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arXiv:0807.1683 · Physical Review B

Hubbard model on the triangular lattice using dynamical cluster approximation and dual fermion methods

Hunpyo Lee, Gang Li, H. Monien

Published Nov 24, 2008• 46 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.78.205117

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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 employ dynamical mean-field theory (DMFT) with a quantum Monte Carlo atomic solver to investigate the finite-temperature Mott transition in the Hubbard model with nearest-neighbor hopping on a triangular lattice at half-filling. We estimate the value of the critical interaction to be ${U}_{c}=12.0\ifmmode\pm\else\textpm\fi{}0.5$ in units of the hopping amplitude ttt through the evolution of the magnetic moment, spectral function, internal energy, and specific heat as the interaction UUU and temperature TTT are varied. This work also presents a comparison between DMFT and finite-size determinant quantum Monte Carlo calculations and a discussion of the advantages and limitations of both methods.
The one-dimensional t 1 − t 2 half-filled Hubbard model is considered at finite temperatures T within a dynamical cluster approximation (DCA) with N c = 24 in combination with a semiclassical approximation (SCA) impurity solver. The SCA approach accounts for long-range spatial fluctuations, where exact numerical impurity solvers can not capture due to computational expense, even though dynamical fluctuations are freezing. Therefore, it can consider both frequency- and momentum-resolved physical properties beyond the DCA with small cluster in combination with exact impurity solvers. By the computation of the static spin-spin correlation, the density of states, and the double occupancy, we examine the description of the frustrated one-dimensional systems at finite T within given approximations. We confirm not only the interaction-driven metal-insulator transition in the regions of t 2/t 1 > 0.5, but also the commensurate-incommensurate transition by tunning t 2/t 1 in the strong interaction region. We also observe finite T-driven metal-insulator transition.
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.
This thesis will describe efforts to enhance our ability to simulate the 2D Hubbard model. Chapter 2 provides a background on the main computational techniques used throughout the work, including quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), the dynamical cluster approximation (DCA), the continuous time auxiliary field algorithm (CTAUX), and the Maximum Entropy Method (MEM) for numeric analytic continuation. Chapter 3 presents new work on applying Twisted Boundary Conditions to the DCA framework. This method is applied in a effort to access thermodynamic (i.e. large system) information about the Hubbard model without the immense computational expense required to simulate large lattices directly. Chapter 4 describes efforts to study the extended 2D Hubbard model, which re-introduces non-local interactions between electrons that drive the formation of charge ordered phases. The work includes a thorough analysis of the phase diagram of the model away from half-filling, as well as analysis of the effect of non-local interactions on anti-ferromagnetic fluctuations and competition between the charge order and AFM states. Chapter 5 includes a derivation of the dual fermions diagrammatic expansion and the dual fermions ladder approximation used to compute corrections to single site DMFT calculations. The method is applied to the 2D Hubbard model in order to study the evolution of its spectral function, Fermi surface, and momentum dependent mass renormalization as the temperature, interaction strength, and doping are changed. The great advantage of this method is that we are able to access arbitrary momenta throughout the Brillouin zone, in contrast to the limitation to a few cluster momenta that characterize cluster methods like DCA.
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous-time auxiliary-field quantum Monte Carlo to solve this model for 1-, 4-, 6-, 12-, and 16-site clusters with detailed analysis performed for the 6-site cluster. We show that (a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; (b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; and (c) the loss of spectral weight in the metal-to-Mott-insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.