Tensor Networks for Lattice Gauge Theories with Continuous Groups

• Main Authors: L. Tagliacozzo, A. Celi, M. Lewenstein
• Format: Article
• Language: English
• Published: American Physical Society 2014-11-01
• Series: Physical Review X
• Online Access: http://doi.org/10.1103/PhysRevX.4.041024

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-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z_{2} lattice gauge theory and the Rokhsar-Kivelson point of the U(1) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.