Nonequilibrium Critical Dynamics with Emergent Supersymmetry

TL;DR

This work investigates nonequilibrium critical dynamics at a quantum critical point with emergent $\mathcal{N}=2$ SUSY that separates a Dirac semimetal from a superconductor in a system with SLAC fermions. Using large-scale determinant quantum Monte Carlo, the authors simulate imaginary-time driving across the critical point with a linear protocol and verify full finite-time scaling forms governed by SUSY exponents across the whole drive. A central finding is the equivalence of boson and fermion anomalous dimensions, $\eta_b=\eta_f=\tfrac{1}{3}$, together with a dynamic scaling form for the fermion correlator $G_{\mathrm{f}}$ that reveals a new scaling relation linking the Dirac semimetal phase and the SUSY critical point. The results extend the role of SUSY into nonequilibrium dynamics and provide practical guidance for detecting emergent SUSY in programmable quantum platforms via KZM and FTS.

Abstract

Proposed as an elegant symmetry relating bosons and fermions, spacetime supersymmetry (SUSY) has been actively pursued in both particle physics and emergent phenomena in quantum critical points (QCP) of topological quantum materials. However, how SUSY casts the light on nonequilibrium dynamics remains open. In this letter, we investigate the Kibble-Zurek dynamics across a QCP with emergent $\mathcal{N}=2$ spacetime SUSY between the Dirac semimetal and a superconductor through large-scale quantum Monte Carlo simulation. The scaling behaviors in the whole driven process are uncovered to satisfy the full finite-time scaling (FTS) forms. More crucially, we demonstrate that the emergent SUSY manifests in the intimate relation between the FTS behaviors of fermionic and bosonic observables, namely the fermions and bosons acquire the identical anomalous dimensions. Our work not only brings a fundamental new ingredient into the critical theory with SUSY, but also provide the theoretical guidance to experimental detect of QCP with emergent SUSY from the perspectives of Kibble-Zurek mechanism and FTS.

Figures (3)

• Figure 1: Sketch of the phase diagram with SUSY critical point and the protocol for driven dynamics with different initial states. The correlation time scales for both boson (yellow curve) and fermion (violet curve) are finite in one phase (solid) but divergent (dotted) in the other phase. Far from the critical point, different from usual KZM, the transition time (long-dashed line) here is smaller than the correlation time of part freedom, but larger than that of the other freedom. Around the critical point, FTS region with emergent SUSY (short-dashed line) dominates the scaling behaviors.
• Figure 2: Driven dynamics from the DSM phase.(a) Log-log plots of $M_2$ versus $R$ driven to $U_c$ before (a1) and after (a2) rescaling. Inset in (a1) shows $M_2 \propto L^{-2}$ at $R=5$ (dash-dotted line). For large $R$, power fitting for $L=21$ (brown solid line) shows $M_2 \propto R^{-0.285(3)}$ with the exponent close to $(1+\eta_{\mathrm{b}}-d)/r=-0.312$ (dash line) from Ref. lzx.18sciadv. (b) Curves of $M_2$ versus $g$ for fixed $RL^r=347.5$ and different $L$ before (b1) and after (b2) rescaling. (c) Log-log plots of $G_{\mathrm{f}}$ versus $R$ driven to $U_c$ before (c1) and after (c2) rescaling. Inset in (c1) shows $G_{\mathrm{f}} \propto L^{-2}$ at $R=5$ (dash-dotted line). For large $R$, power fitting for $L=13$ (brown solid line) shows $G_{\mathrm{f}} \propto R^{0.152(4)}$ with the exponent close to $\eta_{\mathrm{f}}/r=0.154$ (dash line) from Ref. lzx.18sciadv. (d) Curves of $G_{\mathrm{f}}$ versus $g$ for fixed $RL^r=347.5$ and different $L$ before (d1) and (d2) after rescaling.
• Figure 3: Driven dynamics from the SC phase.(a) Log-log plots of $M_2$ versus $R$ driven to $U_c$ before (a1) and after (a2) rescaling. For large $R$, power fitting for $L=21$ (brown solid line) shows $M_2 \propto R^{0.61(3)}$ with the exponent close to $(1+\eta_{\mathrm{b}})/r=0.62$ (dash line) from Ref. lzx.18sciadv. (b) Curves of $M_2$ versus $g$ for fixed $RL^r=347.5$ and different $L$ before (b1) and (b2) after rescaling. (c) Semi-log plots of $G_{\mathrm{f}}$ versus $R$ driven to $U_c$ before (c1) and after (c2) rescaling, where the appearance of straight lines indicate the presence of exponential decay. (d) Curves of $G_{\mathrm{f}}$ versus $g$ for fixed $RL^r=20.85$ and different $L$ before (d1) and (d2) after rescaling.