Holographic metamagnetism, quantum criticality, and crossover behavior

• Published in: The journal of high energy physics Vol. 2010; no. 5
• Main Authors: D’Hoker, Eric, Kraus, Per
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2010; Springer Nature B.V
• Subjects: Charge density; Classical and Quantum Gravitation; Critical field (superconductivity); Critical point; Crossovers; Elementary Particles; Fermi liquids; Field theory (physics); High energy physics; Magnetic fields; Magnetization; Mathematical analysis; Numerical analysis; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Relativity Theory; Scaling laws; Specific heat; String Theory; Symmetry; Black Holes in String Theory; Gauge-gravity correspondence; AdS-CFT Correspondence
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2010)083

Using high-precision numerical analysis, we show that 3+1 dimensional gauge theories holographically dual to 4 + 1 dimensional Einstein-Maxwell-Chern-Simons theory undergo a quantum phase transition in the presence of a finite charge density and magnetic field. The quantum critical theory has dynamical scaling exponent z = 3, and is reached by tuning a relevant operator of scaling dimension 2. For magnetic field B above the critical value B c , the system behaves as a Fermi liquid. As the magnetic field approaches B c from the high field side, the specific heat coefficient diverges as 1/( B - B c ), and non-Fermi liquid behavior sets in. For B < B c the entropy density s becomes non-vanishing at zero temperature, and scales according to . At B = B c , and for small non-zero temperature T , a new scaling law sets in for which s ∼ T 1/3 . Throughout a small region surrounding the quantum critical point, the ratio s / T 1/3 is given by a universal scaling function which depends only on the ratio ( B - B c )/ T 2/3 . The quantum phase transition involves non-analytic behavior of the specific heat and magnetization but no change of symmetry. Above the critical field, our numerical results are consistent with those predicted by the Hertz/Millis theory applied to metamagnetic quantum phase transitions, which also describe non-analytic changes in magnetization without change of symmetry. Such transitions have been the subject of much experimental investigation recently, especially in the compound Sr 3 Ru 2 O 7 , and we comment on the connections.