Session B16: Hubbard Model

Charge and magnetic order in the triangular lattice Hubbard model at one-third filling

Experimental work over the last decade on layered triangular lattice materials with itinerant electrons has increased the motivation to study these systems theoretically. As in insulating magnets, frustration in itinerant systems enriches the phase diagram of the material. In a class of organic charge transfer salts and sodium cobalt oxide spin liquid, superconducting, charged ordered, and magnetically ordered phases have been observed. With the kinetic energy of electrons, a Hubbard type model on a triangular lattice is an appropriate starting point to study much of the correlated physics of these systems. We consider a single band Hubbard model on a triangular lattice with variable electron filling and anisotropic hopping. Within mean-field theory we observe a transition at one-third filling on the isotropic lattice to a charge ordered antiferromagnet on a honeycomb sublattice at a critical interaction $U_c/t = 5.0$. We will also present preliminary results for other regions of the phase diagram.   

Electronic reconstruction of doped Mott insulator heterojunctions

Correlated electron heterostructures became a possible alternative when thin-film deposition techniques achieved structures with a sharp interface transition [1]. Soon thereafter, Okamoto \& Millis introduced the concept of ``electronic reconstruction'' [2]. We study here the electronic reconstruction of doped Mott insulator heterostructures based on a Cluster Dynamical Mean Field Theory (CDMFT) calculations of the Hubbard model in the limit where electrostatic energy dominates over the kinetic energy associated with transport across layers. The grand potential of individual layers is first computed within CDMFT and then the electrostatic potential energy is taken into account in the Hartree approximation. The charge reconstruction in an ensemble of stacked planes of different nature can lead to a distribution of electron charge and to transport properties that are unique to doped-Mott insulators.\\[4pt] [1] J. Mannhart, D. G. Schlom, Science 327, 1607 (2010).\\[0pt] [2] S. Okamoto and A. J. Millis, Nature 428, 630 (2004).   

Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling

We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods are limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models.   

Correlation effects of one band hubbard model beyond the Gutzwiller Approximation

A novel scheme is introduced to go beyond the Gutzwiller approximation (GA). Starting from the scheme, we can see how the standard GA is recovered by relaxing physical constraints step by step. This not only adds to validity of the current scheme, but provides new insights into understanding the GA. Performance of the scheme on several testing cases is superior to the standard GA. We studied the one band Hubbard model in one, two and three dimensions to revisit relevant conclusions made under the GA as well as the slave boson formalism.   

Local electronic nematicity in the 2-dimensional Hubbard model

Recent measurements on magnetic and transport properties of some strongly correlated materials show a local electronic nematic phase which locally breaks the $C_4$ symmetry but keeps translational symmetry. We studied the 2-dimensional Hubbard model using the variational cluster approach and found a similar phase. The results showed this local nematicity is a property of the electron liquid and would appear even if there is no lattice distortion. Calculations of spin correlation were preformed and compared to results from magnetic neutron scattering of real materials, which showed a distinct asymmetry along x and y directions.   

Evolution of insulator-metal-insulator transitions under staggered lattice potentials

It is known that in the ionic Hubbard model metallic phases exist between band and Mott insulators in the presence of staggered lattice potentials. We investigate how the phase diagram depends on the strength of the staggered lattice potential, by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Observed at finite temperatures is the crossover between metallic and band insulating phases while a first-order transition ending up with a critical point shows up between the metallic and Mott insulating phases. It is discussed how such transition behaviors evolve as the lattice potential grows at low temperatures.   

Mott transition and ferrimagnetism in the Hubbard model on the anisotropic kagome lattice

Mott transition and ferrimagnetism are studied in the Hubbard model on the anisotropic kagome lattice using the variational cluster approximation and the phase diagram at zero temperature and half-filling is analyzed. The ferrimagnetic phase rapidly grows as the geometric frustration is relaxed, and the Mott insulator phase disappears in moderately frustrated region, showing that the ferrimagnetic fluctuations stemming from the relaxation of the geometric frustration is enhanced by the electron correlations. In metallic phase, heavy fermion behavior is observed and mass enhancement factor is computed. Enhancement of effective spatial anisotropy by the electron correlations is also confirmed in moderately frustrated region, and its effect on heavy fermion behavior is examined.   

Graphene two-leg ladder. A system with conducting, insulating and superconductive properties

We use DMRG to study the ground-state phases of the Hubbard model defined on a one dimensional ladder of edge-sharing hexagons - a model which may be relevant to the electronic structure of polyacenes or graphene strips. At half filling we find a robust insulating phase with a large spin-gap, even at small U/t which, as a function of the strength of the third-neighbor hopping, exhibits a non-trivial cross-over from a band -insulator to a Mott insulator. The doped system exhibits a variety of conducting phases. Possible relevance of our results to the recently discovered high temperature superconductivity in K doped dibenzpentacene will be discussed, as well.   

Dominant superconducting fluctuations in the 1D extended Holstein-extended Hubbard model

The search for realistic 1D models that exhibit dominant superconducting (SC) fluctuations has a long history. In these 1D systems, the effects of commensurate band fillings - strongest at half-filling - and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. We study a model - the extended Hubbard-extended Holstein (EHEH) model - with non-local electron-phonon interactions, in addition to electron-electron interactions. The EHEH model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using multi-scale functional renormalization group for the full model and a renormalization group for a bosonized form of the model, we prove the existence of dominant SC fluctuations in this model. Dominant SC fluctuations arise because the spin-charge coupling at high energy is weakened by the non-local electron-phonon interaction and the charge gap is destroyed by the suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that non-local boson-meditated interactions may be important in the superconductivity observed in high $T_c$ cuprate and organic superconductors.   

