Related papers: Vertex Representation of Hyperbolic Tensor Network…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
The uniform two-dimensional variational tensor product state is applied to the transverse-field Ising, XY, and Heisenberg models on a regular hyperbolic lattice surface. The lattice is constructed by tessellation of the congruent pentagons…
We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different…
We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that…
To explore the non-Euclidean generalization of higher-order topological phenomena, we construct a higher-order topological insulator model in hyperbolic lattices by breaking the time-reversal symmetry (TRS) of quantum spin Hall insulators.…
We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces.…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better…
Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces.…
Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First, we identify the quantum phase transition for…