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We consider the spin polarized fermions for the filling fraction 5/2 in abi-layer quantum well system. Since the kinetic energy of the system infractional quantum Hall states (FQHS) is totally quenched, the Hamiltoniandescribing the system comprises of the electron correlation and tunnelingterms. The correlations are captured by the 'so-called' Haldanepseudo-potentials(HPP). We employ the finite-temperature formalism involvingMatsubara propagators to deal with this Hamiltonian. We show that the systemundergoes a zero-order quantum phase transition (QPT), at fixed chargeimbalance regulatory(CIR) parameter and constant layer separation as theinter-layer tunneling (ILT)strength is increased, from the effectivetwo-component state (two independent layers) to an effective single-componentstate (practically a single layer). At finite and constant ILT strength, atransition from the latter state to the former state is also possible uponincreasing CIR parameter. We identify the order parameter to describe this QPTas a pseudo-spin component and calculate the order parameter with the aid ofthe Matsubara propagators. The clear finger-print of this QPT is obtained up totemperature equal to 100 K.

Fingerprint of QPT in a bilayer-quantum-well system at the filling fraction {\nu} = 5/2 in the low temperature range (1K-100 K)