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Suppressed correlation-spreading in a one-dimensional Bose-Hubbard model with strong interactions

Jose Carlos Pelayo, Ippei Danshita

Abstract

We investigate signatures of non-ergodic behavior in the real-time evolution of a one-dimensional Bose-Hubbard model, where the initial state is a doubly occupied density-wave state. We show that the occupation dynamics at strong interactions is dominated by doublon-holon exchange which leads to a domain wall excitation and propagation. The latter manifests as a negated staggered pattern in the density-density correlations. While the single-particle and the pair correlation functions show highly localized correlations that decay rapidly away from the nearest neighbor. We show that the time scale of the domain-wall excitations depends on the inverse of the interaction strength and therefore dictates the slow relaxation dynamics. In the presence of a parabolic trap, the occupation dynamics at the edges become frozen and further suppresses the propagation of correlations. This suppression happens even for trap strengths weaker than the tunneling rate. We also show that the model can be mapped to an antiferromagnetic transverse-field Ising model in the limit of strong interactions and that the correlation-propagation velocity in the original model is well captured by the group velocity of the spin-wave excitation in the effective spin model.

Suppressed correlation-spreading in a one-dimensional Bose-Hubbard model with strong interactions

Abstract

We investigate signatures of non-ergodic behavior in the real-time evolution of a one-dimensional Bose-Hubbard model, where the initial state is a doubly occupied density-wave state. We show that the occupation dynamics at strong interactions is dominated by doublon-holon exchange which leads to a domain wall excitation and propagation. The latter manifests as a negated staggered pattern in the density-density correlations. While the single-particle and the pair correlation functions show highly localized correlations that decay rapidly away from the nearest neighbor. We show that the time scale of the domain-wall excitations depends on the inverse of the interaction strength and therefore dictates the slow relaxation dynamics. In the presence of a parabolic trap, the occupation dynamics at the edges become frozen and further suppresses the propagation of correlations. This suppression happens even for trap strengths weaker than the tunneling rate. We also show that the model can be mapped to an antiferromagnetic transverse-field Ising model in the limit of strong interactions and that the correlation-propagation velocity in the original model is well captured by the group velocity of the spin-wave excitation in the effective spin model.
Paper Structure (8 sections, 7 equations, 4 figures)

This paper contains 8 sections, 7 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model and Methods
  3. Results
  4. Site occupation dynamics
  5. Correlations
  6. Effective Models
  7. Conclusions
  8. Mapping to Transverse Field Ising model

Figures (4)

  • Figure 1: Time-evolved site occupations at strong interaction $U/J = 40$. For $M=16$, results are shown for $\Omega/J=0$ (a) and $\Omega/J=0.02$ (b), with the corresponding neighboring two-site occupations in (c) and (d). Panels (e) and (f) show the site occupation for $M=15$ with particle number $N=M-1$ and $N=M+1$, respectively.
  • Figure 2: Evolution of different correlation functions (see colorbar label) for $\Omega/J = 0$ (upper row) and $\Omega/J = 0.02$ (lower row). In all cases, the interaction strength is $U/J = 40$ and $M=16$ while the correlations at $d=0$ are not shown.
  • Figure 3: Correlation width as a function of increasing evolution time for (a) $\Omega/J = 0$ and (b) $\Omega/J = 0.02$, where $M=16$. (c) Long-time average of correlation width as a function of increasing interactions for different trap strengths (see figure legend), where $M=12$.
  • Figure 4: (a) Site occupation dynamics and (b) density-density correlation function of the transverse field Ising model obtained by exact time evolution. The dotted line in (a) denotes the time at which the excitation occurs while the dashed lines in (a) and in (b) equals $v_g^{-1}$ and $(2v_g)^{-1}$, respectively. See main text for details.