Submitted for the MAR16 Meeting of The American Physical Society Monte Carlo and Exact Diagonalization of Copper (II) Trimer Spin Frustrated Systems1 HAILEY X. EGIDO-BETANCOURT, LEONARD W. TER HAAR, CHRISTOPHER N. VARNEY, University of West Florida — We discuss the use and importance of trimer-based systems because of the spin frustration that may arise within extended lattices comprised of trimers. The possible intraand inter-trimer exchange pathways they posses due to interconnections are evaluated using density functional theory (DFT) to identify the optimal structures that may be used in designing extended lattices. As example, trinuclear Cu 3 cores with each pair of copper atoms bridged by carboxylate ligands have three-fold symmetry. As trimers these structures have the potential to be modeled as a frustrated quantum spin-1/2 system. To analyze the magnetic ground state and topological properties, we utilize exact diagonalization on small clusters and compare with Monte Carlo simulations for a range of system sizes. 1Research reported in this abstract was supported by UWF NIH MARC U-STAR 1T34GM110517-01. Hailey Egido-Betancourt University of West Florida Date submitted: 06 Nov 2015 Electronic form version 1.4

It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators.This calls for new methods for engineering and manipulating of the vortex states.One of the possible routes utilizes type-1.5 superconducting layered systems with multi-scale inter-vortex interactions.In order to explore the possible vortex states that can be engineered, we present two phase diagrams of phenomenological vortex matter models with multi-scale inter-vortex interactions featuring several attractive and repulsive length scales.The phase diagrams exhibit a plethora of phases, including conventional 2D lattice phases, five stripe phases, dimer, trimer, and tetramer phases, void phases, and stable low-temperature disordered phases.The transitions between these states can be controlled by the value of an applied external field.

The recent proposal of Romero-Isart et al. [Phys. Rev. Lett. 111, 145304 (2013)] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultracold-atom-based quantum emulators raises the need to create and control vortex lattices of different symmetries. Here we propose a mechanism by which honeycomb, hexagonal, square, and kagome vortex lattices could be created in superconducting systems with multiscale intervortex interactions. Multiple scales of the intervortex interaction can be created and controlled in layered systems made of different superconducting materials or with differing interlayer spacings.

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing--cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.

We demonstrate the formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and stripes in a cluster. We propose to realize such systems in vortex matter (where a vortex is mapped onto a particle with multi-scale interactions) in layered superconducting systems with varying inter-layer thicknesses and different layer materials.

Using fermionic representation of spin degrees of freedom within the Popov-Fedotov approach, we develop an algorithm for Monte Carlo sampling of skeleton Feynman diagrams for Heisenberg-type models. Our scheme works without modifications for any dimension of space, lattice geometry, and interaction range, i.e., it is suitable for dealing with frustrated magnetic systems at finite temperature. As a practical application, we compute uniform magnetic susceptibility of the antiferromagnetic Heisenberg model on the triangular lattice and compare our results with the best available high-temperature expansions. We also report results for the momentum dependence of the static magnetic susceptibility throughout the Brillouin zone.

We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and stripes in a cluster. We propose to realize such systems in vortex matter (where a vortex is mapped onto a particle with multi-scale interactions) in layered superconducting systems with varying inter-layer thicknesses and different layer materials.

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose-Hubbard-Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.