Quantum Disentangled Liquids

Abstract

We propose and explore a new finite temperature phase of translationally invariant multi-component liquids which we call a 'Quantum Disentangled Liquid' (QDL) phase. We contemplate the possibility that in fluids consisting of two (or more) species of indistinguishable quantum particles with a large mass ratio, the light particles might 'localize' on the heavy particles. We give a precise, formal definition of this QDL phase in terms of the finite energy density many-particle wavefunctions. While the heavy particles are fully thermalized, for a typical fixed configuration of the heavy particles, the entanglement entropy of the light particles satisfies an area law; this implies that the light particles have not thermalized. Equivalently, but more intuitively, if the positions of all the heavy particles are measured, the projected wavefunction for the unmeasured light particles has as an area law entanglement entropy. Thus, in a QDL phase, thermal equilibration is incomplete, and the canonical assumptions of statistical mechanics are not fully operative. The definition of the QDL phase for heavy/light particles can be readily generalized to other cases with two (or more) conserved currents, such as spin/charge in a system of spin-1/2 fermions (as in a Hubbard model). Indeed, we argue that the finite energy-density eigenstates of the t–J model will generically be in such a spin/charge QDL, although the fate of the QDL in the large U Hubbard model is uncertain. We explore the possibility of QDL in water, with the light proton degrees of freedom becoming 'localized' on the oxygen ions. While we do not presently know whether a local, generic Hamiltonian can have eigenstates of the QDL form, if not, then the non-thermal behavior discussed here will exist as an interesting crossover phenomena at a time scale that diverges as the ratio of the mass of the heavy to the light particles also diverges.