Abstract
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high local symmetry content native to these systems by describing only the gauge invariant subspace. Compared to a standard tensor network description, the gauge invariant model allows one to increase real and imaginary time evolution up to a factor that is square of the dimension of the link variable. The gauge invariant tensor network description is based on the quantum link formulation, a compact and intuitive formulation for gauge theories on the lattice, which is alternative to and can be combined with the global symmetric tensor network description. We present some paradigmatic examples that show how this architecture might be used to describe the physics of condensed matter and high-energy physics systems. Finally, we present a cellular automata analysis which estimates the gauge invariant Hilbert space dimension as a function of the number of lattice sites that might guide the search for effective simplified models of complex theories.
Highlights
In modern science gauge theories play a fundamental role, with examples ranging from quantum electrodynamics to the standard model of elementary particle physics [1, 2]
Quantum link models on, as we focus on numerical simulations, we assume that the space of the gauge degrees of freedom is finite dimensional
We have presented all the ingredients that are necessary to define a quantum link version of a lattice gauge theory, for the sake of clarity and concreteness, we present four particular examples: the simplest (1 + 1) dimensional quantum link model (QLM) with the abelian U (1) symmetry, the simplest (1 + 1) dimensional QLM with non-abelian U (2) symmetry, and applications for two relevant models in condensed matter physics: quantum dimer [6, 59] and spin-ice [56, 57] models on the square lattice [60]
Summary
In modern science gauge theories play a fundamental role, with examples ranging from quantum electrodynamics to the standard model of elementary particle physics [1, 2]. Several physical contexts have been found where tensor networks are an exact description of the ground states of gauge-invariant Hamiltonians (e.g., 2D toric code that is an Ising gauge theory [8, 41, 42]) This framework has been successfully applied to LGT related problems [20, 43,44,45,46,47,48,49]. We show how tensor networks can exactly encode lattice gauge symmetries providing an architecture that is completely general and computationally efficient: our approach outperforms straightforward approaches that do not explicitly exploit gauge symmetries To achieve this goal, the use of alternative formulations of gauge theories are highly desirable, with the principal motivation being the identification of models with a finite dimensional Hilbert space at each link or site which can be simulated by tensor networks algorithms. We analyze in detail these elements in a quantum link formulation, while stressing the connection to typical lattice gauge theory models
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
