相关论文: Continuum limit of gauged tensor network states

We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…

The Lattice Gauge Theory Hilbert space is divided into gauge-invariant sectors selected by the background charges. Such a projector can be directly embedded in a tensor network ansatz for gauge-invariant states as originally discussed in…

We solve the Gauss law as well as the corresponding Mandelstam constraints of (d+1) dimensional SU(2) lattice gauge theory in terms of harmonic oscillator prepotentials. This enables us to explicitly construct a complete orthonormal and…

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems,…

We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant…

The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for $U(1)$ gauge theories regularized via finite-dimensional Hilbert spaces of quantum…

Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…

We describe a general procedure to give effective continuous descriptions of quantum lattice systems in terms of quantum fields. There are two key novelties of our method: firstly, it is framed in the hamiltonian setting and applies equally…

A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P -> M, there is a canonical `generalized measure' on the space A/G of smooth connections on P modulo gauge transformations. This allows one to…

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body…

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal…

Lattice regularizations are pivotal in the non-perturbative quantization of gauge field theories. Wilson's proposal to employ group-valued link fields simplifies the regularization of gauge fields in principal fiber bundles, preserving…

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…

We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor…