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arXiv:0912.4197 · Physical Review B

Interaction-induced Fermi-surface renormalization in the t1−t2 Hubbard model close to the Mott-Hubbard transition

Luca F. Tocchio, Federico Becca, Claudius Gros

Published May 11, 2010• 10 citations
arXivHTMLPDF

Abstract

We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled ${t}_{1}\ensuremath{-}{t}_{2}$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.

DOI
10.1103/physrevb.81.205109

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We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled t1\ensuremath−t2{t}_{1}\ensuremath{-}{t}_{2}t1​\ensuremath−t2​ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating state, with a first-order reorganization when crossing into the conducting state.
The underlying Fermi surface is a key concept for strongly interacting electron models and has been introduced to generalize the usual notion of the Fermi surface to generic (superconducting or insulating) systems. By using improved correlated wave functions that contain backflow and Jastrow terms, we examine the two-dimensional ttt-${t}^{\ensuremath{'}}$ Hubbard model and find a nontrivial renormalization of the topology of the underlying Fermi surface close to the Mott insulator. Moreover, we observe a sharp crossover region, which arises from the metal-insulator transition, from a weakly interacting metal at small coupling to a resonating valence-bond superconductor at intermediate coupling. A violation of the Luttinger theorem is detected at low hole dopings.
Abstract We present a T = 0 K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possesses the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped phases can be obtained. We find that the normal and insulating phases of the half-filled Hubbard model correspond, for any on-site repulsion, to a marginal Fermi liquid normal phase and a topologically-ordered gapped Mott insulating liquid respectively. The marginal Fermi liquid is found to arise from singular forward scattering in directions normal to the nested Fermi surface, while singular backscattering events lead to Mott liquid state. The transition between these two phases involves passage through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. The pseudogap phase is observed to arise from the electronic differentiation encoded within the nested Fermi surface, and involves the gradual gapping of the Fermi surface from antinodes to nodes via charge and spin excitations that are mutually entangled. We obtain effective Hamiltonians for various phases, as well as wavefunctions for the low-energy many-body eigenstates of the Mott liquid. Benchmarking of the ground-state energy per particle and the double-occupancy fraction for the Mott liquid against existing numerical results yields excellent agreement. Presence of a Néel ordering symmetry-breaking perturbation in the RG leads to an antiferromagnetic spin-ordered charge insulating Mott state. Our results thus offer novel insights on a variety of aspects of the Mott–Hubbard problem, and can be extended to the doped system.
We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a nonperfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi-one-dimensional model displays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $\ensuremath{\nu}\ensuremath{\approx}1.0$. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.
Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account of the ground-state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite on-site repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonic finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.
We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t 1 - t 2 Hubbard model (the zigzag Hubbard chain) with the density matrix renormalization group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gaped state in their respective ground-state momentum distribution functions.
We study transport properties of the half-filled two-dimensional (2D) Hubbard model with spatially varying interactions, where a pattern of interacting and non-interacting sites is formed. We use Determinantal Quantum Monte Carlo method to calculate the double occupation, effective hopping and Drude weight. These data point to two phase transitions, driven by fermionic correlations. The first is the expected metal to a Mott insulating state. The second one, is an exotic transition from a Mott insulating state to a highly anisotropic metal, that takes place at large values of the fermion-fermion interaction. This second transition occurs when the layers formed by the spatially varying interactions decouple due to the suppression of the hopping between interacting and non-interacting sites, leading to fermionic transport along the non-interacting ones.