相关论文: Chirally Factorised Truncated Conformal Space Appr…

Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

We introduce a new optimization procedure for Euclidean path integrals which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed.…

Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data resulting from queries. The similarity identification task is to identify the items in a…

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality)…

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…

Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the 2-dimensional time-frequency representation to a…

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density…

We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new…

Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization…

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…

We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…

Tensor networks are often used to accurately represent ground states of quantum spin chains. Two popular choices of such tensor network representations can be seen to implement linear maps that correspond, respectively, to euclidean time…

This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…

In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a $T\bar{T}$-deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the…

Two-timescale stochastic approximation (TTSA) is among the most general frameworks for iterative stochastic algorithms. This includes well-known stochastic optimization methods such as SGD variants and those designed for bilevel or minimax…

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…

Noncollinear (NC) magnetism and spin-orbit coupling (SOC) are indispensable for predictive ab initio materials simulations with pronounced relativistic effects and magnetic frustration, yet they significantly increase the cost of…

In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions $D=1,2$ is considered democratically as the input of a…