Towards overcoming the Monte Carlo sign problem with tensor networks

¹ Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
² Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
³ Adam Mickiewicz University, Faculty of Physics, Umultowska 85, 61-614 Poznń, Poland
⁴ NIC, DESY, Platanenallee 6, 15738 Zeuthen, Germany
⁵ AISIN AW Co., Ltd., 10 Takane, Fujii-cho, Anjo, Aichi, 444-1192, Japan

^a e-mail: kcichy@th.physik.uni-frankfurt.de

Published online: 22 March 2017

Abstract

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.