Expansion Dynamics in the One-Dimensional Fermi-Hubbard Model

Abstract

Expansion dynamics of interacting fermions in a lattice are simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and non-paired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.PACS numbers: 71.10. Fd , 03.75.Ss, 73.20.Mf Important physical phenomena such as magnetism and high-temperature superconductivity are often approached by theories based on the Hubbard model [2, 3] which describes interacting particles in a lattice. Within ultracold gas systems [3, 4], the Hubbard model can be efficiently realized and studied in experiments with bosonic [5] and recently with fermionic atoms [6,7]. Intriguingly, the dimension can be easily controlled. Low-dimensional systems such as nanowires, iron pnictides and graphene are currently highlighted topics of research. Models for the quantum many-body physics of 2D and 1D systems can explored with ultracold gases, c.f. recent experiments on fermions in one dimension [8] and expanding fermions in a 2D lattice [5]. For one-dimensional systems, an advantage is that the experiments can be compared to exact theoretical descriptions. However, although the ground state and static properties of one-dimensional systems are known to an impressive degree [2, 3], dynamics is largely unexplored. Work on theory and simulation of dynamical properties of interacting fermions in 1D has recently been emerging [12].In this Letter, we study with exact numerical methods the expansion of fermions within the one-dimensional Hubbard model. We show that the resulting complex dynamics can be efficiently described by a two-fluid model in which we deduce the dynamics of the fluids from the dynamics of a Hubbard dimer. Our results explain several main features of the experiment [5] performed in 2D, and give exact predictions for future experiments in 1D. The simple Hubbard-dimer two-fluid model that we have developed provides a basis for the description of various types of expansion, collision and oscillation dynamics for fermions in lattices.We use the time-evolving block decimation (TEBD) algorithm [13] to describe the time evolution generated by the Hubbard Hamiltonian wheren i,σ = c † i σ c i σ with c † i σ and c i σ representing the creation and annihilation of a fermion with spin σ at the site i = 1 . . . L. Moreover, the initial state is given by |φ(0) = |∅ 1 . . . Fig. 1). The initial state consists thus of a band insulator occupying the central O L − O R sites of an oth...

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model with spin imbalance

“…Moreover, we analyze the relaxation dynamics of the double occupancy, a much discussed quantity in studies of quantum quenches in the repulsive Fermi-Hubbard model [62][63][64][65][66][67][68][69][70][71], which has been measured in nonequilibrium experiments [29,37,51]. We then turn our attention to quenches from the attractive regime, U < 0, to the repulsive one, U > 0.…”

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

“…the formation of entanglement between distant atoms [29] as well as the existence of bound or repulsively bound states. While the expansion can be modeled in 1D [32] using DMRG methods [31], so far no methods are available to calculate the dynamics quantum-mechanically in higher dimensions. The separation between ballistically expanding atoms carrying high entropy and the high density core in the center could be used to locally cool the atoms via quantum distillation processes [30].…”

Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder

“…(ii) Another possibility is without any external coupling to reservoirs, by simply preparing a nonequilibrium initial state, and then observing how the initial disturbance spreads. Such experiments have been performed [13,14] as well as appropriate numerical simulations [26]. For our ladder system one could prepare initial states from the ballistic subspace by quenching a strong dimerized rung coupling strength, so that the ground state would be |STS .…”