Related papers: Fractons on Graphs and Complexity
We present a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal…
We derive the equation of matter density perturbations on sub-horizon scales around a flat Friedmann-Lema\^\i tre-Robertson-Walker background for the general Lagrangian density $f(R,\GB)$ that is a function of a Ricci scalar $R$ and a…
We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least one Dirichlet vertex. Using a variational characterization…
A new representation of the scalar electrodynamics is discovered which gives a more redundant description of electromagnetic theory and suitable to construct an appropriate matter action which contains two global symmetries . The symmetries…
Divergence functions of a metric space estimate the length of a path connecting two points $A$, $B$ at distance $\le n$ avoiding a large enough ball around a third point $C$. We characterize groups with non-linear divergence functions as…
We analyze the subdivision properties of certain lattice gauge theories for the discrete abelian groups $Z_{p}$, in four dimensions. In these particular models we show that the Boltzmann weights are invariant under all $(k,l)$ subdivision…
In this communication, we present a class of Brans-Dicke-like theories with a universal coupling between the scalar field and the matter Lagrangian. We show this class of theories naturally exhibits a decoupling mechanism between the scalar…
We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an N-component complex scalar field, characterized by a global SU(N) symmetry. In agreement with the…
The unitarity of the 4D lattice theory of gravity in the case of the Minkowski signature is proved. The proof is valid only for lattices that conserve the number of degrees of freedom during time evolution. The Euclidean signature and the…
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this…
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…
We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree…
The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum…
We perform lattice studies of the gauge theory with Sp(4) gauge group and two flavours of (Dirac) fundamental matter. The global SU(4) symmetry is spontaneously broken by the fermion condensate. The dynamical Wilson fermions in the lattice…
We perform numerical calculations of masses and decay constants of the lightest (flavoured) pseudoscalar, vector and axial vector mesons in the $Sp(4)$ lattice gauge theory with three Dirac fermions in the antisymmetric representation. The…
Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are…
The two-dimensional carbon allotrope graphene has recently attracted a lot of attention from researchers in the disciplines of Lattice Field Theory, Lattice QCD and Monte Carlo calculations. This interest has been prompted by several…
Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…