative example, weinvestigate the behaviors of the trace distance and quantum phase transition ina Jaynes-Cummings lattice at finite temperature. It is found that the tracedistance can be used to describe the critical point of the quantum phasetransition at finite low temperatures and the critical points are sensitive tothe atom-field interaction strength and the detuning factor. Fornon-equilibrium states, we demonstrate that the time evolution of the tracedistance's maximum value is also a good indicator of the critical points.Moreover, we show that the scaling behavior of derivative of the trace distanceat the critical points and the scaling rule are dependent on the externalparameters of the Hamiltonian.

Trace distance and scaling behavior of coupled cavity lattice at finite temperature