Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

Data of the molecular dynamics simulations of mutations in the human connexin46 docking interface

The structure of hCx26 derived from the X-ray analysis was used to generate a homology model for hCx46. Interacting connexin molecules were used as starting model for the molecular dynamics (MD) simulation using NAMD and allowed us to predict the dynamic behavior of hCx46wt and the cataract related mutant hCx46N188T as well as two artificial mutants hCx46N188Q and hCx46N188D. Within the 50 ns simulation time the docked complex composed of the mutants dissociate while hCx46wt remains stable. The data indicates that one hCx46 molecule forms 5-7 hydrogen bonds (HBs) with the counterpart connexin of the opposing connexon. These HBs appear essential for a stable docking of the connexons as shown by the simulation of an entire gap junction channel and were lost for all the tested mutants. The data described here are related to the research article entitled "The cataract related mutation N188T in human connexin46 (hCx46) revealed a critical role for residue N188 in the docking process of gap junction channels" (Schadzek et al., 2015) [1].