Marginal Fermi liquid at magnetic quantum criticality from dimensional confinement

Metallic quantum criticality is frequently discussed as a source for non-Fermi liquid behavior, but controlled theoretical treatments are scarce. Here we identify and study a novel magnetic quantum critical point in a two-dimensional antiferromagnet coupled to a three-dimensional environment of conduction electrons. Using sign-problem-free quantum Monte Carlo simulations and an effective field-theory analysis, we demonstrate that the quantum critical point is characterized by marginal Fermi liquid behavior. In particular, we compute the electrical resistivity for transport across the magnetic layer, which effectively acts like a Kondo impurity. Due to the presence of the marginal Fermi liquid excitations, the resistivity exhibits a linear decrease with temperature at criticality, in contrast to the usual quadratic decrease. Experimental realizations in Kondo heterostructures are discussed.

Figure 1

(a) Schematic setup of proposed transport experiment on Kondo heterostructure. (b) Schematic temperature dependence of resistivity $\rho \left(T\right)$. The marginal Fermi liquid at the quantum critical point gives rise to a linear decrease with temperature for temperatures below the coherence scale $T_{\text{coh}}$, in contrast to the conventional quadratic decrease in case of a Fermi liquid. At larger temperatures beyond $T_{\text{coh}}$, intrinsic interaction effects in the metal lead to an increase of $\rho \left(T\right)$ (dashed line). (c) Resistivity at the quantum critical point from effective field theory and QMC simulations, both indicating the expected linear scaling and very good quantitative agreement.

Figure 2

Self-energy for (a) order-parameter and (b) fermion fields. Dashed internal lines correspond to $D$ propagators and dotted-dashed ones to $G_{\psi \psi }$ propagators. Squares denote the effective interaction strength $g_{\text{eff}}$.

Figure 3

(a) 3D Fermi surface. (b) Projected 2D Fermi surface. (c) Thermal gap as a function of temperature from Hertz-Millis asymptotics $M^2\left(T\right)\sim TlogT$ (solid line) and QMC at linear system size $L=12$ (dots). (d) Imaginary part of fermionic self-energy as a function of Matsubara frequency from effective field theory (triangles) and $L=12$ QMC (dots) for different temperatures. The black dashed line corresponds to the result at $T=0$. The inset shows the variation at the Matsubara frequency ${\omega }_n=3\pi T$ as a function of temperature, which follows a logarithmic asymptotics (solid line). (e) Imaginary part of retarded fermionic self-energy as a function of real frequency $\omega$ from effective field theory.

Figure 4

Conductivity as a function of temperature from effective field theory at criticality (red solid line) and QMC simulations for $J_{\mathrm{K}}=3.04t\approx J_{\mathrm{K}}^{\mathrm{c}}$ (blue triangles) and $J_{\mathrm{K}}=4.50t>J_{\mathrm{K}}^{\mathrm{c}}$ (yellow triangles) for linear system size $L=10$. The black dotted (dashed) line indicates the linear (quadratic) marginal-Fermi-liquid (Fermi-liquid) scaling.