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Register a new userGutzwiller Wave-Function Solution for Anderson Lattice Model: Emerging Universal Regimes of Heavy Quasiparticle States
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The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM). This approach allows for a systematic evaluation of the expectation values with GWF in the finite dimensional systems. It introduces results extending in an essential manner those obtained by means of standard Gutzwiller Approximation (GA) scheme which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss principal paramagnetic properties of ALM and their relevance to heavy fermion systems. We demonstrate the formation of an effective, narrow $f$-band originating from atomic $f$-electron states and subsequently interpret this behavior as a mutual intersite $f$-electron coherence; a combined effect of both the hybridization and the Coulomb repulsion. Such feature is absent on the level of GA which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow effective $f$-band rationalizes common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of CeCoIn$_5$. Moreover, we show that the emerging $f$-electron coherence leads in a natural manner to three physically distinct regimes within a single model, that are frequently discussed for 4$f$- or 5$f$- electron compounds as separate model situations. We identify these regimes as: (i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii) Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$ electrons half-filling, $langlehat n_{f}ranglerightarrow1$. The non-Landau features of emerging correlated quantum liquid state are stressed.
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A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes t (and t) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (U, delta, t) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, U/t > 3, and for not too large hole doping, delta < 0.32 for t = 0.25 t; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles $d_{x^2-y^2}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.
Partially-projected Gutzwiller variational wavefunctions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered one-dimensional chains, with the goal of determining a minimal set of variational parameters required to accurately describe the spatially-inhomogeneous charge densities and spin correlations. We find that, for weak and intermediate disorder, it is sufficient to include spatial variations of the charge densities in the product state alone, provided that screening of the disorder potential is accounted for. For strong disorder, this prescription is insufficient and it is necessary to include spatially inhomogeneous variational parameters as well.
A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) proposed very recently is used for the description of superconducting (SC) ground state in the two-dimensional square-lattice $t$-$J$ model with the hopping electron amplitudes $t$ (and $t$) between nearest (and next-nearest) neighbors. On the example of the SC state analysis we provide a detailed comparison of the method results with other approaches. Namely: (i) the truncated DE-GWF method reproduces the variational Monte Carlo (VMC) results; (ii) in the lowest (zeroth) order of the expansion the method can reproduce the analytical results of the standard Gutzwiller approximation (GA), as well as of the recently proposed grand-canonical Gutzwiller approximation (GCGA). We obtain important features of the SC state. First, the SC gap at the Fermi surface resembles a $d_{x^2-y^2}$-wave only for optimally- and overdoped system, being diminished in the antinodal regions for the underdoped case in a qualitative agreement with experiment. Corrections to the gap structure are shown to arise from the longer range of the real-space pairing. Second, the nodal Fermi velocity is almost constant as a function of doping and agrees semi-quantitatively with experimental results. Third, we compare the doping dependence of the gap magnitude with experimental data. Fourth, we analyze the $mathbf{k}$-space properties of the model: Fermi surface topology and effective dispersion. The DE-GWF method opens up new perspectives for studying strongly-correlated systems, as: (i) it works in the thermodynamic limit, (ii) is comparable in accuracy to VMC, and (iii) has numerical complexity comparable to GA (i.e., it provides the results much faster than the VMC approach).
We present benchmark calculations of the Anderson lattice model based on the recently-developed ghost Gutzwiller approximation. Our analysis shows that, in some parameters regimes, the predictions of the standard Gutzwiller approximation can be incorrect by orders of magnitude for this model. We show that this is caused by the inability of this method to describe simultaneously the Mott physics and the hybridization between correlated and itinerant degrees of freedom (whose interplay often governs the metal-insulator transition in real materials). Finally, we show that the ghost Gutzwiller approximation solves this problem, providing us with results in remarkable agreement with dynamical mean field theory throughout the entire phase diagram, while being much less computationally demanding. We provide an analytical explanation of these findings and discuss their implications within the context of ab-initio computation of strongly-correlated matter.
We assess the ground-state phase diagram of the $J_1$-$J_2$ Heisenberg model on the kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that comprise of hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For $J_2=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $pi$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405 (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017)]. Here, we show that its accuracy improves in presence of a small $antiferromagnetic$ super-exchange $J_2$, leading to a finite region where the gapless spin liquid is stable; then, for $J_2/J_1=0.11(1)$, a first-order transition to a magnetic phase with pitch vector ${bf q}=(0,0)$ is detected, by allowing magnetic order within the fermionic Hamiltonian. Instead, for small $ferromagnetic$ values of $|J_2|/J_1$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on $36$ sites where exact diagonalization is possible. Then, upon increasing the ratio $|J_2|/J_1$, a magnetically ordered state with $sqrt{3} times sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic regime, the magnetic transition is definitively first order, at $J_2/J_1=-0.065(5)$.
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