Spin subdiffusion in perturbed infinite-U Hubbard chain

Abstract

The $t$-model represents the Hubbard model in the limit $U \to \infty$ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free spinless fermions. However, the sequence of spins is frozen, leading to the Hilbert space fragmentation and nontrivial spin dynamics. We consider integrable and perturbed models with perturbations that break integrability while preserving fragmentation, and show that they exhibit various types of spin dynamics, from ballistic transport to anomalous diffusion in the integrable case, and from diffusion to subdiffusion in the perturbed case. Due to fragmentation, in all cases considered, spin transport is mediated by charge transport, with a particular magnetization dependence, most notably leading to subdiffusion in the grandcanonical average of the perturbed model, with a mechanism distinct from subdiffusion in disordered or dipole-conserving models.

Figures (9)

• Figure 1: Spectrum of the integrable $t$-model vs. flux $\varphi$ for a system of $L =8$ sites. (a) shows results for magnetization $m =0$ with $N_\uparrow =N_\downarrow = 3$, and (b) for $m \ne 0$ with $N_\uparrow =2$ and $N_\downarrow =3$.
• Figure 2: (a),(b) Time-dependence of the spin current, $\langle j_s \rangle(\tau)$, obtained from numerical solution of Eq.\ref{['eq:lindblad']} for $H_t$, given by Eq.\ref{['tjz']} with $\Delta t=0$ on $L=8$. We chose the initial state $|\downarrow0\uparrow0\downarrow0\uparrow0\rangle$ in (a) and $|\downarrow0\uparrow0\uparrow0\uparrow0\rangle$ in (b). (c) and (d) show cumulative averages of the spin currents shown in (a) and (b), respectively.
• Figure 3: (a) Integrated spin diffusion $I_s(\omega)$, as calculated within the integrable $t$-model at $n = 1/2$ for magnetization $m=0$ using MCLM for systems with PBC on $L = 12, 16, 20$ sites. Dotted line denotes the simplest $L \to \infty$ extrapolation. (b) $I_s(\omega)$ (in log-log scale) for $L = 20$ sites, but for different magnetizations $m =0, 0.1, 0.2, 0.4$.
• Figure 4: (a) Integrated $I_s(\omega)$, as calculated within perturbed $t$-model with $\Delta t/t =0.8$ at $n = 1/2$ and $S^z_{tot}=0$ on $L = 12, 16, 20$ sites. (b) Dynamical ${\cal D}_s(\omega)$ (in log-log scale) calculated for $L = 20$ sites at $n = 1/2$ and $m = 0.1$, for different $\Delta t / t = 0.2 - 0.8$.
• Figure 5: Local spin correlations $C_l(\omega)$ (in the log-log scale), at $n=1/2$ and $m=0$ calculated on $L = 20$ sites within the $t-J_z$ model at $J_z/t = 4$, as well as within $t-\Delta t$ at $\Delta t/t = 1$ . The dotted line represents the power-law dependence $\propto \omega^{-3/4}$.