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Casimir amplitudes in topological quantum phase transitions
M A Griffith1, M A Continentino1
1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150-Urca, 22290-180, Rio de Janeiro, RJ, Brazil.
Physical Review. E
|February 17, 2018
Summary
Topological phase transitions are a new class of quantum critical phenomena. A finite-size scaling approach, using Casimir force calculations, successfully determined universal Casimir amplitudes and confirmed critical exponents.
Area of Science:
- Condensed Matter Physics
- Quantum Critical Phenomena
Background:
- Topological phase transitions represent a novel class of quantum critical phenomena.
- These transitions often lack order parameters or symmetry changes, defying traditional Landau theory.
- A characteristic diverging length scale typically emerges at these transitions.
Purpose of the Study:
- To investigate quantum topological transitions using a scaling approach.
- To determine critical exponents and universality classes for these phenomena.
- To obtain universal Casimir amplitudes at quantum critical points.
Main Methods:
- Application of a finite-size scaling approach to models of quantum topological transitions.
- Utilizing techniques adapted from Casimir force calculations in electromagnetism.
- Analysis of critical exponents and their relation via quantum hyperscaling.
Main Results:
- Successful determination of universal Casimir amplitudes at quantum critical points.
- Verification of the validity of finite-size scaling in topological transition systems.
- Confirmation of previously obtained critical exponent values.
Conclusions:
- Finite-size scaling is a valid and effective method for studying quantum topological transitions.
- The study provides universal Casimir amplitudes, offering new insights into critical phenomena.
- The findings reinforce the understanding of critical exponents and universality in these systems.
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