On prethermal time crystals from semi-holography

Abstract

We demonstrate the existence of a pair of almost dissipationless oscillating modes at low temperatures in both the shear and sound channels of a hybrid quantum system, comprised of a weakly self-interacting perturbative sector coupled to strongly self-interacting holographic degrees of freedom described by a black hole geometry. We argue that these modes realize prethermal time-crystal behavior in semiholographic systems without fine-tuning and can be observed by measuring operators that probe either the hard (perturbative) or the soft (holographic) sector. We also find novel Gregory Laflamme type instabilities that lead to the formation of inhomogeneities at higher temperatures. These results provide evidence that black holes with planar horizons and dynamical boundary conditions can develop both inhomogeneous and metastable time crystal phases over a wide range of temperatures set by an intermediate scale. Furthermore, they suggest that such phases can be realized without external driving in nonAbelian plasmas of asymptotically free gauge theories in the large-$N$ limit.

Figures (9)

• Figure 1: The QNM of AdS$_4$-Schwarzschild black brane form an infinite tower of paired gapped modes arranged in the characteristic "Christmas tree" structure. At zero momentum, the shear hydrodynamic modes of both the holographic and MIS sectors reside at the origin. The inset zooms into the near-origin region, clearly showing the two coincident shear hydrodynamic poles at $\mathfrak{w} = 0$ and the MIS gapped pole lying on the negative imaginary axis.
• Figure 2: Prethermal time crystal modes in the shear channel. The shear hydrodynamic (gapless) mode is displayed in orange and the non-hydrodynamic (gapped) mode in blue. The solid dots represent their respective positions in the complex frequency plane for $\mathfrak{q} = 0$. The respective colored lines with arrows show the trajectories of these modes as $\mathfrak{q}$ is increased from zero. The crosses denote the smallest $|\text{Im}(\mathfrak{w})|$. We refer to these modes as prethermal time crystal (PTC) modes with the corresponding PTC frequency (crosses) and momentum denoted by $(\mathfrak{w}_g, \mathfrak{q}_g)$. The colored lines are generated with $\gamma T^3=0.0005$, while the gray dashed line denotes the trajectory of the MIS k-gap modes for $\gamma = 0$. In this figure, we have set $T=1$.
• Figure 3: Prethermal time crystal modes in the shear channel: Dispersion relations. Panels (a) and (b) show $|\text{Re}\, \mathfrak{w} (\mathfrak{q})|$ and $\text{Im} \,\mathfrak{w} (\mathfrak{q})$ respectively, corresponding to the PTC modes in \ref{['fig:shear-collision']}. All parameters are identical to those in \ref{['fig:shear-collision']}. The orange curve denotes the gapless branch, while the blue curve corresponds to the gapped branch. $|\text{Re}\, \mathfrak{w} |$ is equal for both, so the two curves overlap in (a). The vertical gray dashed line marks $\mathfrak{q} = \mathfrak{q}_g$, where $| \text{Im } \mathfrak{w} |$ has the samllest value. The inset panels zoom into the small-$\mathfrak{q}$ region, where the dispersion relation coincides with that of the decoupled MIS sector. At larger momenta, $|{\rm Re} \mathfrak{w} (\mathfrak{q})|$ exhibits linear scaling with a clear crossover between two distinct slopes.
• Figure 4: The absolute value of the imaginary part of frequency, $\mathfrak{w}_g$, of the PTC modes of the shear channel as a function of $\gamma T^3$. The crosses are the data points. The line is the power-law fit.
• Figure 5: (a) The absolute value of the real part of frequency, $\mathfrak{w}_g$, and (b) the momentum, $\mathfrak{q}_g$ of the PTC modes of the shear channel as functions of $\gamma T^3$ with a power law fitting. The crosses are the data points. The lines are the power-law fits.