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Register a new userHigh temperature superconductivity in the two-dimensional $t$-$J$ model: Gutzwiller wave function solution
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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).
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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.
Motivated by the recently observed pattern of unidirectional domains in high-T_c superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the d-wave superconducting resonating valence bond phase using the t-J model at x=1/8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axis leading to modulated superconductivity with out-of-phase d-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations yield that the energies of modulated and uniform phases are very close to each other.
A comparison of microscopic theories of superconductivity in the limit of strong electron correlations is presented. We consider results for the two-dimensional t-J model obtained within the projection technique for the Green functions in terms of the Hubbard operators and the slave-fermion representation for the RVB state. It is argued that the latter approach resulting in the odd-symmetry p-wave pairing for fermions is inadequate.
Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore possible superconductivity state in the doped Mott insulator, we study a square-lattice $t$-$J$ model with both the nearest and next-nearest-neighbor electron hoppings and spin Heisenberg interactions. By using the state-of-the-art density matrix renormalization group simulations with imposing charge $U(1)$ and spin $SU(2)$ symmetries on the large-scale six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation decaying much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
We develop the Gutzwiller approximation method to obtain the renormalized Hamiltonian of the SU(4) $t$-$J$ model, with the corresponding renormalization factors. Subsequently, a mean-field theory is employed on the renormalized Hamiltonian of the model on the honeycomb lattice under the scenario of a cooperative condensation of carriers moving in the resonating valence bond state of flavors. In particular, we find the extended $s$-wave superconductivity is much more favorable than the $d+id$ superconductivity in the doping range close to quarter filling. The pairing states of the SU(4) case reveal the property that the spin-singlet pairing and the spin-triplet pairing can exist simultaneously. Our results might provide new insights into the twisted bilayer graphene system.
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