Toward a microscopic theory of the lambda transition in liquid He-4

A microscopic many-body analysis of Bose-Einstein condensation in a strongl y interacting system of identical bosons is presented in the framework of c orrelated density matrix theory. With the aid of hypernetted-chain techniqu es and a replica ansatz for the entropy, the free energy is constructed for a trial density matrix incorporating temperature-dependent two-point dynam ical and statistical correlations. The free energy decomposes naturally int o contributions from phonon excitations and from two types of guasiparticle excitations (identified as "holes" and "particles"), in addition to a comp onent that becomes the ground-state energy at zero temperature. The subsequ ent analysis is conducted in terms Of two order parameters: A condensation strength B-cc and an exchange strength M. The former measures the breaking of gauge symmetry associated with the development of off-diagonal long-rang e order that signals Bose condensation; the latter characterizes the violat ion of particle-hole exchange symmetry. A description of exchange-symmetry breaking is formulated in terms of an analogy with the behavior of a diamag netic material in a magnetic field, and a physically plausible model for th e coupling of the oi der parameters B-cc and M is proposed The "particle" a nd "hole" excitation br branches coincide in the normal phase, but follow d ifferent dispersion relations in the condensed phase, where exchange symmet ry is broken. In a first application of the theory to lambda transition ira liquid He-4, phonon effects (dominant at very low temperatures) me neglect ed, and simple parametrized forms are assumed for the dynamical correlation s and for the hole spectrum, which determines the remaining statistical cor relations. Numerical results are reported for the two older parameters and for the quasihole and quasiparticle energies, as functions of temperature t hrough the condensation point. The calculated specific heat shows the chara cteristic lambda shape. Exchange symmetry breaking reduces the Bose-Einstei n temperature from that of the ideal Bose gas to a predicted value near 2.2 K.