Efficient evaluation of high-order moments and cumulants in tensor network states

Understand

We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several applications for such quantities.

• For example, the second cumulant of the energy of a state, $\langle \Delta H^2 \rangle$, gives a straightforward method to check the convergence of numerical ground-state approximation algorithms.
• Additionally, we discuss the use of moments and cumulants in the study of phase transitions.
• Of particular interest is the application of our method to calculate the so-called Binder's cumulant, which we use to detect critical points and study the critical exponent of the correlation length with only small finite numerical calculations.