Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study

摘要

In spite of their intrinsic one-dimensional nature matrix product states havebeen systematically used to obtain remarkably accurate results fortwo-dimensional systems. Motivated by basic entropic arguments favoringprojected entangled-pair states as the method of choice, we assess the relativeperformance of infinite matrix product states and infinite projectedentangled-pair states on cylindrical geometries. By considering the Heisenbergand half-filled Hubbard models on the square lattice as our benchmark cases, weevaluate their variational energies as a function of both bond dimension aswell as cylinder width. In both examples we find crossovers at moderatecylinder widths, i.e. for the largest bond dimensions considered we find animprovement on the variational energies for the Heisenberg model by usingprojected entangled-pair states at a width of about 11 sites, whereas for thehalf-filled Hubbard model this crossover occurs at about 7 sites.