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Universal Finite-Size Scaling around Topological Quantum Phase Transitions.

Tobias Gulden1, Michael Janas1, Yuting Wang1

  • 1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.

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|January 30, 2016
PubMed
Summary

We found a universal scaling function to distinguish topological phases of matter. This function is valid across different symmetry classes and provides insights into quantum phase transitions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Topological Matter

Background:

  • Topological phase transitions are characterized by critical points described by conformal field theories.
  • Finite-size corrections to energy at criticality relate to the central charge.
  • Understanding behavior away from criticality is crucial for characterizing topological phases.

Purpose of the Study:

  • Investigate finite-size scaling behavior away from topological criticality.
  • Develop a scaling function to differentiate between topological phases.
  • Establish the universality of this function across different symmetry classes.

Main Methods:

  • Analysis of finite-size scaling theory.
  • Derivation of an analytic form for the scaling function.
  • Comparison with numerical simulations.

Main Results:

  • A novel scaling function was identified for finite-size scaling away from criticality.
  • This function effectively discriminates between topological phases based on their topological indices.
  • The scaling function demonstrates universality across all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension.

Conclusions:

  • The derived scaling function provides a universal tool for characterizing topological matter.
  • This work offers new insights into the behavior of quantum systems away from critical points.
  • The findings are applicable to diverse systems in condensed matter physics and quantum field theory.