Arrested Relaxation in a Disorder-Free Coulomb Spin Liquid

Abstract

We investigate Coulomb spin liquids in classical spin-3/2 ice and show that the enlarged on-site Hilbert space gives rise to a qualitatively new class of such phases. Beyond the conventional magnetic monopoles of spin-1/2 ice, the system hosts additional low-energy crystal-field excitations, whose interplay with monopoles significantly modifies both equilibrium and non-equilibrium properties. Following a thermal quench, we find a pronounced dynamical arrest manifested in an exponentially long-lived {athermal} plateau in spin autocorrelations. This constitutes a rare example of dynamical arrest in a short-range interacting, disorder-free system. We demonstrate that the arrested dynamics originate from novel composite excitation structures unique to spin-3/2 ice and from kinetically constrained relaxation pathways that require activated processes. Our results establish higher-spin ice as a fertile platform for realising unconventional Coulomb spin liquids and dynamical arrest without quenched disorder.

Figures (9)

• Figure 1: The spin autocorrelation, ${\cal A}(t_{\rm MC}) = \braket{S^z_i(t_{\rm MC})S^z_i(0)}$ (where $\braket{\cdot}$ denotes average over space and Monte-Carlo runs), shows dynamical arrest following a thermal quench from a high-temperature $T_i=1$ to a final temperature of $T_q=0.01$ (measured in units such that $J=1$). This is manifested in a long-lived plateau in Monte-Carlo time, $t_{\rm MC}$. Different colours denote different values of $\varepsilon_{\delta}$ (legend in the main panel) whereas different markers/intensities denote different system sizes $L$ (legend in inset). The height as well as the temporal extent of the plateau are independent of $L$. The scaling collapse in the inset shows that the plateau extends up to timescales which grow exponentially with $|\varepsilon_\delta|$.
• Figure 2: Elementary lowest-energy excitations in different parameter regimes. The circles of different colours denote the four different states of a local $S=3/2$ degree of freedom as indicated in the legend. The translucent grey and red circles in (a) and (d) denote a magnetic monopole charge of ${\cal Q}_\boxtimes=1$ and $-1$ respectively in the corresponding tetrahedra. For ${1.8J<\Delta<2J}$ (panels (b) and (c)), the lowest-energy excitations are charge-neutral $\delta$ excitations as exemplified by the absence of any monopole.
• Figure 3: The joint probability $P(N_{\rm cl}^\delta,N_{\rm cl}^{\cal Q})$ of the cluster sizes and their monopole content as well the conditional probability $P({\cal Q}_{\rm cl}|N_{\rm cl}^{\cal Q}\neq 0)$ of the monopole charge at three different Monte-Carlo times (different columns) following a thermal quench from $T_i=1$ to $T_q=0.01$ for $\varepsilon_\delta=-0.08$. The $t_{\rm MC}=0$ data (shown in panels (a)) corresponds to equilibrium at $T_i$. The inset in (a2) evinces the system-spanning clusters with $N_{\rm cl}^\delta\sim O(L^3)$. The middle and right columns correspond to representative $t_{\rm MC}$ during the initial fast quench and metastable plateau respectively. The red circles in (c2) and (c3) highlight clusters with $(N_{\rm cl}^\delta,N_{\rm cl}^{\cal Q},{\cal Q}_{\rm cl})=(2,3,\pm 3)$ as discussed in the text.
• Figure 4: Arrested relaxation dynamics of the excitations under thermal quench from $T_i=1$ to $T_q=0.01$ for $\varepsilon_\delta<0$, manifested in the exponentially long lived, athermal plateaux in the densities of $\delta$ and monopole excitation, $\rho_\delta$ and $\rho_{|\cal Q|}$, respectively. Different colours denote different values of $\varepsilon_\delta$ and different markers/intensities denote different system sizes. The insets show the lifetime of the plateaux is $\tau = \exp(|\varepsilon_\delta|/T_q)$, identical to that of the spin-autocorrelation in Fig. \ref{['fig:autocorr']}, as scaling $t_{\rm MC}$ by $\tau$ collapses the knees of the plateaux.
• Figure 5: Dynamics of (a) $\rho_{|\cal Q|}$ and (b) $\rho_\delta$ as function of $t_{\rm MC}$ following a thermal quench from $T_i=0.08$ to $T_q=0.005$, for $\varepsilon_\delta = 0.012$. The inset in (a) shows the final crash of $\rho_{|\cal Q|}$ for different $L$ collapses when $t_{\rm MC}$ is rescaled by $t_R\sim O(L^3)$. The inset in (b) shows the residual plateau in $\rho_\delta$, quantified by $\Delta\rho_\delta = \rho_\delta(t_{\rm MC}\to\infty)-\rho_{\rm eq}$ vanishes as $L\to\infty$ polynomially.