arXiv subjects

Mehmet Dede

Publications and source records attributed to Mehmet Dede.

3 recordsLinked to original sources

arXiv2026

Kitaev spin liquid in superconducting networks

We propose a realization of the Kitaev honeycomb Hamiltonian -- an archetypal spin-liquid model -- in a superconducting metamaterial. The architecture consists of Cooper-pair boxes coupled through depleted semiconductor--superconductor heterostructures that do not require spin--orbit coupling. The Cooper-pair boxes encode effective spin degrees of freedom, while normal and anomalous virtual propagation through the heterostructures mediate bond-directional interactions. Two key control parameters are an out-of-plane magnetic flux and the semiconductor Fermi energy. The former controls interference and distinguishes the bond directions, while tuning the latter close to the bottom of the band gives rise to an emergent Nambu-exchange symmetry that enforces the required bond directionality. Through numerical calculations, we identify an operating regime with controlled corrections, with associated energy and length scales within experimental reach. These results establish a route toward equilibrium quantum spin liquids in engineered superconducting networks.

cond-mat.str-el↗

arXiv2026

Graph-based emulation of $d$-dimensional curved spaces with superconducting arrays

We introduce a framework for emulating graphs and, through them, curved spaces of arbitrary dimension, using arrays of superconducting wires. The array consists of two stacked layers of wires, horizontal and vertical, such that wires are parallel within each layer and perpendicular between layers. By discretizing a space into a graph, assigning a superconducting wire with a rigid phase to each vertex, and coupling pairs of wires through Josephson junctions according to the graph edges, arbitrary geometries and topologies can be engineered in a controlled setting. The superconducting phases then realize scalar field theories on the emergent geometry. We establish experimentally realistic conditions for implementing these architectures and develop a dictionary relating measurable circuit observables to quantities in the emulated field theory. As an application, we develop the implementation of hyperbolic (Anti-de Sitter) spaces of constant negative curvature and use them as an experimentally accessible platform to explore holographic duality in arbitrary dimensions. We investigate the effects of disorder in the Josephson couplings, which translate into metric variations in the bulk-boundary correspondence, and analyze their impact on boundary scaling exponents both analytically and numerically, finding that holographic duality remains robust even in the presence of strong disorder. Beyond holography, the framework opens a broad range of architectural possibilities, including the exploration of physics on highly nontrivial graphs and toy models of dynamical spacetimes.

cond-mat.supr-con↗

arXiv2022

A comment on the solutions of the generalized Faddeev-Volkov model

We consider two recent generalizations of the Faddeev-Volkov model, which is exactly solvable Ising-type lattice spin model. The first generalization based on using of the non-compact quantum dilogarithm over Pontryagin self-dual LCA group $\mathbb{R}\times \mathbb{Z}/N\mathbb{Z}$, and another one constructed in a recent study via the gauge/YBE correspondence. We show that weight functions of these models obtained by different techniques are the same up to a constant.

math-ph↗