Related papers: A tensor network approach to 2D bosonization

Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In…

We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…

This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic…

We implement and benchmark tensor network algorithms with $SU(2)$ symmetry for systems in two spatial dimensions and in the thermodynamic limit. Specifically, we implement $SU(2)$-invariant versions of the infinite Projected Entangled Pair…

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum…

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…

We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic…

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…

Sampling a quantum systems underlying probability distributions is an important computational task, e.g., for quantum advantage experiments and quantum Monte Carlo algorithms. Tensor networks are an invaluable tool for efficiently…

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…

We present two algorithms to initialize layers of tensorized neural networks and general tensor network algorithms using partial computations of their Frobenius norms and positive lineal entrywise sums, depending on the type of tensor…

We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded…

Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…