Three-point functions in ABJM and Bethe Ansatz

We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

Ultrafast carrier dynamics at organic donor-acceptor interfaces - A quantum-based assessment of the hopping model

We investigate the charge transfer dynamics of photogenerated excitons at the donor-acceptor interface of an organic solar cell blend under the influence of molecular vibrations. This is examined using an effective Hamiltonian, parametrized by density functional theory calculations, to describe the full quantum behaviour of the relevant molecular orbitals, which are electronically coupled with each other and coupled to over one hundred vibrations (via Holstein coupling). This electron-phonon system is treated in a numerically quasi-exact fashion using the matrix-product-state ansatz. We provide insight into different mechanisms of charge separation and their relation to the electronic driving energy for the separation process. We find ultrafast electron transfer, which for small driving energy is dominated by kinetic processes and at larger driving energies by dissipative phonon emission connected to the prevalent vibration modes. Using this fully quantum mechanical model we perform a benchmark comparison to a recently developed semi-classical hopping approach, which treats the hopping and vibration time scales consistently. We find qualitatively and quantitatively good agreement between the results of the sophisticated matrix-product-state based quantum dynamics and the simple and fast time-consistent-hopping approach.

Multi-Modal Image Fusion Based on Matrix Product State of Tensor

Multi-modal image fusion integrates different images of the same scene collected by different sensors into one image, making the fused image recognizable by the computer and perceived by human vision easily. The traditional tensor decomposition is an approximate decomposition method and has been applied to image fusion. In this way, the image details may be lost in the process of fusion image reconstruction. To preserve the fine information of the images, an image fusion method based on tensor matrix product decomposition is proposed to fuse multi-modal images in this article. First, each source image is initialized into a separate third-order tensor. Then, the tensor is decomposed into a matrix product form by using singular value decomposition (SVD), and the Sigmoid function is used to fuse the features extracted in the decomposition process. Finally, the fused image is reconstructed by multiplying all the fused tensor components. Since the algorithm is based on a series of singular value decomposition, a stable closed solution can be obtained and the calculation is also simple. The experimental results show that the fusion image quality obtained by this algorithm is superior to other algorithms in both objective evaluation metrics and subjective evaluation.

Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine learning techniques, thereby facilitating an improved interpretability of neural networks. This study presents the discrimination of top quark signal over QCD background processes using a Matrix Product State classifier. We show that entanglement entropy can be used to interpret what a network learns, which can be used to reduce the complexity of the network and feature space without loss of generality or performance. For the optimisation of the network, we compare the Density Matrix Renormalization Group (DMRG) algorithm to stochastic gradient descent (SGD) and propose a joined training algorithm to harness the explainability of DMRG with the efficiency of SGD.