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arXiv:1707.09692 · Physical review. B./Physical review. B

Spin-selective thermalization plateau in the mass-imbalanced Hubbard model

Liang Du, Li Huang, Gregory A. Fiete

Published Oct 30, 2017• 6 citations
arXivHTMLPDF

Abstract

We use time-dependent nonequilibrium dynamical mean-field theory with weak-coupling auxiliary-field continuous time quantum Monte Carlo as an impurity solver to study the thermalization behavior of the mass-imbalanced single-band Hubbard model after a quench of the Coulomb interaction from the noninteracting limit to a finite positive value. When the Coulomb interaction in our model is increased under equilibrium conditions, the quasiparticle weights for spin-up and spin-down (the mass imbalance) electrons approach zero simultaneously, indicating the absence of a spin-selective Mott transition. By contrast, our out-of-equilibrium study of the mass-imbalanced Hubbard model suggests that there exists the spin-selective dynamical phase transition (one spin orientation undergoes a fast thermalization at its critical Coulomb interaction strength while the other spin orientation shows prethermalization behavior). The spin-selective dynamical phase transition is characterized by the relaxation behavior of the spin-resolved kinetic energy and the spin-resolved momentum-dependent occupation. To connect with possible experiments, we calculate the spin-resolved two-time optical conductivity, which confirms the spin-selective thermalization plateau. We find that the critical Coulomb interaction of each spin orientation for the spin-selective thermalization grows as the mass imbalance decreases.

DOI
10.1103/physrevb.96.165151

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We use time-dependent nonequilibrium dynamical mean-field theory with weak-coupling auxiliary-field continuous time quantum Monte Carlo as an impurity solver to study the thermalization behavior of the mass-imbalanced single-band Hubbard model after a quench of the Coulomb interaction from the noninteracting limit to a finite positive value. When the Coulomb interaction in our model is increased under equilibrium conditions, the quasiparticle weights for spin-up and spin-down (the mass imbalance) electrons approach zero simultaneously, indicating the absence of a spin-selective Mott transition. By contrast, our out-of-equilibrium study of the mass-imbalanced Hubbard model suggests that there exists the spin-selective dynamical phase transition (one spin orientation undergoes a fast thermalization at its critical Coulomb interaction strength while the other spin orientation shows prethermalization behavior). The spin-selective dynamical phase transition is characterized by the relaxation behavior of the spin-resolved kinetic energy and the spin-resolved momentum-dependent occupation. To connect with possible experiments, we calculate the spin-resolved two-time optical conductivity, which confirms the spin-selective thermalization plateau. We find that the critical Coulomb interaction of each spin orientation for the spin-selective thermalization grows as the mass imbalance decreases.
Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the one-dimensional ionic-mass imbalanced Hubbard chain driven by a quantum quench of the on-site Coulomb interaction, where the system is prepared in the ground state of the Hamiltonian with a different Hubbard interaction. The exact diagonalization method (Lanczos algorithm) is adopted to study the zero temperature phase diagram in equilibrium, which is shown to be in good agreement with previous studies using density matrix renormalization group (DMRG). We then study the nonequilibrium quench dynamics of the spin and charge order parameters by fixing the initial and final Coulomb interactions while changing the quenching time protocols. Our study shows that the time evolution of the charge and spin order parameters strongly depend on the quenching time protocols. In particular, the effective temperature of the system will decrease monotonically as the quenching time is increased. By taking the final Coulomb interaction strength to be in the strong coupling regime, we find that the oscillation frequency of the charge order parameter increases monotonically with the Coulomb interaction. By contrast, the frequency of the spin order parameter decreases monotonically with increasing Coulomb interaction. We explain this result using an effective spin model and a two-site Hubbard model in the strong coupling limit. Finally, we take the final Coulomb interaction strength to be in the weak coupling regime and find that the oscillation frequency of both the charge and spin order parameters increases monotonically with decreasing Coulomb interaction. Our study suggests strategies to engineer the relaxation behavior of interacting quantum many-particle systems.
We use nonequilibrium dynamical mean-field theory with iterative perturbation theory as an impurity solver to study the recovery of SU(2) symmetry in real time following a hopping integral parameter quench from a mass-imbalanced to a mass-balanced single-band Hubbard model at half filling. A dynamical order parameter $\ensuremath{\gamma}(t)$ is defined to characterize the evolution of the system towards SU(2) symmetry. By comparing the momentum-dependent occupation from an equilibrium calculation [with the SU(2) symmetric Hamiltonian after the quench at an effective temperature] with the data from our nonequilibrium calculation, we conclude that the SU(2) symmetry recovered state is a thermalized state. Further evidence from the evolution of the density of states supports this conclusion. We find the order parameter in the weak Coulomb interaction regime undergoes an approximate exponential decay. We numerically investigate the interplay of the relevant parameters (initial temperature, Coulomb interaction strength, initial mass-imbalance ratio) and their combined effect on the thermalization behavior. Finally, we study evolution of the order parameter as the hopping parameter is changed with either a linear ramp or a pulse. Our results can be useful in strategies to engineer the relaxation behavior of interacting quantum many-particle systems.
We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling JJJ when the bandwidth ratio is small and only beyond a critical value of JJJ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J=0J=0J=0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization VVV and replaced at small VVV by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.
The Hubbard model (HM) and the Falicov-Kimball model (FKM), which are two standard models of strongly correlated electrons, provide an interesting benchmark for the physics of locally correlated systems. We study the intermediate model, mass-imbalanced Hubbard model at half-filling on a 2D square lattice which connects continuously the HM to the FKM.We employ dynamical mean field theory (DMFT) and dynamical cluster approximation (DCA) using continuous-time auxiliary field method (CT-AUX) as self-consistent impurity solver to study the single particle spectral function and self-energy allowing us to map-out the phase diagram of the system. Solutions to the mass-imbalanced model cannot enforce paramagnetic self-consistency and therefore at low temperature result in paramagnetic (PM) to antiferromagnetic (AFM) transition. In addition, in the PM state and at finite temperature, we observed a spin dependent crossover from Fermi liquid (FL) regime to non-Fermi liquid (nFL) regime in which the FL regime is destroyed, monotonically, induced not only by the interaction but also by the mass imbalance. We present the results for small cluster DCA and explore its dependency on cluster size as well.
The Mott - Hubbard metal - insulator transition in the half-filled mass imbalanced ionic Hubbard model is investigated using the two-site dynamical mean field theory. We find that for a fixed mass imbalanced parameter r the critical interaction Uc increases when the ionic energy Δ\DeltaΔ is increased. In the other hand, for a fixed Δ\DeltaΔ, UcU_cUc​ decreases with increasing the mass imbalance. We also show the existence of BI phase in the system for the case Δ≠0\Delta \ne 0Δ=0, U=0U=0U=0 and calculate the staggered charge density nB−nAn_B − n_AnB​−nA​ as a function of the interaction for different values of the mass imbalance. Our results in the limiting cases (r=1r = 1r=1; Δ≠0\Delta \ne 0Δ=0 or/and Δ=0\Delta = 0Δ=0; r≠1r\ne 1r=1) are in good agreement with those obtained from full dynamical mean field theory.
We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.