Using Tensor Network States for Lattice Gauge Theories

Tensor Network (TN) potential for the study of strongly correlated systems extends far beyond their original realm of application in the context of condensed matter problems. One particular scenario where TN techniques should be helpful is that of Lattice Gauge Theories in their Hamiltonian version. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by traditional Monte Carlo simulations, Tensor Networks can be readily used for problems which more standard techniques cannot easily tackle, due to the appearance of a sign problem, such as in the presence of a chemical potential, or out-of-equilibrium dynamics.

The last years have seen an increasing interest in this particular application of Tensor Network methods. In this talk I will present some of the work we have been developing in this area. In particular, using the Schwinger model as a testbench, we have shown that Matrix Product States (MPS) are suitable to approximate low energy states precisely enough to allow for extremely accurate finite size and continuum limit extrapolations of ground state properties, mass gaps and temperature dependent quantities. The feasibility of the method has already been tested also for non-Abelian models, out-of-equilibrium scenarios, and non-vanishing chemical potential.