Toward a microscopic theory of the λ transition in liquid 4He

Abstract

A microscopic many-body analysis of Bose–Einstein condensation in a strongly interacting system of identical bosons is presented in the framework of correlated density matrix theory. With the aid of hypernetted-chain techniques and a replica ansatz for the entropy, the free energy is constructed for a trial density matrix incorporating temperature-dependent two-point dynamical and statistical correlations. The free energy decomposes naturally into contributions from phonon excitations and from two types of quasiparticle excitations (identified as “holes” and “particles”), in addition to a component that becomes the ground-state energy at zero temperature. The subsequent analysis is conducted in terms of two order parameters: A condensation strength Bccand an exchange strength M. The former measures the breaking of gauge symmetry associated with the development of off-diagonal long-range order that signals Bose condensation; the latter characterizes the violation of particle-hole exchange symmetry. A description of exchange-symmetry breaking is formulated in terms of an analogy with the behavior of a diamagnetic material in a magnetic field, and a physically plausible model for the coupling of the order parameters Bccand M is proposed. The “particle” and “hole” excitation branches coincide in the normal phase, but follow different dispersion relations in the condensed phase, where exchange symmetry is broken. In a first application of the theory to the λ transition in liquid4He, phonon effects (dominant at very low temperatures) are neglected, and simple parametrized forms are assumed for the dynamical correlations and for the hole spectrum, which determines the remaining statistical correlations. Numerical results are reported for the two order parameters and for the quasihole and quasiparticle energies, as functions of temperature through the condensation point. The calculated specific heat shows the characteristic λ shape. Exchange symmetry breaking reduces the Bose–Einstein temperature from that of the ideal Bose gas to a predicted value near 2.2 K.