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### Anomalous Spin-Charge Separation in a Driven Hubbard System

#### Abstract

Spin-charge separation (SCS) is a striking manifestation of strong correlations in low-dimensional quantum systems, whereby a fermion splits into separate spin and charge excitations that travel at different speeds. Here, we demonstrate that periodic driving enables control over SCS in a Hubbard system near half filling. In one dimension, we predict analytically an exotic regime where charge travels slower than spin and can even become “frozen,” in agreement with numerical calculations. In two dimensions, the driving slows both charge and spin and leads to complex interferences between single-particle and pair-hopping processes.

• Accepted 5 October 2020

DOI:http://doi.org/10.1103/PhysRevLett.125.195301

General PhysicsCondensed Matter & Materials PhysicsAtomic, Molecular & Optical

#### Authors & Affiliations

Hongmin Gao1,*, Jonathan R. Coulthard1, Dieter Jaksch1,2, and Jordi Mur-Petit1,†

• 1Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
• 2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore

• *hongmin.gao@physics.ox.ac.uk
• jordi.murpetit@physics.ox.ac.uk

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##### Issue

Vol. 125, Iss. 19 — 6 November 2020

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• ###### Figure 2

Dynamics of local spin, $⟨{\stackrel{^}{s}}_{j}^{z}⟩$ (top row), and density, $⟨{\stackrel{^}{n}}_{j}⟩$ (bottom row), for the 1D $t\text{−}J\text{−}\alpha$ model as a function of position, $j$, and time, $\tau$, after the removal of the spin-dependent potential. From left to right, the driving strengths used are $K=0$, 1.5, 2.0, and 2.1, respectively. Note the different colorbar scales for each panel. The straight red lines are ballistic propagation velocity predictions from mean-field spin-charge separation (MF-SCS) theory (Supplemental Material [50]). Simulation parameters are: $U=21{t}_{0}$ (such that ${J}_{0}=0.19{t}_{0}$), $\mathrm{\Omega }=6{t}_{0}$, ${E}_{↑}=0.5×\mathrm{max}\left\{|t|,J,|\alpha |\right\}$ and $s=2$. The lattice contains $L=36$ sites, of which the central 26 are shown. The total number of fermions is 28 (14 spin-$↑+14$ spin-$↓$), resulting in an average filling of $n=7/9$.

• ###### Figure 3

Density (blue solid line, left axis) and spin (red dashed line, right axis) imbalance as a function of time for different driving strengths as indicated. The system is a diagonal stripe covering 12 sites of a square lattice perpendicular to the driving direction, with five spin-$↑$ and five spin-$↓$ fermions (Supplemental Material [50]). Simulation parameters are $U=50{t}_{0}$ (such that ${J}_{0}=0.08{t}_{0}$), $\mathrm{\Omega }=14{t}_{0}$, and ${E}_{↑}^{2\mathrm{D}}\approx 0.05\mathrm{max}\left\{|t|,J,|{\alpha }_{±}|\right\}$. Note the change of left $y$-axis limits in the lower two panels.

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