For translationally invariant infinite MPS, finite entanglement scaling has emerged as a powerful alternative that has many advantages over finite-size scaling for the calculation of critical phenomena. I will give an overview of the ideas behind finite entanglement scaling, and discuss in detail approaches using higher moments, leading to the infinite-size version of the 4th order (Binder) cumulant. By choosing appropriate cumulant ratios, critical points can be determined without the need to use the bond dimension as a scaling parameter, which is a major advantage over earlier approaches. The scheme also applies to quantities that are not normally regarded as local order parameters, such as time reversal and spatial inversion, which allows the quick and accurate determination of critical points separating symmetry-protected phases.
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