Related papers: Quantum Hall Ground States and Regular Graphs
Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this…
The quasiholes of the Read-Rezayi clustered quantum Hall states are considered, for any number of particles and quasiholes on a sphere, and for any degree k of clustering. A set of trial wavefunctions, that are zero-energy eigenstates of a…
Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize…
The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice…
We investigate putative quantum Hall effect states, labeled by their K-matrix equal to (1 1 3), by defining them on the torus and computing their Hall viscosity. Such states have been introduced on the sphere as a phase distinct from…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
We study the many-body ground states of SU($N$) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
Some purely chiral fractional quantum Hall states are described by symmetric or anti-symmetric polynomials of infinite variables. In this article, we review a systematic construction and classification of those fractional quantum Hall…
We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent states, very well captures the fundamental…
Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p…
Extending upon the observations of the emergence of quantum-like states from classical complex synchronized networks, this work adds mathematical rigor to the analysis of single Quantum-Like (QL) bits constructed by eigenvectors of the…
We give a general construction leading to different non-isomorphic families $\Gamma_{n,q}(\K)$ of connected $q$-regular semisymmetric graphs of order $2q^{n+1}$ embedded in $\PG(n+1,q)$, for a prime power $q=p^h$, using the linear…
The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density…
A recently proposed step-by-step procedure, to merge the low-energy physics of the $\pi$-bonds electrons of graphene, and quantum field theory on curved spacetimes, is recalled. The last step there is the proposal of an experiment to test a…
We briefly summarize properties of quantum Hall states with a pairing or clustering property. Their study employs a fundamental connection with parafermionic Conformal Field Theories. We report on closed form expressions for the many-body…
Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties like the Moore-Read Pfaffian for filling factor nu = 5/2. This wavefunction has been…