Related papers: Discrete scale invariant fixed point in a quasiper…
In 2013, Balasubramanian presented a 5+1 dimensional holographic toy model that allows for an exact solution to Einstein's equations in the bulk in which the isometries of $AdS_5$ appear to be broken to an isometry group describing a…
We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward…
The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…
We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type $n^{-\alpha}$ for $\alpha>0$. We recover all the spectral regimes…
In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete…
The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of…
We study the low-lying spectrum of the bilinear-biquadratic Heisenberg model in the dimerized and Haldane phases using a tensor renormalization method. At the (Takhtajan-Babujian) critical point the finite size spectrum predicted by the…
Dimer coverings (or perfect matchings) of a finite graph are classical objects of graph theory appearing in the study of exactly solvable models of statistical mechanics. We introduce more general dimer labelings which form a topological…
We extend our previous work [J. Chem. Phys, \textbf{136}, 124121], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group (DMRG) algorithm, to additionally utilize general non-Abelian point group symmetries. A…
The dimer model is a classical statistical mechanics model which is exactly solvable in two dimensions, but about which little is known in higher dimensions. In analogy with large $N$ limits in lattice gauge theory, we study a large $N$…
This paper is concerned with locally damped semilinear wave equations defined on compact Riemannian manifolds with boundary. We present a construction of measure-controlled damping regions which are sharp in the sense that their summed…
We construct an exactly solvable relativistic model that embeds the anomalous inverse-square interaction into a non-Hermitian Klein-Gordon field theory through a purely imaginary, scale-invariant scalar potential. The stationary field…
Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of…
In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
Aharony and Fisher showed that non-local dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point, called the dipolar fixed point. The non-perturbative nature of the new fixed…
We prove a sharp regularity threshold for uniqueness in two anisotropic Calder\'on-type inverse problems in dimension $n\ge 3$. The main setting is the Riemannian Schr\"odinger problem with fixed scalar potential: for a prescribed…
This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights [arXiv:1503.00289]. Specific instances of such models were studied in [arXiv:052711, arXiv:1612.09082, arXiv1801.00207]; we…
We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum…
We study XY and dimerized XX spin-1/2 chains with random exchange couplings by analytical and numerical methods and scaling considerations. We extend previous investigations to dynamical properties, to surface quantities and operator…