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Extracting critical exponents for sequences of numerical data via series extrapolation techniques
Kris Cöster1, Kai Phillip Schmidt2
1Lehrstuhl für Theoretische Physik I, Otto-Hahn-Str. 4, TU Dortmund, D-44221 Dortmund, Germany.
Physical Review. E
|September 15, 2016
Summary
We present a new method to find critical exponents in quantum lattice models using numerical data. This approach reformulates data as series expansions, enabling accurate extraction of critical points and exponents.
Area of Science:
- Quantum physics
- Condensed matter physics
- Statistical mechanics
Background:
- Extracting critical exponents is crucial for understanding quantum phase transitions.
- Existing methods for nonperturbative calculations can be computationally intensive.
- Numerical data from methods like linked-cluster expansions often require sophisticated analysis.
Purpose of the Study:
- To develop a generic, versatile scheme for extracting critical exponents from numerical data sequences.
- To provide a method applicable to various nonperturbative techniques in quantum lattice models.
- To demonstrate the scheme's efficacy on a relevant physical system.
Main Methods:
- Reformulating numerical data sequences as a series expansion in a pseudoparameter.
- Utilizing standard series expansion extrapolation techniques.
- Applying the scheme to analyze the deconfinement transition in the spin-1/2 Heisenberg chain.
Main Results:
- Successfully extracted critical exponents from numerical data.
- Demonstrated the scheme's applicability to a realistic quantum model.
- Validated the method's potential for analyzing critical phenomena.
Conclusions:
- The proposed generic scheme offers an efficient way to determine critical exponents.
- This approach enhances the analysis of numerical data from quantum lattice models.
- It provides a powerful tool for studying critical properties in condensed matter systems.
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