Phase transition in the one-dimensional quantum discreteφ4−φ2model

Abstract

We consider the ground-state phase transition from broken to restored phases of the one-dimensional quantum discrete ${\ensuremath{\varphi}}^{4}\ensuremath{-}{\ensuremath{\varphi}}^{2}$ model as a function of two parameters: the strength of the quantum fluctuations (measured by a dimensionless Planck constant $\overline{\ensuremath{\Elzxh}}$), and the classical dimensionless coupling parameter \ensuremath{\gamma}, which characterizes the strength of interaction of the neighboring atoms. We introduce several distinct variational methods based on self-consistent phonons and soliton wave functions, and compare their predictions for the phase diagram with the (numerically exact) results of previous quantum Monte Carlo simulations. Our calculations show that in the region of weak coupling $(\ensuremath{\gamma}<1),$ both the ``tunneling soliton'' and the ``two-level'' approaches provide good approximations to the true result. In the intermediate coupling region $({\ensuremath{\gamma}}_{c}>\ensuremath{\gamma}>1),$ the method of self-consistent phonons gives a satisfactory description of phase transition. We also compare and contrast our results with previously published approximate methods, and discuss problems for further investigation.