Temporal decay of Néel order in the one-dimensional Fermi-Hubbard model

Abstract

Motivated by recent experiments with ultracold quantum gases in optical lattices we study the decay of the staggered moment in the one-dimensional Fermi-Hubbard model starting from a perfect Néel state using exact diagonalization and the infinite-system-size time-evolving-block-decimation method. This extends previous work in which the same problem has been addressed for pure spin Hamiltonians. As a main result, we show that the relaxation dynamics of the double occupancy and of the staggered moment are different. The former is controlled by the nearest-neighbor tunneling rate while the latter is much slower and strongly dependent on the interaction strength, indicating that spin excitations are important. This difference in characteristic energy scales for the fast charge dynamics and the much slower spin dynamics is also reflected in the real-time evolution of nearest-neighbor density and spin correlations. A very interesting time dependence emerges in the von Neumann entropy, which at short times increases linearly with a slope proportional to the tunneling matrix element while the long-time growth of entanglement is controlled by spin excitations. Our predictions for the different relaxation dynamics of the staggered moment and the double occupancy should be observable in state-of-the-art optical lattice experiments. We further compare time averages of the double occupancy to the expectation values in both the canonical and diagonal ensembles, which quantitatively disagree with each other on finite systems. We relate the question of thermalization to the eigenstate thermalization hypothesis.PHYSICAL REVIEW A 91, 053628 (2015)

Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

“…The results in Fig. S8 suggest that for large U/J, the asymptotic radial velocity is indeed primarily a function of the interaction energy that is generated due to the interaction quantum quench over the first tunneling times [69,70]. There is a noticeable and expected additional U -dependence (see the inset where we plot v r versus E int /U ).…”

Many-body localization and thermalization in disordered Hubbard chains

“…The third one, the antiferromagnetic structure factor S = 1/L i,j e iπ(i−j) (n i↑ −n i↓ )(n j↑ −n j↓ ) is related to the spin degrees of freedom (from now on we refer to it as the structure factor). The relaxation times of the charge and spin degrees of freedom are expected to be different for very strong interactions [37]. Figure 2 displays the disorder averaged time evolution of the imbalance [Fig.…”

Bounding the finite-size error of quantum many-body dynamics simulations

“…Introduction Numerical simulations are crucial to our understanding of many-body quantum matter, and are routinely applied in all fields of physics and in chemistry. Numerical calculations are used to understand equilibrium properties of strongly correlated quantum materials [1][2][3][4][5][6][7][8][9], model nonequilibrium dynamics of ultracold matter [10][11][12][13][14][15][16][17][18], calculate molecular properties [19][20][21], and determine nuclear structure [22][23][24][25][26], as a few examples.…”

“…We similarly demonstrate this for the non-equilibrium dynamics of the Fermi-Hubbard model (FHM) relaxation from a checkerboard state, inspired by experiments and theory of Refs. [12,16]. The precision of these bounds is enabled by the major quantitative improvements offered by recent LR bounds [77,78].…”