Quantum Physics Division
Faculty of PhysicsAdam Mickiewicz University

Matrix Product States for Lattice Field Theories

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

Proceedings of Science, PoS(LATTICE 2013) 332 (2013)


The term Tensor Network States (TNS) refers to a number of families 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 systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (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 achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbative manner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.


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