Multiscale quantum criticality: Pomeranchuk instability in isotropic metals
- 12 October 2009
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 80 (16), 165116
- https://doi.org/10.1103/physrevb.80.165116
Abstract
As a paradigmatic example of multiscale quantum criticality, we consider the Pomeranchuk instability of an isotropic Fermi liquid in two spatial dimensions, . The corresponding Ginzburg-Landau theory for the quadrupolar fluctuations of the Fermi surface consists of two coupled modes, critical at the same point, and characterized by different dynamical exponents: one being ballistic with dynamical exponent and the other one is Landau damped with , thus giving rise to multiple dynamical scales. We find that at temperature , the ballistic mode governs the low-energy structure of the theory as it possesses the smaller effective dimension . Its self-interaction leads to logarithmic singularities, which we treat with the help of the renormalization group. At finite temperature, the coexistence of two different dynamical scales gives rise to a modified quantum-to-classical crossover. It extends over a parametrically large regime with intricate interactions of quantum and classical fluctuations leading to a universal dependence of the correlation length independent of the interaction amplitude. The multiple scales are also reflected in the phase diagram and in the critical thermodynamics. In particular, we find that the latter cannot be interpreted in terms of only a single dynamical exponent whereas, e.g., the critical specific heat is determined by the mode, the critical compressibility is found to be dominated by the fluctuations.
Keywords
Other Versions
This publication has 38 references indexed in Scilit:
- Quantum criticality in heavy-fermion metalsNature Physics, 2008
- Fermi-liquid instabilities at magnetic quantum phase transitionsReviews of Modern Physics, 2007
- Multiple Energy Scales at a Quantum Critical PointScience, 2007
- Breakdown of the Perturbative Renormalization Group at Certain Quantum Critical PointsPhysical Review Letters, 2004
- Quantum Field Theory and Critical PhenomenaPublished by Oxford University Press (OUP) ,2002
- Transport Anomalies and Marginal-Fermi-Liquid Effects at a Quantum Critical PointPhysical Review Letters, 2000
- Quantum critical behavior of clean itinerant ferromagnetsZeitschrift für Physik B Condensed Matter, 1997
- Anomalous Properties around Magnetic Instability in Heavy Electron SystemsJournal of the Physics Society Japan, 1995
- Effect of a nonzero temperature on quantum critical points in itinerant fermion systemsPhysical Review B, 1993
- Quantum critical phenomenaPhysical Review B, 1976