Ground state and finite temperature behavior of 1/4-filled zigzag ladders

We consider the simplest example of lattice frustration in the $\frac{1}{4}$-filled band, a one-dimensional chain with next-nearest neighbor interactions. For this zigzag ladder with electron-electron as well as electron-phonon interactions we present numerical results for ground state as well as thermodynamic properties. In this system the ground state bond distortion pattern is independent of electron-electron interaction strength. The spin gap from the ground state of the zigzag ladder increases with the degree of frustration. Unlike in one-dimension, where the spin-gap and charge ordering transitions can be distinct, we show that in the ladder they occur simultaneously. We discuss spin gap and charge ordering transitions in $\frac{1}{4}$-filled materials with one, two, or three dimensional crystal structures. We show empirically that regardless of dimensionality the occurrence of simultaneous or distinct charge and magnetic transitions can be correlated with the ground state bond distortion pattern.   

Phases of the two-leg Hubbard ladder in the large U limit

We study the phase diagram of the two-leg Hubbard ladder in the large U limit using the density matrix renormalization group (DMRG). Already in the limit of infinite on-site repulsion U, we find a rich phase diagram in which commensurability effects are unexpectedly prominent: A fully spin-polarized ``Nagaoka'' metallic phase occurs for electron density, n, in the range $1> n> n_1$, where $n_1 \approx 0.8$ is not obviously locked by any commensurability. There is an insulating, anti-ferromagnetic commensurate plaquette phase at n=3/4, and two-phase coexistence for $n_1 > n > 3/4$. For $3/4 > n > n_2 \approx 0.6$, there is a partially spin-polarized metallic state with a magnetization peak centered at n=2/3. For the most part, the ground state is a paramagnetic Luttinger liquid for $n_2 \geq n$, although an antiferromagnetic phase with a substantial charge gap (and which may or may not have a small spin-gap) arises at n=1/2. Interesting soliton excitations with fractional charge are found for the plaquette phase at n=3/4. We have also explored the evolution of these phases as a function of decreasing (but still large) U, both by studying the t-J model and of the underlying Hubbard model.   

Quantum Phase Transitions in an Ionic Hubbard Model in One Dimension

We study quantum phase transitions in an ionic Hubbard model in one dimension. This model accounts for electrons in alternating potentials with a lattice period of 2. For a specified alternating potential of strength $\Delta$, we change the local repulsion between spin-up and spin-down electrons, $U$, for the model to exhibit a quantum phase transition from a band insulator to a Mott insulator. Via exact diagonalization with a modified Lanczos method, we find that, as we tune $U$, the ground-state energy shows a level crossing at half-filling. We obtain a phase diagram of the model by using a finite-size scaling method. Also, we find an interesting feature of double occupancy around the phase transitions.   

Ground state properties of the ionic Hubbard model on a two-leg triangular ladder at 3/4 filling

We study numerically the ionic Hubbard model on a two-leg triangular ladder at 3/4 filling. This model is believed to be the minimal microscopic model describing the physics of Na$_{x}$CoO$_{2}$ at $x=0.5$, and shows a rich phase diagram that depends on a delicate balance between the Coulomb interaction $U$, the hopping amplitude $t$, and the ionic potential $\Delta$. Motivated by experiments analyzing the dopant distribution on Na$_{0.5}$CoO$_{2}$, we focus in the case of a stripe-type ionic potential. In the correlated limit where the Coulomb interaction is large, the ground state of the model is a charge-transfer insulator for large ionic potential and turns metallic for zero ionic potential. Electronic structure calculations point to the regime $\Delta\sim |t|, t<0$ as the one relevant for Na$_{0.5}$CoO$_{2}$, but previous calculations [1] have not fully clarify the nature of ground state of the model in such regime. The aim of this work is to study the metal-insulator transition that occurs in the region $U\gg\Delta\sim |t|$ of the phase diagram as well as the magnetic and charge structures of the associated ground states. \newline [1] J. Merino et al. Phys. Rev. B 80, 045116 (2009).   

Quantum Monte Carlo Studies on Attractive Hubbard Model with Anisotropic Spin-dependent Hopping on Two-leg Ladder Lattice

Using spin-dependent hopping, it is possible to have a fully paired state with a gap for single fermion excitation and gapless Cooper pair excitation, called `Cooper-pair Bose-metal' phase. Recently, the existence of this phase was suggested by a density matrix renormalization group studies\footnote{ Feiguin, A.E. and M.P.A. Fisher, \textit{Exotic paired phases in ladders with spin-dependent hopping.} Physical Review B, 2011. \textbf{83}(11): p. 115104.} on the attractive Hubbard Model with two-leg ladder geometry and anisotropic spin-dependent hopping. We here present a detailed Quantum Monte Carlo (QMC) studies on this model to investigate its finite temperature properties, including correlation function, s-wave and d-wave pairing function, and finally to deduce the existence and behavior of `Cooper-pair Bose-metal' phase.   

An Exotic Spin Mode in a Non-Polarized Fermi Liquid With Net Spin-Current

We find an exotic spin excitation in an ordered magnetic system with an order parameter with a net spin current but no net magnetization. Starting from a Fermi liquid theory, similar to that for a weak ferromagnet, this excitation emerges from a state that is protected by a Pomeranchuck instability. We derive the propagating mode using Landau kinetic equation, using two different approaches and find that the dispersion of the mode is the same for both approaches in leading order.