Simulating quantum critical molecular assemblies: from path integrals to matrix product states When molecules are confined in nano-cavities such as fullerenes, their translational degrees of freedom become quantized. The molecules however retain well-defined rovibrational levels . These building blocks are termed endofullerenes with H2O@C60 as a prime example . The endofullerenes can themselves be embedded in larger nanostructures such as carbon nanotubes to form so-called endofullerene peapods [3,4]. In such an assembly, polar molecules will interact with each other via dipole-dipole interactions. Depending on the strength of the interactions and on the monomer’s rovibrational level spacings, these system can undergo a phase transition from an disordered to ordered phase. This phenomenon is called a Quantum Phase Transition (QPT) . Such a QPT was recently predicted for the case of one water in one dimension . An important computational tool for the study of quantum chains of rotors is the density matrix renormalization group (DMRG) [7-9] and we will present the features of that approach. We will present recent results obtained using DMRG and will explore the concept of a quantum phase transition in the context of chains of asymmetric tops molecules like water. We will finally present conditions under which water chains can become ferroelectric [10,11]. As current DMRG approaches are most efficient for one-dimensional chains, we will discuss alternative computational approaches based on Path Integral Monte Carlo to compute two and three dimensional assemblies.
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