Related papers: Evaluation of state integrals at rational points
We explore the topological defects of the critical three-state Potts spin system on the torus, Klein bottle and cylinder. A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT…
We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for…
We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the functional equations of Dirichlet $L$-functions, and another modeled…
In this article, we investigate the problem of state reconstruction of four-level quantum systems. A realistic scenario is considered with measurement results distorted by random unitary operators. Two frames which define injective…
We dicuss some curious aspects of the Rogers dilogarithm and the functional relations in integrable systems in two dimensions. This is for the proceedings of the XX1 Differential Geometry Methods in Theoretical Physics, Tianjin, China, 5-9…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…
A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parameterised by a pivotal functor from a spherical fusion…
To each local field, Garoufalidis and Kashaev recently associate a quantum dilogarithm that satisfies a pentagon identity and some symmetries. By employing an angled version of these quantum dilogarithms, they developed three generalized…
In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the Spin Foam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov (EPRL-FK). To tackle the problem, we restrict…
We analyze certain compositions of rational inner functions in the unit polydisk $\mathbb{D}^{d}$ with polydegree $(n,1)$, $n\in \mathbb{N}^{d-1}$, and isolated singularities in $\mathbb{T}^d$. Provided an irreducibility condition is met,…
Quantum processors based on neutral atoms trapped in arrays of optical tweezers have appealing properties, including relatively easy qubit number scaling and the ability to engineer arbitrary gate connectivity with atom movement. However,…
In this paper we use an elementary approach by using numerical semigroups (specifically, those with two generators) to give a formula for the number of integral points inside a right-angled triangle with rational vertices. This is the basic…
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation,…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and…
We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…
We prove a priori estimates and, as sequel, existence of Euclidean Gibbs states for quantum lattice systems. For this purpose we develop a new analytical approach, the main tools of which are: first, a characterization of the Gibbs states…
In this paper we pursue the use of information measures (in particular, information diagrams) for the study of entanglement in symmetric multi-quDit systems. We use generalizations to U(D) of spin U(2) coherent states and their adaptation…
A spin system is studied, with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions, in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalizaton-group solution with the…