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Register a new userControlling magnetic correlations in a driven Hubbard system far from half-filling
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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 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 utilising 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.
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We consider the optical conductivity $sigma_1(omega)$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, $sigma_1(omega)$ is computed for a range of interaction strengths and dopings. We identify an energy scale $E_{rm opt}$ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of $sigma_1(omega)$ for frequencies just above $E_{rm opt}$ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.
We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different algorithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT.
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.
We have investigated the half-filling two-orbital Hubbard model on a triangular lattice by means of the dynamical mean-field theory (DMFT). The densities of states and optical conductivity clearly show the occurence of metal-insulating transition (MIT) at U$_{c}$, U$_{c}$=18.2, 16.8, 6.12 and 5.85 for J=0, 0.01U, U/4 and U/3, respectively. The distinct continuities of double occupation of electrons, local square moments and local susceptibility of the charge, the spin and the orbital at J > 0 suggest that the MIT is the first-order; however at J=0, the MIT is the second-order in the half-filling two-orbital Hubbard model on triangular lattices. We attribute the first-order nature of the MIT to the low symmetry of the systems with finite Hunds coupling J.
The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the $(U,g_{rm ph})$ plane for the phonon-mediated interaction $g_{rm ph}$ and the Coulomb interaction $U$. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency $omega_0$. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical $ U^*approx g^*_{rm ph}$, followed at larger $Usim g_{rm ph}$ by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on $U$. For the Peierls-Hubbard model, the region of the $(U,g_{rm ph})$ plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency $omega_D$ decreases. A power law dependence $g_{rm ph} sim U^{2eta}$ is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term $V$ is added to the Hubbard interaction.
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