Real-time dynamics in the one-dimensional Hubbard model

We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Green's function by matrix-product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral function with very high frequency resolution.

Figure 1

Spectral function $A(\omega ,k)$ of the Hubbard model calculated with TEBD at filling $\rho =1/4$ for (a) $U=5$ and (b) $U=10$ and at filling $\rho =1/6$ for (a) $U=5$ and (b) $U=10$. The black dashed lines are the singularity thresholds obtained from the Bethe ansatz solution. In all cases, the spectral function is nonzero everywhere below the absolute threshold indicated by the thin blue lines, although the intensity is mostly very small.

Figure 2

Exponent ${\mu }_{0,-}^c$ for $\rho =1/4$ as a function of momentum as derived from the mobile impurity model approach for various fillings and values of $U$.

Figure 3

Exponent ${\mu }_{0,-}^c$ for $\rho =1/6$ as a function of momentum as derived from the mobile impurity model approach for various fillings and values of $U$.

Figure 4

Time decay of the imaginary part of the Green's function $G(t,k)$ for filling $\rho =1/4$. Symbols are numerical TEBD data and red lines are fits to the power-law decay of the form of (18).

Figure 5

Time decay of the imaginary part of the Green's function $G(t,k)$ for filling $\rho =1/6$. Symbols are numerical TEBD data and red lines are fits to the power-law decay of the form of (18).

Figure 6

Comparison between the spectral function $A(\omega ,k)$ at fixed momentum $k$ calculated with raw TEBD data (red) and TEBD extended in time with ansatz (18) with BA and mobile impurity model parameters (blue). Results for quarter filling and $U=10$.