Universally Diverging Grüneisen Ratio of Holographic Quantum Criticality

Abstract

Quantum criticality is a hallmark of strongly correlated electron systems, as seen in heavy-fermion materials and high-temperature superconductors. Holographic duality provides a powerful framework to investigate these systems by translating them into weakly coupled classical gravity living in one higher dimension. Here, we harness this approach to study a field-induced quantum critical point with dynamical exponent $z=3$ in Einstein-Maxwell-Chern-Simons theory. Our analysis of its thermodynamic properties reveals a new universality class. Notably, we identify a diverging Grüneisen ratio with universal scaling $\sim T^{-2/3}$, a behavior that closely mirrors recent experiments on the heavy-fermion material CeRh$_6$Ge$_4$. These findings advance our understanding of metallic quantum criticality and highlight the potential of holographic duality as a tool for studying correlated quantum matters.

Figures (12)

• Figure 1: Holographic description of quantum criticality. The dual quantum many-body system lives at the boundary ($r=0$) of the bulk gravity system. The holographic radial coordinate $r$ geometries the energy scale or the renormalization group (RG) flow of the boundary system: processes near the boundary ($r\sim0$) describe the short-distance, ultraviolet dynamics of the dual system, while processes in the interior ($r\gg0$) capture its universal low-energy dynamics. Within this holographic framework, operators in the boundary quantum field theory are dual to classical fields in the bulk, where external sources for these operators are encoded in the asymptotic behavior of the corresponding bulk fields. QPTs are realized by tuning the asymptotic boundary conditions of the gravitational theory, which leads to distinct scaling geometries in the deep infrared regions. The finite temperature physics of the boundary QPT, including its QCR, can be obtained by heating up the zero temperature scaling geometries, i.e. by considering a black hole located at $r=r_h$.
• Figure 2: Entropy density $s$ and its quantum critical behavior.a Contour plot of the entropy density in $T$-$B$ plane. White lines represent the isentropic lines, while red dot represents the QCP. b Temperature-dependent power $m$ of entropy $S \propto T^{m}$, where $m = \frac{d\log{s}}{d\log{T}}$. Orange region indicates the QCR hosting the quantum critical scaling $s\propto T^{1/3}$. Blue region represents the fractionalized phase, while the purple region is the cohesive phase. c Temperature dependence of entropy in different fields. Inset illustrates the zero point entropy at the fractionalized phase. d Quantum critical scaling function $\phi_s(x)$ extracted from the collapse of entropy density data for temperatures $10^{-6}\leq T\leq10^{-4}$. The plots are shown for $k=k_{\text{susy}}=2/\sqrt{3}$ and $\mu=1$.
• Figure 3: Specific heat near the QCP.a Isothermal specific heat as a functions of magnetic field. The vertical dashed line marks the critical field $B_c\approx 0.332$ of the QCP. b Scaling function $\phi_c(x)$ of the specific heat.
• Figure 4: Magnetic properties of the QPT.a Magnetic field dependence of magnetization $M_B$ at different temperatures. The vertical dashed line marks the location of QCP. b Behavior of magnetic susceptibility $\chi_B$ with respect to $B$ for various temperatures. The plots are shown for $k=k_{\text{susy}}=2/\sqrt{3}$ and $\mu=1$.
• Figure 5: Order parameter of the holographic QCP.a Magnetic field dependence of the ratio of parallel shear viscosity to entropy density $\eta/s$ at extremely low temperature $T=10^{-6}$. b The ratio of fractionalized charge to total charge $\rho_{\text{frac}}/\rho$ at extremely low temperature $T=10^{-6}$. Inset illustrates the behavior of $\rho_{\text{frac}}/\rho$ near the QCP. The plots are shown for $k=k_{\text{susy}}=2/\sqrt{3}$ and $\mu=1$.