Finite-Size Scaling of Typicality-Based Estimates

Schnack J, Richter J, Heitmann T, Richter J, Steinigeweg R (2020)
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES 75(5): 465-473.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Schnack, JürgenUniBi ; Richter, Johannes; Heitmann, Tjark; Richter, Jonas; Steinigeweg, Robin
Abstract / Bemerkung
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.
Stichworte
Spin Systems; Thermodynamic Observables; Trace Estimators; Typicality
Erscheinungsjahr
2020
Zeitschriftentitel
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
Band
75
Ausgabe
5
Seite(n)
465-473
ISSN
0932-0784
eISSN
1865-7109
Page URI
https://pub.uni-bielefeld.de/record/2944201

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Schnack J, Richter J, Heitmann T, Richter J, Steinigeweg R. Finite-Size Scaling of Typicality-Based Estimates. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES. 2020;75(5):465-473.
Schnack, J., Richter, J., Heitmann, T., Richter, J., & Steinigeweg, R. (2020). Finite-Size Scaling of Typicality-Based Estimates. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 75(5), 465-473. doi:10.1515/zna-2020-0031
Schnack, J., Richter, J., Heitmann, T., Richter, J., and Steinigeweg, R. (2020). Finite-Size Scaling of Typicality-Based Estimates. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES 75, 465-473.
Schnack, J., et al., 2020. Finite-Size Scaling of Typicality-Based Estimates. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 75(5), p 465-473.
J. Schnack, et al., “Finite-Size Scaling of Typicality-Based Estimates”, ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, vol. 75, 2020, pp. 465-473.
Schnack, J., Richter, J., Heitmann, T., Richter, J., Steinigeweg, R.: Finite-Size Scaling of Typicality-Based Estimates. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES. 75, 465-473 (2020).
Schnack, Jürgen, Richter, Johannes, Heitmann, Tjark, Richter, Jonas, and Steinigeweg, Robin. “Finite-Size Scaling of Typicality-Based Estimates”. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES 75.5 (2020): 465-473.

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