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

We consider the spin polarized fermions for the filling fraction 5/2 in a bi-layer quantum well system. Since the kinetic energy of the system in fractional quantum Hall states (FQHS) is totally quenched, the Hamiltonian describing the system comprises of the electron correlation and tunneling terms. The correlations are captured by the 'so-called' Haldane pseudo-potentials(HPP). We employ the finite-temperature formalism involving Matsubara propagators to deal with this Hamiltonian. We show that the system undergoes a zero-order quantum phase transition (QPT), at fixed charge imbalance regulatory(CIR) parameter and constant layer separation as the inter-layer tunneling (ILT)strength is increased, from the effective two-component state (two independent layers) to an effective single-component state (practically a single layer). At finite and constant ILT strength, a transition from the latter state to the former state is also possible upon increasing CIR parameter. We identify the order parameter to describe this QPT as a pseudo-spin component and calculate the order parameter with the aid of the Matsubara propagators. The clear finger-print of this QPT is obtained up to temperature equal to 100 K.