Holographic metamagnetism, quantum criticality, and crossover behavior

Open Access


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 \( s \sim \sqrt {{B_c} - B} \). At B = B c , and for small non-zero temperature T, a new scaling law sets in for which sT 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 Sr3Ru2O7, and we comment on the connections.


Gauge-gravity correspondence Black Holes in String Theory AdS-CFT Correspondence 


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© The Author(s) 2010

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Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesU.S.A.

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