Related papers: Lattice Gauge Tensor Networks
We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the…
Tensor network methods have demonstrated their suitability for the study of equilibrium properties of lattice gauge theories, even close to the continuum limit. We use them in an out-of-equilibrium scenario, much less explored so far, by…
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it…
We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…
Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states,…
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be…
Tensor network states have been a very prominent tool for the study of quantum many-body physics, thanks to their physically relevant entanglement properties and their ability to encode symmetries. In the last few years, the formalism has…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The…
I point out two of the subtleties referred to in the title. The first is that gauge-invariant magnetic systems may realized under general circumstances, as suggested by a simple theorem. The second subtlety is that care is needed to…
The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance…
Entanglement is assuming a central role in modern quantum many-body physics. Yet, for lattice gauge theories its certification remains extremely challenging. A key difficulty stems from the local gauge constraints underlying the gauge…
In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due…