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Breakdown of the perturbative renormalization group at certain quantum critical points
D Belitz1, T R Kirkpatrick, Jörg Rollbühler
1Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA.
Physical Review Letters
|November 5, 2004
Summary
Multiple time scales at quantum critical points disrupt perturbative renormalization-group calculations for critical exponents. This breakdown means finite-order results may not approximate true asymptotic behavior, indicating a nonrenormalizable theory.
Area of Science:
- Condensed matter physics
- Quantum criticality
- Statistical mechanics
Background:
- Quantum critical points (QCPs) exhibit unique behavior at absolute zero temperature.
- Renormalization-group (RG) methods are crucial for understanding critical phenomena.
- Perturbative RG expansions can face limitations in complex systems.
Purpose of the Study:
- To investigate the impact of multiple time scales on perturbative RG treatments at QCPs.
- To identify the theoretical implications of such multi-time-scale behavior.
- To provide a physical example illustrating these theoretical challenges.
Main Methods:
- Analysis of loop expansion for critical exponents.
- Identification of conditions leading to coefficient divergence.
- Theoretical framework for nonrenormalizable field theories.
Main Results:
- Presence of multiple time scales at QCPs causes loop expansion breakdown.
- Coefficients in the expansion diverge, invalidating finite-order approximations.
- The issue is equivalent to a nonrenormalizable field theory or a dangerous irrelevant variable.
Conclusions:
- Finite-order perturbative RG results may not approximate true asymptotic critical behavior at QCPs with multiple time scales.
- This phenomenon highlights the limitations of standard perturbative approaches in certain quantum critical systems.
- The quantum ferromagnetic transition in disordered metals serves as a relevant physical example.