Related papers: Matrix Model and Refined Wall-Crossing Formula
In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…
We consider $\mathfrak{so}_4$ invariant matrix product states (MPS) in the $\mathfrak{so}_6$ symmetric integrable spin chain and prove their integrability. These MPS appear as fuzzy three-sphere solutions of matrix models with…
We establish a relation between the refined Hopf link invariant and the S-matrix of the refined Chern-Simons theory. We show that the refined open string partition function corresponding to the Hopf link, calculated using the refined…
In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix…
In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts…
The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…
BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
We propose a modified mode-expansion of the bulk fields in a BPS domain wall background to obtain the effective theory on the wall. The broken SUSY is nonlinearly realized on each mode defined by our mode-expansion. Our work clarifies a…
Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty,…
Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted…
We investigate the computational difficulty of approximating the partition function of the ferromagnetic Ising model on a regular matroid. Jerrum and Sinclair have shown that there is a fully polynomial randomised approximation scheme…
In $D=4,N=2$ theories on $R^{3,1}$, the index receives contributions not only from single-particle BPS states, counted by the BPS indices, but also from multi-particle states made of BPS constituents. In a recent work [arXiv:1406.2360], a…
We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…