The Potential Energy Landscape Formalism for Quantum Liquids in the Continuous Ring-Polymer Limit

In the quantum case, this theoretical framework is based on the path-integral formulation of statistical mechanics where the liquid/non-annealing glass is mapped onto a classical system of ring-polymers. In previous studies, and motivated by path-integral (PI) computer simulations, the PEL formalism was developed assuming that the ring-polymers were discrete, i.e., each ring-polymer was composed of a finite number of beads, <i>n</i>_<i>b</i>.

In this work, we revisit the PEL formalism for the case where the ring-polymers of the system are continuous, i.e., <i>n</i>_<i>b</i> → ∞ (as required in the PI formulation of statistical mechanics). We find that in this limit, the PEL of the quantum liquid is unique and well-defined. The main PEL properties of the system, including the average inherent structure energy <i>E</i>_<i>IS</i>, configurational entropy <i>S</i>_<i>IS</i>, and vibrational Helmholtz free energy <i>F</i>_<i>vib</i>, are also well-defined (i.e., they converge).