Filling-dependent doublon dynamics in the one-dimensional Hubbard model

Rausch, Roman; Potthoff, Michael

doi:10.1103/physrevb.95.045152

Cited by 18 publications

(23 citation statements)

References 48 publications

(70 reference statements)

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“…In contrast, the doublon cloud size grows much slower and we even observe a weak shrinking of the cloud for U = 20J. For comparison, we show the expected expansion of a fictitious cloud of non-interacting doublons expanding according to J eff [47]. The difference highlights the nontrivial nature of this transient dynamics.…”

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confidence: 68%

“…Quantum distillation occurs for large interactions. It relies on the dynamical demixing of fast singlons (one atom per site) and slow doublons (two atoms per site) during the expansion: while isolated doublons only move with a small effective second-order tunneling matrix element J eff = 2J 2 /U J for U J [46,47], neighboring singlons and doublons can exchange their positions via fast, resonant first-order tunneling processes. Thus, after opening the trap, singlons escape from regions of the cloud initially occupied by singlons and doublons, leading (a) Initial state with doublons (b) Initial state without doublons to a spatial separation of the two components.…”

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confidence: 99%

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Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

et al. 2018

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We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly-interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench.Many-body physics in one dimension (1D) differs in numerous essential aspects from its higher-dimensional counterparts. Several familiar concepts, such as Fermiliquid theory [1,2], are not applicable in 1D. Moreover, many 1D models are integrable, meaning that there exist exact solutions. Examples include the Lieb-Liniger model [3], the Heisenberg chain [4] or the 1D Fermi-Hubbard model (FHM) [5]. These models exhibit extensive sets of conserved quantities that prevent thermalization [6][7][8][9][10][11] and can, in lattice systems, lead to anomalous transport properties [12][13][14][15]. Coldatom experiments offer the possibility to study transport properties of strongly-correlated quantum gases in a clean environment. Their excellent controllability enabled far-from-equilibrium experiments [16][17][18][19][20] as well as close-to-equilibrium measurements in the linear-response regime [21][22][23][24] both in extended lattices and mesoscopic systems [25][26][27].Here, we investigate mass transport in the 1D FHM in far-from-equilibrium expansion experiments [18][19][20], where an initially trapped gas is suddenly released into a homogeneous potential landscape as illustrated in Fig. 1. There are two distinct regimes of interest in suddenexpansion studies: the asymptotic one, where the expanding gas has become dilute and effectively noninteracting [28][29][30][31][32][33][34][35][36] and the transient regime, where the dynamical quasi-condensation of hardcore bosons [37-41] and quantum distillation [20, 42-44] have been found. Quantum distillation occurs for large interactions. It relies on the dynamical demixing of fast singlons (one atom per site) and slow doublons (two atoms per site) during the expansion: while isolated doublons only move with a small effective second-order tunneling matrix element J eff = 2J 2 /U J for U J [46, 47], neighboring singlons and doublons can exchange their positions via fast, resonant first-order tunneling processes. Thus, after opening the trap, singlons escape from regions of the cloud initially occupied by singlons and doublons, leading (a) Initial state with doublons (b) Initial state without doublons x d U J x J J 10 20 30 40 50 Site index i 2 4 6 8 Time t (¿) 10 20 30 40 50 Site index i 0.0 0.4 0.8 1.2 1.6 n i ® FIG. 1. Schematics of the expansion experiment. Top: Initial state of the harmonically trapped two-component Fermi gas with (a) singlons (red) and doublons (blue) and (b) o...

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Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

et al. 2018

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“…The memory effects discussed here in isolated quantum systems can be understood in the following way: As the states evolve with different but conserved energy, they result in different final states even if the final Hamiltonian is the same. Similar effect are also discussed in doublon dynamics in both theoretical and experimental studies [108][109][110][111], where the highly occupied states cannot be easily relaxed due to energy conservation.…”

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confidence: 68%

Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems

Lai

Chien

2017

Phys. Rev. A

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Dynamics of a system in general depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady state currents form in finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.

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“…The larger J, the closer it stays to unity. As compared to doublon dynamics in the Hubbard model [6,28,29], there are important differences resulting from the different binding mechanisms: A Fourier analysis (not shown) indicates that there are two dominating oscillation frequencies in the Kondo case, which are roughly given by J/2 and 3J/2. Furthermore, in the Hubbard case the maximal velocity of the wavefront is basically given by the Fermi velocity v max ≈ 2T , while in the Kondo case we find v max ≈ T , which in fact corresponds to the polaron velocity in the strong-J limit [18].…”

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Magnetic Doublon Bound States in the Kondo Lattice Model

2019

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We present a novel pairing mechanism for electrons, mediated by magnons. These paired bound states are termed "magnetic doublons". Applying numerically exact techniques (full diagonalization and the density-matrix renormalization group, DMRG) to the Kondo lattice model at strong exchange coupling J for different fillings and magnetic configurations, we demonstrate that magnetic doublon excitations exist as composite objects with very weak dispersion. They are highly stable, support a novel "inverse" colossal magnetoresistance and potentially other effects.

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Filling-dependent doublon dynamics in the one-dimensional Hubbard model

Cited by 18 publications

References 48 publications

Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model

Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems

Magnetic Doublon Bound States in the Kondo Lattice Model

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