Composite-fermion theory for the strongly correlated Hubbard model

Cs, Hellberg; Ej, Mele

doi:10.1103/physrevb.44.1360

Cited by 21 publications

(13 citation statements)

References 22 publications

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“…The phase diagram and the Luttinger liquid correlations of the t − J-model have also been established from variational wave functions [131,132,133]. This result is particularly noteworthy because these functions can be generalized into higher dimensions where exact solutions generally are not possible and numerical studies are severely limited by finite size effects (Section 6.2).…”

Section: Low-energy Properties Of One-dimensional Lattice Modelsmentioning

confidence: 95%

One-dimensional Fermi liquids

1995

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We review the progress in the theory of one-dimensional (1D) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particlehole bubble producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless one-dimensional quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t − J-or the extended Hubbard model. Also 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.We discuss in detail various solutions of the Luttinger model which emphasize different aspects of the physics of 1D Fermi liquids. Correlation functions are calculated in detail using bosonization, and the relation of this method to other approaches is discussed. The correlation functions decay as non-universal power-laws, and scaling relations between their exponents are parameterized by the effective coupling constant. Charge-spin separation only shows up in dynamical correlations. The Luttinger liquid concept is developed from perturbations of the Luttinger model. Mainly specializing to the 1D Hubbard model, we review a variety of mappings for complicated models of interacting electrons onto Luttinger models, and thereby obtain their correlation functions. We also discuss the generic behaviour of systems not falling into the Luttinger liquid universality class because of gaps in their low-energy spectrum. The Mott transition provides an example for the transition from Luttinger to non-Luttinger behaviour, and recent results on this problem are summarized. Coupling chains by interactions or tunneling allows transverse coherence to establish in the single-or two-particle dynamics, and drives the systems away from a Luttinger liquid. We discuss the influence of charge-spin separation and of the anomalous dimensions on the transverse dynamics of the electrons. The edge states in the quani tum Hall effect provide a realization of a modified, chiral Luttinger liquid whose detailed properties differ...

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Section: Low-energy Properties Of One-dimensional Lattice Modelsmentioning

confidence: 95%

One-dimensional Fermi liquids

1995

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“…The spin operator associated with site i is defined as For highly correlated electron systems, Gutzwiller-Jastrow-type wave functions with twobody correlation factor are fairly common. [14][15][16][17][18][19] The Gutzwiller wave function, [20] which is a prototype of the trial function of this type, is often used as a starting trial function for its simplicity. It is defined as…”

Section: Trial Wave Functionmentioning

confidence: 99%

“…So far, various kinds of variational functions have been proposed for strongly correlated electron systems. [14][15][16][17][18][19] The Gutzwiller wave function [20] has been extensively studied for its simplicity, and shown to be a good trial function for the supersymmetric (J/t = 2) 1D t-J model. [17] This wave function was improved for other values of J/t by introducing a conventional Jastrow-correlation factor, but the expected TLL behavior was not recovered.…”

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confidence: 99%

Variational state based on the Bethe-ansatz solution and a correlated singlet liquid state in the one-dimensionalt-Jmodel

1996

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The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe ansatz solution is newly proposed, where the spin-charge separation is realized, and a longrange correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; Both of the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters 1 in the trial functions are derived.

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“…We restrict ourselves in this work to a spin singlet and therefore have equal numbers of up and down electrons in the Slater factor. The Jastrow factor |F(r^,r/)| v in (2) uses the modulus of a Slater determinant in all electron coordinates to correlate the particles [9,10]. This factor is manifestly symmetric under all permutations, thus preserving the spin-singlet nature of the unmodified state.…”

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confidence: 99%

Phase diagram of the one-dimensional t-J model from variational theory

1991

Phys. Rev. Lett.

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We study a class of variational wave functions for strongly interacting one-dimensional lattice fermions in which correlations among the particles are specified by a single variational parameter. We find that the wave functions describe the ground-state properties of the one-dimensional t-J model remarkably well over the entire phase diagram in which interaction strength and density are varied. