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arXiv:1404.6598 · Physical Review B

Doublon dynamics of the Hubbard model on a triangular lattice

Toshihiro Sato, Hirokazu Tsunetsugu

Published Sep 8, 2014• 9 citations
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Abstract

We study the dynamics of doublons in the half-filled Hubbard model on the triangular lattice by using cellular dynamical mean-field theory. Investigating the nearest-neighbor dynamical correlations, we demonstrate that a nearest-neighbor doublon-holon pair shows a strong attraction, in particular in the insulating phase. The nearest-neighbor doublon and holon dynamics obtained indicate that the characteristic time scales inversely with the Coulomb interaction in the short-time region in both the metallic and insulating phases. We find that the metallic phase has larger fluctuations in their dynamics. In the long-time region, the metallic phase has persistent fluctuations in various nearest-neighbor configurations, while the fluctuations are vanishingly small in the insulating phase. We also calculate the on-site dynamical correlation of doublons and find that the lifetime of the doublon is longer in the metallic phase than in the insulating phase.

DOI
10.1103/physrevb.90.115114

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We study the dynamics of doublons in the half-filled Hubbard model on the triangular lattice by using cellular dynamical mean-field theory. Investigating the nearest-neighbor dynamical correlations, we demonstrate that a nearest-neighbor doublon-holon pair shows a strong attraction, in particular in the insulating phase. The nearest-neighbor doublon and holon dynamics obtained indicate that the characteristic time scales inversely with the Coulomb interaction in the short-time region in both the metallic and insulating phases. We find that the metallic phase has larger fluctuations in their dynamics. In the long-time region, the metallic phase has persistent fluctuations in various nearest-neighbor configurations, while the fluctuations are vanishingly small in the insulating phase. We also calculate the on-site dynamical correlation of doublons and find that the lifetime of the doublon is longer in the metallic phase than in the insulating phase.
Dynamics in a triangular-lattice Hubbard model is studied at half filling on the basis of the cluster dynamical mean field theory. Numerical calculations use a solver of the continuous-time quantum Monte Carlo method based on the strong-coupling expansion. We examine the change in the nearest-neighbor dynamical correlations of doublon and holon in the time domain with varying the Coulomb repulsion near the Mott transition. We demonstrate that the nearest-neighbor doublon-holon pair shows a strong attractive correlation, particularly in the insulating phase, while the nearest-neighbor doublon-doublon pair shows a repulsive correlation. Useful information is provided by the trajectories in the complex plane of the dynamical correlation functions. The short-time dynamics of the nearest-neighbor doublon and holon in the metallic phase indicates larger fluctuations than in the insulating phase. Their trajectories in the complex plane show that the short-time dynamics of the doublon-holon pair has an opposite behavior to that of the doublon-doublon pair. We find that their time scale of dynamics can be characterized by the period in which the phase rotates π around the long-time limit in both phases. In the long-time region, fluctuations persist up to a very long time in the metallic phase, while they quickly vanish in the insulating phase.
We investigate the Hubbard model on the triangular lattice at half filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte Carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Pad\'e approximation in CT QMC are in good agreement. We determine the metal-insulator transition and the hysteresis associated with a first-order transition in the double-occupancy and nearest-neighbor spin-correlation functions as functions of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean-field theory, DCA, and recently developed DF methods by comparing the Green's functions. We find an enhancement of antiferromagnetic correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.
We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field Theory. We compute the low-temperature phase diagram, displaying a metallic phase and a symmetry-broken phase for strong intersite repulsions. We describe the correlation effects on both single-particle and two-particle observables in the metallic phase. Whereas single-particle spectra feature a Hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non-interacting limit, even for large on-site repulsions. We argue that this behaviour is typical of the strongly doped case. We also report a region in parameter space with negative static local screening.
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle-point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On a half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from a paramagnetic semimetal/metal to an antiferromagnetic-ordered Slater insulator with coherent quasiparticles at Uc1{U}_{c1}Uc1​, followed by a Mott transition into an electron-fractionalized AF∗{}^{*}∗ phase without coherent excitations at Uc2{U}_{c2}Uc2​. Such a phase structure appears to be generic for bipartite lattices without frustration. We show that doublon-holon binding unites the three important ideas of strong correlation: coherent quasiparticles, incoherent Hubbard bands, and deconfined Mott insulator.
Dynamical mean-field theory (DMFT) studies frequently observe a fine structure in the local spectral function of the SU(2) Fermi-Hubbard model at half filling: In the metallic phase close to the Mott transition, subpeaks emerge at the inner edges of the Hubbard bands. Here we demonstrate that these subpeaks originate from the low-energy effective interaction of doublon-holon pairs, by investigating how the correlation functions of doublon and holon operators contribute to the subpeaks. A mean-field analysis of the low-energy effective Hamiltonian provides results consistent with our DMFT calculation using the numerical renormalization group as an impurity solver. In the SU(3) and SU(4) Hubbard models, the subpeaks become more pronounced due to the increased degeneracy of doublon-holon pair excitations.
We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system a single holon-doublon (HD) pair exhibits a binding transition on a 3D lattice, or a sharp crossover on a 2D lattice, corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards nonpolarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximation. Both approaches lead to a discontinuous transition away from the fully polarized system and give density correlations consistent with numerical results on a triangular lattice.