The dynamics of quantum criticality via Quantum Monte Carlo and holography

TL;DR

The paper tackles the challenge of real-time quantum-critical dynamics in systems without quasiparticles by combining high-precision quantum Monte Carlo simulations of the 2D Bose-Hubbard QCP with holographic continuation based on the AdS/CFT correspondence. It first establishes universal imaginary-frequency conductivity $\sigma(i\omega/T)$ and thermodynamic scaling, then uses a holographic model with a Weyl coupling $\gamma$ to perform an analytic continuation to real frequencies, extracting $\sigma(\omega/T)$ and the quasinormal-mode spectrum. The analysis finds a particle-like charge response ($\gamma>0$) and identifies a dominant D-QNM on the imaginary axis that governs low-frequency transport, all consistent with a universal scaling framework and sum rules. This work demonstrates a concrete, quantitative bridge between holographic theories and realistic condensed-matter CFTs, with implications for cold-atom experiments near the Mott transition and extensions to other universality classes such as $O(N)$.

Abstract

Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose excitations cannot be described in a quasiparticle basis. We present detailed quantum Monte Carlo results for two separate lattice realizations: their low-frequency conductivities are found to have the same universal dependence on imaginary frequency and temperature. We then use the structure of the real time dynamics of conformal field theories described by the holographic gauge/gravity duality to make progress on the difficult problem of analytically continuing the Monte Carlo data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point, and on the spectrum of quasinormal modes in the vicinity of the superfluid-insulator quantum phase transition. Extensions to other observables and universality classes are discussed.

Figures (7)

• Figure 1: Probing quantum critical dynamics(a) Phase diagram of the superfluid-insulator quantum phase transition as a function of $t/U$ (hopping amplitude relative to the onsite repulsion) and temperature $T$ at integer filling of the bosons. The conformal QCP at $T=0$ is indicated by a blue disk. (b) Quantum Monte Carlo data for the frequency-dependent conductivity, $\sigma$, near the QCP along the imaginary frequency axis, for both the quantum rotor and Villain models. The data has been extrapolated to the thermodynamic limit and zero temperature. The error bars are statistical, and do not include systematic errors arising from the assumed forms of the fitting functions, which we estimate to be 5--10%.
• Figure 2: Quantum Monte Carlo data (a) Finite-temperature conductivity for a range of $\beta U$ in the $L\to\infty$ limit for the quantum rotor model at $(t/U)_c$. The solid blue squares indicate the final $T\to 0$ extrapolated data. (b) Finite-temperature conductivity in the $L\to\infty$ limit for a range of $L_\tau$ for the Villain model at the QCP. The solid red circles indicate the final $T\to 0$ extrapolated data. The inset illustrates the extrapolation to $T=0$ for $\omega_n/(2\pi T)=7$. The error bars are statistical for both a) and b).
• Figure 3: Holographic spacetime, which is asymptotically AdS and contains a planar black hole. The current operator of the CFT, $J_\mu$, is holographically dual to a gauge field, $A_\mu$, in the higher-dimensional bulk. The temperature associated with the horizon of the black hole is equal to the temperature of the CFT.
• Figure 4: Holographic continuation.(a) The markers represent Monte Carlo data for the conductivity at the superfluid-insulator QCP at imaginary frequencies, see Fig. \ref{['fig:sigmaonlyextrap']}. The solid green line is the best fit to the holographic conductivity, obtained when $\gamma=0.08$, with a rescaling of the $\omega/T$-dependence by $\alpha=0.35$ (the purple dotted line is without the rescaling). The red dashed curve is for $\gamma=-0.08$, and suggests that a vortex-like $\sigma$ does not occur. (b) Real part of the holographic conductivity evaluated at complex frequencies, where the imaginary/real axis dependence is highlighted by the green/blue line. The arrow represents the continuation procedure. (c) Resulting conductivity at real frequencies (solid blue line). The dashed line is the vortex-like response obtained for $\gamma=-0.08$.
• Figure 5: Spectrum of quasinormal charge excitations of the superfluid-insulator QCP. The crosses/circles identify poles/zeros of $\sigma(\omega/T)$ in the complex frequency plane. The dominant QNM, labeled D-QNM, is found to be a pole. It gives rise to a peak in $\mathop{\mathrm{Re}}\nolimits\sigma(\omega/T)$ at small frequencies.