Holographic Metamagnetism, Quantum Criticality, and Crossover Behavior

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 s\sim 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.Comment: 23 pages, 8 figures v2: added ref

The break up of heavy electrons at a quantum critical point

The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite temperature electronic properties of the material. Magnetic fields are ideal for tuning a material as close as possible to a QCP, where the most intense effects of criticality can be studied. A previous study on theheavy-electron material $YbRh_2Si_2$ found that near a field-induced quantum critical point electrons move ever more slowly and scatter off one-another with ever increasing probability, as indicated by a divergence to infinity of the electron effective mass and cross-section. These studies could not shed light on whether these properties were an artifact of the applied field, or a more general feature of field-free QCPs. Here we report that when Germanium-doped $YbRh_2Si_2$ is tuned away from a chemically induced quantum critical point by magnetic fields there is a universal behavior in the temperature dependence of the specific heat and resistivity: the characteristic kinetic energy of electrons is directly proportional to the strength of the applied field. We infer that all ballistic motion of electrons vanishes at a QCP, forming a new class of conductor in which individual electrons decay into collective current carrying motions of the electron fluid.Comment: Pdf files of article available at http://www.physics.rutgers.edu/~coleman/online/breakup.pdf, pdf file of news and views article available at http://www.physics.rutgers.edu/~coleman/online/nvbreakup.pd

Criticality in correlated quantum matter

At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the cuprates are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.Comment: Final accepted version not including minor stylistic correction

Field-induced quantum fluctuations in the heavy fermion superconductor CeCu2Ge2

Quantum-mechanical fluctuations in strongly correlated electron systems cause unconventional phenomena such as non-Fermi liquid behavior, and arguably high temperature superconductivity. Here we report the discovery of a field-tuned quantum critical phenomenon in stoichiometric CeCu2Ge2, a spin density wave ordered heavy fermion metal that exhibits unconventional superconductivity under ~ 10 GPa of applied pressure. Our finding of the associated quantum critical spin fluctuations of the antiferromagnetic spin density wave order, dominating the local fluctuations due to single-site Kondo effect, provide new information about the underlying mechanism that can be important in understanding superconductivity in this novel compound.Comment: Heavy Fermion, Quantum Critical Phenomeno

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question concerns whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin density wave (SDW) type, or suddenly as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient ($R_H$) - a measure of the Fermi surface volume - in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. $R_H$ undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.Comment: 20 pages, 3 figures; to appear in Natur

Locally critical quantum phase transitions in strongly correlated metals

When a metal undergoes a continuous quantum phase transition, non-Fermi liquid behaviour arises near the critical point. It is standard to assume that all low-energy degrees of freedom induced by quantum criticality are spatially extended, corresponding to long-wavelength fluctuations of the order parameter. However, this picture has been contradicted by recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. In particular, neutron scattering from CeCu$_{6-x}$Au$_x$ has revealed anomalous dynamics at atomic length scales, leading to much debate as to the fate of the local moments in the quantum-critical regime. Here we report our theoretical finding of a locally critical quantum phase transition in a model of heavy fermions. The dynamics at the critical point are in agreement with experiment. We also argue that local criticality is a phenomenon of general relevance to strongly correlated metals, including doped Mott insulators.Comment: 20 pages, 3 figures; extended version, to appear in Natur

Interplay of quantum and classical fluctuations near quantum critical points

For a system near a quantum critical point (QCP), above its lower critical dimension $d_L$, there is in general a critical line of second order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, $d_{eff}=d+z$ ($d$ is the Euclidean dimension of the system and $z$ the dynamic quantum critical exponent) is above its upper critical dimension $d_C$, there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation $\psi=\nu z$ between the shift exponent $\psi$ of the critical line and the crossover exponent $\nu z$, for $d+z>d_C$ by a \textit{dangerous irrelevant interaction}. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.Comment: 10 pages, 6 figures, to be published in Brazilian Journal of Physic

Dynamics and transport near quantum-critical points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N=1 d=1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N=3, d=1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N=3, d=2,3 models describe Heisenberg antiferromagnets with collinear N\'{e}el correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N=2, d=2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical properties of unconventional magnetic systems", Geilo, Norway, April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be published. 46 page

Semi-Holographic Fermi Liquids

We show that the universal physics of recent holographic non-Fermi liquid models is captured by a semi-holographic description, in which a dynamical boundary field is coupled to a strongly coupled conformal sector having a gravity dual. This allows various generalizations, such as a dynamical exponent and lattice and impurity effects. We examine possible relevant deformations, including multi-trace terms and spin-orbit effects. We discuss the matching onto the UV theory of the earlier work, and an alternate description in which the boundary field is integrated out.Comment: 26 pages, 4 figures; v2: typos corrected and report number adde

Overdiagnosis and overtreatment of breast cancer: Progression of ductal carcinoma in situ: the pathological perspective

Ductal carcinoma in situ (DCIS) is encountered much more frequently in the screening population compared to the symptomatic setting. The behaviour of DCIS is highly variable and this presents difficulties in choosing appropriate treatment strategies for individual cases. This review discusses the current data on the frequency and rate of progression of DCIS, the value and limitations of clinicopathological and biological variables in predicting disease behaviour and suggests strategies to develop more robust means of predicting progression of DCIS