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We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as a special subfamily, and then prove T-systems among them…
We investigate the robustness of Majorana edge modes under disorder and interactions. We exploit a recently found mapping of the interacting Kitaev chain in the symmetric region ($\mu = 0$, $t = \Delta$) to free fermions. Extending the…
Despite about forty years of investigations, the nature of the melting transition in two dimensions is not completely clear. In the framework of the most popular Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) theory, 2D…
We study the boundary criticality in 2D interacting topological insulators. Using the determinant quantum Monte Carlo method, we present a nonperturbative study of the boundary quantum phase diagram in the Kane-Mele-Hubbard-Rashba model.…
Quantum magnets in the $M\mathrm{Nb_2O_6}$ and BaCo$_2$V$_2$O$_8$ families realise frustrated transverse-field Ising models whose competing ferromagnetic and antiferromagnetic couplings generate a sign problem provably intractable for…
Let $I$ be an independent set drawn from the discrete $d$-dimensional hypercube $Q_d=\{0,1\}^d$ according to the hard-core distribution with parameter $\lambda>0$ (that is, the distribution in which each independent set $I$ is chosen with…
Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…
It has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex…
We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a…
Let $E \subset \mathbb{C}$ be a Borel set such that $0<\mathcal{H}^1(E)<\infty$. David and L\'eger proved that the Cauchy kernel $1/z$ (and even its coordinate parts $\textrm{Re}\, z/|z|^2$ and $\textrm{Im}\, z/|z|^2$, $z\in…
We study scaling limits of skew plane partitions with periodic weights under several boundary conditions. We compute the correlation kernel of the limiting point process in the bulk and near turning points on the frozen boundary. The…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
Dimensionality and electronic correlations are crucial elements of many quantum material properties. An example is the change of the electronic structure accompanied by the loss of quasiparticles when a metal is reduced from three…
We perform a systematic analysis of the soft supersymmetry-breaking terms arising from four-dimensional strings. The analysis does not assume any specific supersymmetry-breaking mechanism but provides a means of parametrizing our ignorance…
The amplitudes for $2\rightarrow 2$ scattering processes involving longitudinally polarized gauge bosons $( W_L^\pm, Z_L )$ and the Higgs boson are analyzed up to two loops. Assuming $M_H >> M_W$, the trilinear Higgs coupling, $\lambda v$,…
Fast computation of three-dimensional gravity and magnetic forward models is considered. Measurement data is assumed to be obtained on a uniform grid which is staggered with respect to the discretization of the parameter volume. Then, the…
We develop a coordinate-free probabilistic framework for determinantal point processes associated with Bergman kernels on compact complex manifolds. The basic issue is that Bergman kernels are naturally line-bundle-valued:…
Moire superlattices formed by stacking atomically thin two-dimensional materials with a relative twist angle have emerged as a versatile platform for engineering quantum electronic, optical, and ferroic properties. Computational modelling…
The technique developed in Hochschild's works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task…