Excitations and impurity dynamics in a fermionic Mott insulator with nearest-neighbor interactions

We study analytically and with the numerical time-evolving block decimation method the dynamics of an impurity in a bath of spinless fermions with nearest-neighbor interactions in a one-dimensional lattice. The bath is in a Mott insulator state with alternating sites occupied and the impurity interacts with the bath by repulsive on-site interactions. We find that when the magnitudes of the on-site and nearest-neighbor interactions are close to each other, the system shows excitations of two qualitatively distinct types. For the first type, a domain wall and an antidomain wall of density propagate into opposite directions, while the impurity stays at the initial position. For the second one, the impurity is bound to the antidomain wall while the domain wall propagates, an excitation where the impurity and bath are closely coupled.

Figure 1

A schematic figure of the initial configuration where the total number of doubly occupied sites is $\langle N_{\uparrow \downarrow }(t=0)\rangle =1$.

Figure 2

(a) The number of doubly occupied sites $\langle N_{\uparrow \downarrow }\left(t\right)\rangle$ calculated analytically in the $V\to \infty$ limit for $U=8J$, and by TEBD for $U=8J$ and $V=20J$. Here, $V\gg U$ and the number of doublons is nearly conserved. (b) TEBD results for $V=10J$ and varying $U$. For $U$ sufficiently close to $V, \langle N_{\uparrow \downarrow }\left(t\right)\rangle$ decays as a function of time. (c) TEBD results for $V=100J$ and varying $U$.

Figure 3

The three-site model comprises of the three central sites between the vertical lines.

Figure 4

The total number of doublons $\langle N_{\uparrow \downarrow }\left(t\right)\rangle$ for $U=90J$ and $V=100J$ has a similar initial behavior in the three-site model as in the many-body TEBD simulations.

Figure 5

(Left column) The difference in the density of spin-up (bath) fermions with respect to the initial state as a function of position and time, $\langle \psi \left(t\right)|n_{j\uparrow }|\psi \left(t\right)\rangle -\langle \psi \left(0\right)|n_{j\uparrow }|\psi \left(0\right)\rangle$ for $U=8J$ and $V=20J$ (upper row) and $U=8J$ and $V=10J$ (lower row). (Right column) The density of the spin-down impurity $\langle \psi \left(t\right)|n_{j\downarrow }|\psi \left(t\right)\rangle$ for the same values of $U$ and $V$. For $U$ close to $V$, the changes in the bath density distribution (lower left panel) are an order of magnitude larger than for $U$ and $V$ far apart (upper left panel), indicating that there is a resonant interval of $U$ around $V$ for creating excitations.

Figure 6

The same quantities as in Fig. 5 for $V=100J$ and $U=90J$ (upper) and $U=100J$ (lower). The parameters of the upper row are in the off-resonant region and those of the lower row in the resonant region.

Figure 7

A schematic figure of the time evolution where a DW-ADW excitation is created by moving a bath particle to the neighboring site from the impurity. Here, the bath particle moves to the left but the symmetric case is equally likely. The DW and ADW excitations can propagate in opposite directions (configuration 1) or the DW can propagate and the ADW form a stationary bound state with the impurity (configuration 2). From 2, the state can evolve for instance so that the DW and ADW propagate in the same direction (2 a) or the DW continues to the left and the ADW remains stationary, with the impurity oscillating between the two sites (2 b). In configurations 2a and 2b, the DW excitation has moved to the left beyond the region drawn here.

Figure 8

The density correlation $\langle \psi \left(t\right)|\mathrm{\Delta }{n}_{i\uparrow }\mathrm{\Delta }{n}_{-i\uparrow }|\psi \left(t\right)\rangle$ for $U=V=100J$ at different time steps shows that the bath evolves in a superposition of configurations (see Appendix pp3).

Figure 9

The energy bands of a free particle in a superlattice with potential difference $U$ between alternating sites.

Figure 10

A DW propagating to the left and a stationary ADW.

Figure 11

A DW propagating to the left and an ADW propagating to the right.

Figure 12

A schematic plot of the correlation $\langle \psi \left(t\right)|\mathrm{\Delta }{n}_{i\uparrow }\mathrm{\Delta }{n}_{-i\uparrow }|\psi \left(t\right)\rangle$ at different time steps for the case of a DW propagating to the left and an ADW propagating to the right.