Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models

摘要: We analyze the problem of extracting correlation length from infinite matrix product states (MPS) and corner transfer (CTM) simulations. When is calculated directly matrix, it typically significantly underestimated for finite bond dimensions used in numerical simulation. This true even when one considers ground at a distance critical point. In this article we introduce extrapolation procedure to overcome problem. To that end quantify how much dominant part MPS/CTM spectrum deviates being continuous. The latter necessary capture exact asymptotics function where exponential decay modified by an additional algebraic term. By extrapolating such refinement parameter zero, show are able recover value with high accuracy. generic setting, our method reduces error factor $\sim 100$ as compared results obtained without 10$ simple schemes employing dimension. test approach number solvable models both 1d 2d. Subsequently, apply one-dimensional XXZ spin-$\frac{3}{2}$ Bose-Hubbard massive regime vicinity Berezinskii-Kosterlitz-Thouless then fit scaling form extract position point obtain comparable or better than those other state-of-the-art methods. Finally, can be recovered within approach.