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Approaching Lattice Gauge Theories with Tensor Networks – From real-time dynamics to overcoming the sign problem - Stefan Kühn

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In recent years there has been quite some effort to apply Matrix Product States (MPS) and more general Tensor Networks (TN) to lattice gauge theories. Contrary to the standard Euclidean-time Monte Carlo approach, which faces a major obstacle in the sign problem, numerical methods based on TN are free from the sign problem and allow to some extent simulating time evolution. Moreover, TN are also a suitable tool to explore proposals for potential future quantum simulators for lattice gauge theories.


In this talk I am going to present some examples where these possibilities allow novel insight into lattice gauge theories. After briefly introducing MPS, I will mainly focus on two models: The first part of the talk is going to be about the Schwinger model. I will show how MPS can help to explore proposals for potential future quantum simulators for this model by studying their spectral properties and simulating adiabatic preparation protocols for the interacting vacuum.

Furthermore, I will show an explicit example where TN allow to overcome the Monte Carlo sign problem in a lattice calculation by studying the zero-temperature phase structure for the two-flavor case at non-zero chemical potential with MPS.


In the second part, I am focusing on a non-Abelian gauge model, namely a 1+1 dimensional SU(2) lattice gauge theory. Using MPS, the phenomenon of string breaking in this theory can be studied in real time, thus allowing to gain new insight into this process. Moreover, I will show how the gauge field can be integrated out for systems with open boundary conditions and how to obtain a formulation which allows to address the model more efficiently with MPS.