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We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.

We describe a practical and efficient approach to represent physically realistic long-range interactions in two-dimensional tensor network algorithms via projected entangled-pair operators (PEPOs). We express the long-range interaction as a linear combination of correlation functions of an auxiliary system with only nearest-neighbor interactions. To obtain a smooth and radially isotropic interaction across all length scales, we map the physical lattice to an auxiliary lattice of expanded size. Our construction yields a long-range PEPO as a sum of ancillary PEPOs, each of small, constant bond dimension. This representation enables efficient numerical simulations with long-range interactions using projected entangled pair states. arXiv:1807.08378v2 [cond-mat.str-el]

Laser cooling is a powerful method to control molecules for applications in precision measurement, as well as quantum information, many-body physics, and fundamental chemistry. However, many optically-active metal centers in valence states which are promising for these applications, especially precision measurement, are difficult to laser cool. In order to extend the control afforded by laser cooling to a wider array of promising atoms, we consider the use of small, hypermetallic molecules that contain multiple metal centers. We provide a detailed analysis of YbCCCa and YbCCAl as prototypical examples with different spin multiplicities, and consider their feasibility for precision measurements making use of the heavy Yb atom. We find that these molecules are linear and feature metal-centered valence electrons, and study the complex hybridization and spin structures that are relevant to photon cycling and laser cooling. Our findings suggest that this hypermetallic approach may be a versatile tool for experimental control of metal species that do not otherwise efficiently cycle photons, and could present a new polyatomic platform for state-of-the-art precision measurements.

The giant {Mn 70 } and {Mn 84 } wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled {Mn 7 } subunits carrying an effective S = 2 spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest energy excitations arising from Heisenberg-ring-like excitations of the {Mn 7 } subunits around the wheel, at energies consistent with the observed temperature dependence of the magnetic susceptibility. We further suggest an important role for weak longer-range couplings in selecting the precise spin ground-state of the Mn wheels out of the nearly degenerate ground-state band.