Dynamical separation of charge and energy transport in one-dimensional Mott insulators

One-dimensional Mott insulators can be described using the sine-Gordon model, an integrable quantum field theory that provides the low-energy effective description of several one-dimensional gapped condensed matter systems, including recent realizations with trapped ultracold atoms. Employing the theory of generalized hydrodynamics, we demonstrate that this model exhibits separation of the transport of topological charge vs energy. Analysis of the quasiparticle dynamics reveals that the mechanism behind the separation is the reflective scattering between topologically charged kinks/antikinks. The effect of these scattering events is most pronounced at strong coupling and low temperatures, where the distribution of quasiparticles is narrow compared to the reflective scattering amplitude. This effect results in a distinctively shaped “arrowhead” light cone for the topological charge.

Figure 1

Illustration of the mechanism behind charge-energy separation and the three-staged “arrowhead” light-cone propagation of the topological charge in the bump release: ($i$) Outwards propagating solitons, whose front follows the dashed line, push all background magnons with them, following reflective kink/antikink scattering. ($ii$) Magnons flow inwards to fill the depleted central region. ($iii$) The remaining magnon depletion propagates outwards. The duration of each stage depends on the coupling strength and temperature.

Figure 2

Half-width of the support of charge-charge (blue) and energy-energy (red) correlators in a bipartition protocol as function of the coupling strength ${\beta }^2/8\pi$. The correlators are computed for dynamics at different temperatures and values of $\xi$ with at most two magnonic levels in the TBA system. The results are computed at discrete points, joined by a line in the plot to emphasize the discontinuous nature of the charge-charge case. The vertical dotted lines indicate the reflectionless points. Dimensionful quantities are given in units defined by setting $m_S=1, \hslash =1$, and $c=1$ as specified in the main text. Note the logarithmic scale of the horizontal axis.

Figure 3

Evolution of topological charge density $\mathtt{q}$ and energy density $\mathtt{e}$ following a bump release in the repulsive $\xi =3$ sine-Gordon model at three different temperatures $T$. Dashed and dotted lines indicate the position of the fastest traveling soliton and magnon for the background state, respectively. The densities are scaled with the factor $(1+t)$ to emphasize features at later times. Dimensionful quantities are given in units defined by setting $m_S=1, \hslash =1$, and $c=1$ as specified in the main text.

Figure 4

Soliton ${\rho }_S$ and (last) magnon ${\rho }_M$ distributions at different times $t$ following a bump release in the repulsive $\xi =3$ sine-Gordon model for three temperatures: (a) $T=0.3$, (b) $T=0.5$, and (c) $T=1.0$. The dashed and dotted lines indicate the positions $z={\overline{v}}_S^{\mathrm{eff}}\left(\theta \right)t$ and $z={\overline{v}}_M^{\mathrm{eff}}\left(\theta \right)t$, respectively. Dimensionful quantities are given in units defined by setting $m_S=1, \hslash =1$, and $c=1$ as specified in the main text.