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Physical review. B, Condensed matter

Composite-fermion theory for the strongly correlated Hubbard model

C. Stephen Hellberg, E. J. Melé

Published Jul 15, 1991• 22 citations
Publisher

Abstract

We study a class of variational wave functions for strongly correlated systems by expanding the electron operators as composites of spin-1/2 Fermi fields and spinless Fermi fields. The composite particles automatically satisfy the local constraint of no double occupancy and include correlations between opposite-spin particles in a very physical way. We calculate the energy and correlation functions for the one-dimensional U=\ensuremath{\infty} Hubbard model, where a comparison with exact results is made. The method is computationally very tractable and can readily be generalized to higher dimensions.

DOI
10.1103/physrevb.44.1360

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We study a class of variational wave functions for strongly correlated systems by expanding the electron operators as composites of spin-1/2 Fermi fields and spinless Fermi fields. The composite particles automatically satisfy the local constraint of no double occupancy and include correlations between opposite-spin particles in a very physical way. We calculate the energy and correlation functions for the one-dimensional U=\ensuremath{\infty} Hubbard model, where a comparison with exact results is made. The method is computationally very tractable and can readily be generalized to higher dimensions.
We present very general techniques for investigating strongly correlated lattice fermions in one dimension. We derive a variational wave function with a long ranged Jastrow factor that automatically satisfies the no double occupancy constraint present in many model Hamiltonians. The wave function is shown to be a generalized Luttinger liquid, and we use it to estimate ground state properties of the strongly correlated Hubbard model and the t-J model. We develop a numerical method to project the ground state from an arbitrary trial state. With the Luttinger liquid wave function as the initial guess, we calculate the exact ground state phase diagram of the t-J model. We discover a new phase in the model where Luttinger liquid behavior breaks down and superconducting correlations dominate the long range behavior of the system.
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We propose a method to calculate the charge dynamical structure factors for the ground states of correlated electron systems based on the variational Monte Carlo method. Our benchmarks for the one- and two-dimensional Hubbard models show that inclusion of composite-fermion excitations in the basis set greatly improves the accuracy, in reference to the exact charge dynamical structure factors for clusters. Together with examination for larger systems beyond tractable sizes by the exact diagonalization, our results indicate that the variational Monte Carlo method is a promising way for studies on the nature of charge dynamics in correlated materials such as the copper oxide superconductors if the composite-fermion excitations are properly included in the restricted Hilbert space of intermediate states in the linear response theory. Our results are consistent with the particle-hole excitations inferred from the single-particle spectral function $A(\mathbit{k},\ensuremath{\omega})$ in the literature. We also discuss the importance of incorporating nonlocal composite fermion for a more accurate description. Future issues for further improvements are also discussed.
Abstract The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and filling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error ∼ 4 % in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and find excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a finite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.
We propose a method to calculate the charge dynamical structure factors for the ground states of correlated electron systems based on the variational Monte Carlo method. Our benchmarks for the one- and two-dimensional Hubbard models show that inclusion of composite-fermion excitations in the basis set greatly improves the accuracy, in reference to the exact charge dynamical structure factors for clusters. Together with examination for larger systems beyond tractable sizes by the exact diagonalization, our results indicate that the variational Monte Carlo method is a promising way for studies on the nature of charge dynamics in correlated materials such as the copper oxide superconductors, if the composite-fermion excitations are properly included in the restricted Hilbert space of intermediate states in the linear response theory. We also discuss the importance of incorporating nonlocal composite fermion for more accurate description.