Domain-wall melting and entanglement in free-fermion chains with a band structure

Abstract

We study the melting of a domain wall in free-fermion chains, where the periodic variation of the hopping amplitudes gives rise to a band structure. It is shown that the entanglement grows logarithmically in time, and the prefactor is proportional to the number of filled bands in the initial state. For a dimerized chain the particle density and current are found to have the same expressions as in the homogeneous case, up to a rescaling of the velocity. The universal contribution to the entropy profile is then doubled, while the non-universal part can be extracted numerically from block-Toeplitz matrices.

Figures (9)

• Figure 1: Fermi points $q_\pm$ as a function of $n/t$, for various dimerizations $\delta$.
• Figure 2: Particle density (left) and current (right) profiles at $t=300$ for various dimerizations. The symbols are the numerical data obtained for an open chain with $N=300$, while the red solid lines show the hydrodynamic limits \ref{['dens']} and \ref{['curr']}, respectively.
• Figure 3: Entropy profile at $t=200$ as a function of the scaling variable $\zeta$, for various dimerizations $\delta$. The red line shows the analytical result \ref{['Sdw']} for the $\delta=0$ case.
• Figure 4: Entropy profile with the universal contribution \ref{['Sudwdim']} subtracted (symbols), and compared to the function $S_0(\zeta)$ in \ref{['SbT']} obtained numerically (solid lines). The red dashed line shows the result \ref{['Sd1']} obtained in the limit $\delta \to 1$.
• Figure 5: Left: entanglement entropy for a half-chain as a function of time and various $\delta$. The blue dashed line shows the function \ref{['Sdw']} with $\nu=0$, while the red one has a doubled prefactor $1/3$. Right: oscillatory part of the entropy, fitted with the ansatz \ref{['Sosc']} as shown by the red lines.