Holographic quantum criticality from multi-trace deformations

TL;DR

This work demonstrates how multi-trace (double-trace) deformations in holographic duals provide a powerful mechanism to induce spontaneous symmetry breaking and to realize a new class of holographic superconductors, including at zero charge density. It identifies a quantum critical point controlled by an intermediate $AdS_2$ region, yielding non-mean-field exponents determined by the IR operator dimension and exhibiting locally quantum critical dynamics. The authors develop a detailed RG and holographic analysis, derive universal IR Green's functions, and verify scaling relations through fully backreacted numerical solutions, while outlining extensions to magnetic fields and Lifshitz-like normal phases. The results offer a robust framework for modeling quantum criticality in strongly correlated systems and connect to phenomena observed in heavy-fermion materials, antiferromagnetism, and unconventional superconductivity.

Abstract

We explore the consequences of multi-trace deformations in applications of gauge-gravity duality to condensed matter physics. We find that they introduce a powerful new "knob" that can implement spontaneous symmetry breaking, and can be used to construct a new type of holographic superconductor. This knob can be tuned to drive the critical temperature to zero, leading to a new quantum critical point. We calculate nontrivial critical exponents, and show that fluctuations of the order parameter are `locally' quantum critical in the disordered phase. Most notably the dynamical critical exponent is determined by the dimension of an operator at the critical point. We argue that the results are robust against quantum corrections and discuss various generalizations.

Figures (14)

• Figure 1: The off-shell potential as we tune $\kappa$. The black dashed curve is the fine-tuned theory with $\kappa=0$, the blue curve is $\kappa<0$, and the red curve is $\kappa>0$. This is a strongly coupled version of the standard Landau-Ginzburg symmetry breaking mechanism.
• Figure 2: The order parameter $\alpha = \langle {\mathcal{O}}\rangle$ and free energy density $f$ across the second order phase transition down to zero temperature. In the figure on the right, the dashed red line is the free energy of the normal phase (Schwarzschild AdS solution) and the black line is the free energy of the condensed phase. We used a case with $\Delta_-=1$, and bulk potential $V(\psi)=\sinh^2(\psi/\sqrt{2})(\cosh(\sqrt{2}\psi)-5)=-6-2\psi^2+{\mathcal{O}}(\psi^4)$Gauntlett:2009dnGubser:2009gp. In Faulkner:2010fh it was found that $s_c=0.56$ for this potential. From (\ref{['k1']}), we have $T_c/(-\kappa) \approx 0.62.$
• Figure 3: The critical temperature as a function of $\Delta_-$ for $q=.1, .25, .5$
• Figure 4: The critical temperature, in units of chemical potential, as a function of the UV double trace coupling $\kappa$ for fixed $\Delta_- = 1$ and $q=1/2$. The top curve has $g=0.2$ and has nonzero critical temperature for all $\kappa$. The lower curve has $g = -0.2$ and ends at a quantum critical point.
• Figure 5: The critical temperature close to $\kappa_c$ for different values of $\delta_-$. These are for theories with $q=0$, $\Delta_-=1$, and from left to right: $\delta_-=0.45,0.30,0.26,0.15,0,-0.15.$ Note that when $\delta_->0$ the critical temperature vanishes with a power law, but for $\delta_- \le 0$ it vanishes linearly.