scholarly journals Lifting SU(2) spin networks to projected spin networks

2010 ◽  
Vol 82 (6) ◽  
Author(s):  
Maïté Dupuis ◽  
Etera R. Livine
Keyword(s):  
Spin Networks

scholarly journals Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 336 ◽  
Author(s):  
Bosiljka Tadić ◽  
Miroslav Andjelković ◽  
Milovan Šuvakov ◽  
Geoff J. Rodgers
Keyword(s):  
Domain Walls ◽  
Spin Dynamics ◽  
Higher Order ◽  
Spin Networks ◽  
Graph Theoretic ◽  
Geometrically Frustrated ◽  
Geometric Frustration ◽  
Antiferromagnetic Materials ◽  
Geometrically Constrained ◽  
Ferromagnetic Interactions

Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n − 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.

scholarly journals Quantum trajectories of interacting pseudo-spin networks

1998 ◽  
Vol 67 (6) ◽  
pp. 733-741 ◽  
Author(s):  
C.M. Granzow ◽  
G. Mahler
Keyword(s):  
Quantum Trajectories ◽  
Spin Networks

Subspace controllability of symmetric spin networks

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Jiahui Chen ◽  
Yehao Zhou ◽  
Ji Bian ◽  
Jun Li ◽  
Xinhua Peng
Keyword(s):  
Spin Networks

scholarly journals Quantum walks on graphs of the ordered Hamming scheme and spin networks

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Hiroshi Miki ◽  
Satoshi Tsujimoto ◽  
Luc Vinet
Keyword(s):  
Magnetic Fields ◽  
Quantum Walks ◽  
Perfect State ◽  
Spin Networks ◽  
Krawtchouk Polynomials ◽  
Energy Eigenstates ◽  
State Transfer ◽  
Perfect State Transfer ◽  
Local Magnetic Fields ◽  
Basis Vectors

It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.

scholarly journals Adiabatic state distribution using anti-ferromagnetic spin systems

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Koen Groenland
Keyword(s):  
Quantum Information ◽  
Spin Systems ◽  
Quantum Computers ◽  
State Distribution ◽  
Spin Networks ◽  
Important Prerequisite ◽  
Linear Chains ◽  
Coupling Strengths ◽  
Maximum Spin ◽  
Adiabatic State

Transporting quantum information is an important prerequisite for quantum computers. We study how this can be done in Heisenberg-coupled spin networks using adiabatic control over the coupling strengths. We find that qudits can be transferred and entangled pairs can be created between distant sites of bipartite graphs with a certain balance between the maximum spin of both parts, extending previous results that were limited to linear chains. The transfer fidelity in a small star-shaped network is numerically analysed, and possible experimental implementations are discussed.

scholarly journals ON THE VOLUME CONJECTURE FOR CLASSICAL SPIN NETWORKS

2012 ◽  
Vol 21 (03) ◽  
pp. 1250022 ◽  
Author(s):  
ABDELMALEK ABDESSELAM
Keyword(s):  
Invariant Theory ◽  
Classical Literature ◽  
Spin Networks ◽  
Classical Invariant Theory ◽  
Classical Spin ◽  
Volume Conjecture ◽  
Symbolic Method ◽  
Exact Determination ◽  
Classical Invariant

We prove an upper bound for the evaluation of all classical SU2 spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the spectral radius, for the special class of generalized drum graphs. Our proof uses a version of Feynman diagram calculus which we developed as a tool for the interpretation of the symbolic method of classical invariant theory, in a manner which is rigorous yet true to the spirit of the classical literature.

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