The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory

The Bethe ansatz local density approximation (LDA) to lattice density functional theory (LDFT) for the one-dimensional repulsive Hubbard model is extended to current-LDFT (CLDFT). The transport properties of mesoscopic Hubbard rings threaded by a magnetic flux are then systematically investigated by this scheme. In particular we present calculations of ground state energies, persistent currents and Drude weights for both a repulsive homogeneous and a single impurity Hubbard model. Our results for the ground state energies in the metallic phase compare favorably well with those obtained with numerically accurate many-body techniques. Also the dependence of the persistent currents on the Coulomb and the impurity interaction strength, and on the ring size are all well captured by LDA-CLDFT. Our study demonstrates the value of CLDFT in describing the transport properties of one-dimensional correlated electron systems. As its computational overheads are rather modest, we propose this method as a tool for studying problems where both disorder and interaction are present.     

Disorder and interaction in 2D: exact diagonalization study of the Anderson-Hubbard-Mott model

We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite-size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is unlikely that there is a 2D metal-insulator quantum phase transition, although the effect of interaction in some range of parameters is to substantially enhance the noninteracting charge stiffness.     

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.     

Projective quantum monte carlo method for the anderson impurity model and its application to dynamical mean field theory

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the frustrated one-band Hubbard model, reconfirming the numerical renormalization group results.     

Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.     

Path integral Monte Carlo calculations of4He and6Li

We have performed Monte Carlo calculations to estimate the exact energies of model problems for⁴He and theL=0,1, and 2 states of⁶Li. Using a Feynman path-integral expression for the imaginary-time evolution operator, we recast the ground state energy as a sum over histories, which are then sampled stochastically. Use of a trial wave function dramatically improves the efficiency of the Monte Carlo method. For a state-independent Malfliet-Tjon potential, together with the Coulomb interaction, we find a ground state energy of ?28.00+0.20 MeV for⁴He, and a degeneracy of theL=0,1, and 2 states in⁶Li at about ?59.65+-0.50 MeV. Density distributions for these nuclei are also calculated.     

Local anharmonic vibrations strong correlations and superconductivity: A quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-T _c materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.     

Supersolids versus phase separation in two-dimensional lattice bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.     

Ferromagnetism in the Hubbard model on fcc-type lattices

The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges. Received: 6 August 1997 / Accepted: 20 August 1997     

Effect of hole doping on the electronic structure and the Fermi surface in the Hubbard model within norm-conserving cluster pertubation theory

The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U. The concentration dependence of the Fermi surface strongly depends on hopping to second (t′) and third (t″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.     

Spectral functions in the hubbard model with half-filling

Under the assumption of long-range antiferromagnetic order at low temperatures, the spectral functions and the density of states are calculated in the two-dimensional Hubbard model with half-filling in the Hubbard-I approximation. The results are compared with the data obtained using an exact numerical technique, namely, the quantum Monte Carlo method. The influence of hopping to the next-to-nearest neighbor on the formation of the electronic structure is considered.     

Analytic evaluation of resonating valence bond states

Expectation values of the one-particle density matrix, the Cooper-pair amplitude and the Hubbard interaction are calculated analytically within locally correlated superconducting wave functions. For weak correlations or small densities, a rapidly converging series-expansion of exact expectation values is derived, while for strong correlations a sum-rule conserving single-site approximation is developed. Explicit results for the kinetic energy of holes within resonating valence bond states are compared with corresponding Monte Carlo data. The characteristic difference between wave functions with fixed and variable particle number, respectively, is pointed out.     

Correlations and conductivity of interacting fermions in a disordered chain

A one dimensional system of interacting fermions in a random potential is investigated within a Hartree-Fock approximation. The model in consideration combines the onsite interaction of the Hubbard model and the stochastic site energies of the Anderson model. For a system of 120 sites and several values of the model parameters the equal time correlation functions for the charge and the spin density as well as the low frequency conductivity are calculated numerically. The gross features of the conductivity thus obtained agree with published results obtained in a Monte Carlo simulation, but there are also interesting differences.     

Energetics of 2D and 3D Repulsive Hubbard Model from Their 1D Counterpart using Dimensional Scaling for an Arbitrary Band Filling

A dimensional scaling computation of the electron concentration-dependent ground-state energy for the repulsive Hubbard model is presented, a generalization of Capelle’s analysis of the 2D and 3D Hubbard Hamiltonians with half-filled bands. The computed ground-state energies are compared with the results of mean-field and density-matrix functional theories and of quantum Monte Carlo calculations. The comparison indicates that dimensional scaling yields moderately accurate ground-state energies close to and at half filling over the wide range of interaction strengths in the study. By contrast, the accuracy becomes poor at low filling for strong interactions.     

Reinvestigation of the sign problem in the two-dimensional Hubbard model

We reinvestigate the sign problem in the two-dimensional Hubbard model using the projector ground state Quantum Monte Carlo scheme with Langevin dynamics. Our interest is mainly motivated by the question: what is the parameter space in which simulations may be performed with reliable results and how does the average sign scales with inverse temperature? In the parameter space in which one may omit the sign problem we have studied the ground state properties: momentum distribution and spin structure. We find an exponential decay of the average sign. At half filling, we find evidence for an antiferromagnetic insulating ground state. At off half band fillings, the antiferromagnetic state is destroyed leaving place to an incommensurate spin density state.     

Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study

We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U>U(c) both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge, and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism but leaves the single-particle signatures of the helical liquid intact.     

Structure of the pairing interaction in the two-dimensional Hubbard model

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.     

Magnetic susceptibility of the two-dimensional two-sublattice Hubbard model calculated in the static-fluctuation approximation

The transverse dynamic susceptibility of the 2D two-sublattice Hubbard model is calculated in the static-fluctuation approximation. The static magnetic susceptibility is studied as a function of various parameters of the system. The results for the special case of the one-dimensional Hubbard model are compared to the exact solution.     

Ground state phases of the half-filled one-dimensional extended hubbard model

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.