Controlling magnetic correlations in a driven Hubbard system far from half-filling

Abstract

We propose using ultracold fermionic atoms trapped in a periodically shaken optical lattice as a quantum simulator of the t-J Hamiltonian, which describes the dynamics in doped antiferromagnets and is thought to be relevant to the problem of high-temperature superconductivity in the cuprates. We show analytically that the effective Hamiltonian describing this system for off-resonant driving is the t-J model with additional pair hopping terms, whose parameters can all be controlled by the drive. We then demonstrate numerically using tensor network methods for a one-dimensional (1D) lattice that a slow modification of the driving strength allows near-adiabatic transfer of the system from the ground state of the underlying Hubbard model to the ground state of the effective t-J Hamiltonian. Finally, we report exact diagonalization calculations illustrating the control achievable on the dynamics of spin-singlet pairs in 2D lattices utilizing this technique with current cold-atom quantum-simulation technology. These results open new routes to explore the interplay between density and spin in strongly correlated fermionic systems through their out-of-equilibrium dynamics.

Anomalous Spin-Charge Separation in a Driven Hubbard System

“…(Supplemental Material [50]). Numerical simulations of high-energy excitations in a lattice at low filling [37], where the dynamics is effectively described in terms of singlet pairs, also support the importance of pair-hopping terms in retaining a nonzero particle transport in 2D systems when jtðKÞj < JðKÞ. These observations are in line with recent numerical findings pointing to the relevance of next-tonearest-neighbor hopping amplitudes (t 0 ) to establish the ground-state charge and spin orderings of the Hubbard model near half filling [8][9][10][11][12][13][14].…”

“…In this Letter, we demonstrate control over SCS via periodic driving of a strongly repulsive Hubbard model near half filling in 1D and 2D. It is known that such a system is well described by a static t-J-α model [32][33][34][35][36][37], where double occupancies are forbidden by the strong onsite repulsion in the underlying Hubbard system. Compared to the standard t-J model, the t-J-α model also includes three-site processes that play, as we show here, an important role in the dynamics.…”

“…The validity of the t-J-α model as a description of the Hubbard model driven witĥ H drive is established in Ref. [37]. Reference [36] presents further evidence that driving-induced Floquet heating in these models remains low for driving durations ≲100=t 0 .…”

“…Under the condition t 0 ≪ fU; Ω; jU þ mΩj ∀ m ∈ Zg, i.e., the driving is off resonant and fast compared to hopping, the dynamics of the driven system is described by an effective static t-J-α model (see Fig. 1) H tJα ¼ P 0 fĤ hop ðtÞ þĤ ex ðJÞ þĤ pair ðfα ijk gÞgP 0 ; ð1Þ with its parameters dependent on Ω and V. The effective model ( 1) can be derived using a generalized Schrieffer-Wolff transformation [32,33] or a perturbative expansion in the Floquet basis [34][35][36][37]; see details in the Supplemental Material [50]. Here, the operator P 0 ¼ Q i ð1 −n i↑ni↓ Þ projects out states with double occupancies,Ĥ ex ðJÞ ¼ −J P hijib † ijbij is the superexchange contribution, by which NN opposite spins switch their positions,b…”

“…3. To understand this, we note that α þ ðKÞ ≈ tðKÞ [37] for K ≈ 2.2, which leads to an interference between hopping events to first and second neighbors FIG. 3.…”