Related papers: Shuffle algebras, lattice paths and Macdonald func…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This…
The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial…
It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to…
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource…
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing…
The structure of a Nuttall partition into sheets of some class of four-sheeted Riemann surfaces is studied. The corresponding class of multivalued analytic functions is a special class of algebraic functions of fourth order generated by the…
The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD, using NRQCD for the b quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD collaborations with the Iwasaki…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…
Let $B_t(n)$ be the number of set partitions of a set of size~$t$ into at most $n$ parts and let $B'_t(n)$ be the number of set partitions of $\{1,\ldots, t\}$ into at most $n$ parts such that no part contains both $1$ and~$t$ or both $i$…
We study nonlinear n-term approximation of harmonic functions on the unit ball in $R^d$ from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Laplace equation) in BMO. A sharp Jackson estimate is…
The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…
We compute the topological partition function (twisted index) of $\mathcal{N}=2$ $U(N)$ Chern-Simons theory with an adjoint chiral multiplet on $\Sigma_g \times S^1$. The localization technique shows that the underlying Frobenius algebra is…
The worldsheet formulation is introduced for lattice gauge theories with dynamical fermions. The partition function of lattice compact QED with staggered fermions is expressed as a sum over surfaces with border on self-avoiding fermionic…
We compute the canonical partition function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R^d. We discuss in detail the 4-dimensional case (where s=1 is the standard Maxwell vector,…
Metal surfaces with disorder or with nanostructure modifications are studied, allowing for a localized charge layer (CL) in addition to continuous charges (CC) in the bulk, both charges having a compressional or diffusive non-local…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
We present preliminary lattice results for the nonperturbative tensor structure of the vector and axial-vector quark-antiquark vertices in QCD. Our lattice calculations are for $N_f=2$ mass-degenerate Wilson fermion flavors whose quark mass…
This is the first in a series of papers devoted to generalisations of statistical loop models. We define a lattice model of $U_q(\mathfrak{sl}_n)$ webs on the honeycomb lattice, for $n \ge 2$. It is a statistical model of closed, cubic…
We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the ones in the $ISO(3)$ Chern-Simons theory. It is shown that, for a handlebody of any genus, a…