Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Finite-Size Scaling of Typicality-Based Estimates


Richter,  Johannes
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 4MB

Supplementary Material (public)
There is no public supplementary material available

Schnack, J., Richter, J., Heitmann, T., Richter, J., & Steinigeweg, R. (2020). Finite-Size Scaling of Typicality-Based Estimates. Zeitschrift für Naturforschung, A, 75(5), 465-473. doi:10.1515/zna-2020-0031.

Cite as: https://hdl.handle.net/21.11116/0000-0006-EE37-1
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation, or trace estimator, provides a powerful approach to, e.g. thermodynamic quantities for systems with large Hilbert-space sizes, which usually cannot be treated exactly, analytically or numerically. Here, we discuss the finite-size scaling of the accuracy of such trace estimators from two perspectives. First, we study the full probability distribution of random-vector expectation values and, second, the full temperature dependence of the standard deviation. With the help of numerical examples, we find pronounced Gaussian probability distributions and the expected decrease of the standard deviation with system size, at least above certain system-specific temperatures. Below and in particular for temperatures smaller than the excitation gap, simple rules are not available.