相关论文: Sharp implications of AGSPs for degenerate ground …
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
A continuum limit treatment of planar spin chains with arbitrary S is presented. The difference between integer and half-integer spins is emphasised. While isotropic half-integer spin chains are gapless,and have power-law decay of…
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that every minimal non-degenerate critical…
We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not…
We consider the XXZ spin chain, characterized by an anisotropy parameter $\Delta>1$, and normalized such that the ground state energy is $0$ and the ground state given by the all spins up state. The energies $E_K = K(1-1/\Delta)$,…
Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of $S$-integral points of varieties over number fields $k$, including many cases with geometrically irreducible boundary divisors. Our approach builds…
Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto…
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic…
Classical U(1) fracton spin liquids feature an extensive ground state degeneracy and follow an effective description in terms of a tensor Gauss' law where charges, so-called fractons, have restricted mobility. Here we introduce a simple…
We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the…
Generally, ``fracton'' topological orders are referred to as gapped phases that support \textit{point-like topological excitations} whose mobility is, to some extent, restricted. In our previous work [Phys. Rev. B 101, 245134 (2020)], a…
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
We explore the shifted $f(R) (\propto R^{1+\delta})$ model with ${\delta}$ as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and…
The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as $L_m[u]=\Delta u+\left(m/x\right)\partial_x u =0$, where $m\in\mathbb{C}$. We generalize results…
We provide a roadmap to establish improved lower bounds on the decay rate of the uniform radius of analyticity $\sigma(T)$ for a given nonlinear dispersive equation, reducing the problem to the derivation of nonlinear smoothing estimates…
We study rational curves on general Fano hypersurfaces in projective space, mostly by degenerating the hypersurface along with its ambient projective space to reducible varieties. We prove results on existence of low-degree rational curves…
We show that, after suitably adjusting a uniform transverse magnetic field, the generic inhomogeneous open XX spin chain has a two-fold degeneracy, and an exact $su(2)$ symmetry whose "inhomogeneous" nonlocal generators depend on…
We study the convergence dynamics of Gradient Descent (GD) in a minimal binary classification setting, consisting of a two-neuron ReLU network and two training instances. We prove that even under these strong simplifying assumptions, while…
We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{N}/2$) with anisotropy parameter $\Delta$. Assuming that $\Delta>2J$, and introducing threshold energies $E_{K}:=K\left(1-\frac{2J}{\Delta}\right)$, we show that the bipartite…