  The critical point and the critical exponents for a phase transition can be
determined using the Finite-Size Scaling (FSS) analysis. This method assumes
that the phase transition occurs only in the infinite size limit. However,
there has been a lot of interest recently in quantum phase transitions occuring
in finite size systems such as a single two-level system interacting with a
single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase
transitions occur at a finite system size, the traditional FSS method is
rendered inapplicable for these cases. For cases like this, we propose an
alternative FSS method in which the truncation of the system is done in the
Hilbert space instead of the physical space. This approach has previously been
used to calculate the critical parameters for stability and symmetry breaking
of electronic structure configurations of atomic and molecular systems. We
calculate the critical point for the quantum phase transition of the QRM using
this approach. We also provide a protocol to implement this method on a digital
quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our
work opens up a new direction in the study of quantum phase transitions on
quantum devices.
