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arXiv:1006.1457 · Journal of Physics Condensed Matter

Field-dependent dynamics in the metallic regime of the half-filled Hubbard model

D Parihari, N S Vidhyadhiraja, A Taraphder

Published Jan 19, 2011• 4 citations

Abstract

A systematic study of the effect of magnetic field (h) on the Hubbard model has been carried out at half-filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strengths (U). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical U, the transition becomes continuous. The region of 'coexistence' of the PM and QFM solutions in the field-U plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field, and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on (3)He indicate that a theory of (3)He based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.

DOI: 10.1088/0953-8984/23/5/055602

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A systematic study of the effect of magnetic field (h) on the Hubbard model has been carried out at half-filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strengths (U). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical U, the transition becomes continuous. The region of 'coexistence' of the PM and QFM solutions in the field-U plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field, and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on (3)He indicate that a theory of (3)He based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.

We study the magnetic field-driven metal-to-insulator transition in half-filled Hubbard model on the Bethe lattice, using the dynamical mean-field theory by solving the quantum impurity problem with density-matrix renormalization group algorithm. The method enables us to obtain a high-resolution spectral densities in the presence of a magnetic field. It is found that the Kondo resonance at the Fermi level splits at relatively high magnetic field: the spin-up and -down components move away from the Fermi level and finally form a spin-polarized band insulator. By calculating the magnetization and spin susceptibility, we clarify that an applied magnetic field drives a transition from a paramagnetic metallic phase to a band insulating phase. In the weak interaction regime, the nature of the transition is continuous and captured by the Stoner's description, while in the strong interaction regime the transition is very likely to be metamagnetic, evidenced by the hysteresis curve. Furthermore, we determine the phase boundary by tracking the kink in the magnetic susceptibility, and the steplike change of the entanglement entropy and the entanglement gap closing. Interestingly, the phase boundaries determined from these two different ways are largely consistent with each other.

We study the Hubbard-Holstein model which includes both the electron-electron and electron-phonon interactions, characterized by

U

and

g

, respectively. The model is solved with

U

and

g

on an equal footing in the infinite dimensions by employing the dynamical mean-field theory in combination with Wilson's numerical renormalization group. A zero temperature phase diagram of symmetry unbroken states at half filling is mapped out which exhibits the interplay between the two kinds of interactions and combines the two separately studied interaction-driven metal-insulator transitions of the Hubbard and Holstein models within a single frame. The ground state is metallic when both

U

and

g

are small, but is insulating when

U

or

g

is large, referred to as, respectively, Mott-Hubbard insulator (MHI) and bipolaron insulator (BPI). As the phase boundary between the metallic and MHI (BPI) states is approached from the metallic region, the quasiparticle weight

z

goes to 0 continuously (discontinuously). Moreover, the two insulating states are distinct and cannot be adiabatically connected, and there is a first order phase transition between them.

We present dynamical mean-field theory (DMFT) results for the local spectral densities of the one- and two-particle response functions for the infinite-dimensional Hubbard model in a magnetic field. We look at the different regimes corresponding to half-filling, near half-filling, and well away from half-filling, for intermediate and strong values of the local interaction

U

. The low energy results are analyzed in terms of quasiparticles with field-dependent parameters. These renormalized parameters are determined by two different methods, both based on numerical renormalization group (NRG) calculations, and we find good agreement. Away from half-filling, the quasiparticle weights, ${z}_{\ensuremath{\sigma}}(H)$, differ according to the spin type $\ensuremath{\sigma}=\ensuremath{\uparrow}$ or $\ensuremath{\sigma}=\ensuremath{\downarrow}$. Using the renormalized parameters, we show that DMFT-NRG results for the local longitudinal and transverse dynamic spin susceptibilities in an arbitrary field can be understood in terms of repeated scattering of these quasiparticles. We also check Luttinger's theorem for the Hubbard model and find it to be satisfied in all parameter regimes and for all values of the magnetic field.

Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.

We study the magnetic properties of the three-dimensional (3D) Hubbard model at half filling in the two particle self-consistent formalism, previously developed for the 2D model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with dynamical mean-field (DMF) results for the isotropic 3D model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3D case, and the 2D or anisotropic 3D cases for the double occupation factor. Even for this local correlation function, 2D or anisotropic 3D cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.

Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or

1+x

the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction

{U}_{c}

at which the metal-insulator transition occurs.