Quantum Physics Division
Faculty of PhysicsAdam Mickiewicz University

The mass spectrum of the Schwinger model with Matrix Product States

M.C. Banuls1 , K. Cichy2,3 , J. I. Cirac 1,2 , K. Jansen2 , H. Sait4

3 Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614, Poznan, Poland
1 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
2 NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
4 Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki

Journal of High Energy Physics, 1311,158 (2013)


The term Tensor Network States (TNS) refers to a number of fam ilies of states that represent different ansätze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body sy stems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theori es (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques . While the dimensions and sizes of the systems amenable to TNS studies are still far from those a chievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems whic h more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tack le. Examples of such problems are the presence of a chemical potential or out-of-equilibr ium dynamics. We have explored the performance of Matrix Product States in the case of the Schwi nger model, as a widely used testbench for lattice techniques. Using finite-size, open b oundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativ e manner. The precision achieved by the method allows for accurate finite size and continuum limi t extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, t hus showing the feasibility of these techniques for gauge theory problems


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