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 [1]. These building blocks are termed endofullerenes with H2O@C60 as a prime example [2]. 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) [5]. Such a QPT was recently predicted for the case of one water in one dimension [6]. 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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[9] T. Serwatka and P.-N. Roy, “Ground state of asymmetric tops with dmrg: Water in one dimension,” J. Chem. Phys. 156, 044116 (2022).
[10] T. Serwatka and P.-N. Roy, “Ferroelectric water chains in carbon nanotubes: Creation and manipulation of ordered quantum phases,” J. Chem. Phys. 157, 234301 (2022).
[11] T. Serwatka and P.-N. Roy, “Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes”, J. Phys. Chem. Lett., 14, 5586 (2023).
