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arXiv:1711.05390 · Physical review. B./Physical review. B

Dynamical recovery of SU(2) symmetry in the mass-quenched Hubbard model

Liang Du, Gregory A. Fiete

Published Feb 27, 2018• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.97.085152

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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 \ensuremathγ(t)\ensuremath{\gamma}(t)\ensuremathγ(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.
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.
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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.
We use nonequilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of a Hubbard model which is driven out of equilibrium by a sudden increase in the on-site repulsion UUU. We discuss the implementation of the self-consistency procedure and some important technical improvements of the QMC method. The exact numerical solution is compared to iterated perturbation theory, which is found to produce accurate results only for weak interaction or short times. Furthermore, we calculate the spectral functions and the optical conductivity from a Fourier transform on the finite Keldysh contour, for which the numerically accessible time scales allow to resolve the formation of Hubbard bands and a gap in the strongly interacting regime. The spectral function, and all one-particle quantities that can be calculated from it, thermalize rapidly at the transition between qualitatively different weak- and strong-coupling relaxation regimes.
We investigate the quench of half-filled one-dimensional and two-dimensional fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is Gaussian, we can use a variety of time-dependent quantum Monte Carlo methods to tackle this problem without generating a dynamical sign problem. Using a continuous time quantum Monte Carlo method, we achieve a system size of 128 sites in one dimension, and using a Blankenbecler-Scalapino-Sugar type algorithm, we were able to simulate $20\ifmmode\times\else\texttimes\fi{}20$ square lattices. Applying these methods to study the dynamics after the quench, we observe that the final state of the system can be reasonably well described by a thermal single-particle density matrix that takes the initial single-particle conservation laws into account. The characteristic decay toward this limit is found to be oscillatory with an additional power law decay that depends on the dimensionality. This numerically exact result is shown to compare favorably to mean-field approximations as well as to perturbation theory. Furthermore, we observe the information propagation in the one-dimensional case in the charge-charge and spin-spin correlations and find that it is linear with a velocity of roughly $v\ensuremath{\approx}4$ in units of the hopping amplitude.
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