Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory
Open Access
- 12 July 2020
- Vol. 6 (7), 97
- https://doi.org/10.3390/universe6070097
Abstract
Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods have been applied to lattice gauge theories, yet these theories remain a challenge in dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages—firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse-graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentanglers. We apply this new algorithm to lattice gauge theories defined for the quantum group and identify a weak and a strong coupling phase for various levels . As we increase the level , the critical coupling decreases linearly, suggesting the absence of a deconfining phase for the continuous group . Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.
Keywords
This publication has 58 references indexed in Scilit:
- Anyon Condensation and Its ApplicationsAnnual Review of Condensed Matter Physics, 2018
- Decorated tensor network renormalization for lattice gauge theories and spin foam modelsNew Journal of Physics, 2016
- A practical introduction to tensor networks: Matrix product states and projected entangled pair statesAnnals of Physics, 2014
- Spin Foam Models with Finite GroupsJournal of Gravity, 2013
- The Spin-Foam Approach to Quantum GravityLiving Reviews in Relativity, 2013
- Coarse-graining renormalization by higher-order singular value decompositionPhysical Review B, 2012
- Coarse graining methods for spin net and spin foam modelsNew Journal of Physics, 2012
- Tensor-entanglement-filtering renormalization approach and symmetry-protected topological orderPhysical Review B, 2009
- Entanglement RenormalizationPhysical Review Letters, 2007
- Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice ModelsPhysical Review Letters, 2007