Related papers: Quantum Hall Ground States and Regular Graphs
We introduce a category $\mathsf{qGph}$ of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs $G$ and $H$ in $\mathsf{qGph}$, we then construct a quantum graph $[G,H]$ of…
Graph states are the key resources for measurement- and fusion-based quantum computing with photons, yet their creation is experimentally challenging. We optimize a hybrid graph-state generation scheme using a single quantum emitter and…
We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$-uniform…
We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable…
We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which…
We propose a matrix model to describe a class of fractional quantum Hall (FQH) states for a system of (N_1+N_2) electrons with filling factor more general than in the Laughlin case. Our model, which is developed for FQH states with filling…
The quantum Hall effect is studied in a spherical geometry using the Dirac operator for non-interacting fermions in a background magnetic field, which is supplied by a Wu-Yang magnetic monopole at the centre of the sphere. Wave functions…
In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is defined on a tensor product of a fermion Fock space and a boson Fock. It is shown that, under spatially localized conditions and…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…
We use the polynomial method of Guth and Katz to establish stronger and {\it more efficient} regularity and density theorems for such $k$-uniform hypergraphs $H=(P,E)$, where $P$ is a finite point set in ${\mathbb R}^d$, and the edge set…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
We quantize the regularity properties of classical graphs that determine spin models for singly-generated Yang-Baxter planar algebras, including the Kauffman polynomial, and construct explicit examples. A source of examples comes from…
We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the…
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…
We consider the number \bar N(q) of points in the projective complement of graph hypersurfaces over \F_q and show that the smallest graphs with non-polynomial \bar N(q) have 14 edges. We give six examples which fall into two classes. One…
Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we…
The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in…
We introduce quantum hypercube states, a class of continuous-variable quantum states that are generated as orthographic projections of hypercubes onto the quadrature phase-space of a bosonic mode. In addition to their interesting geometry,…
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states…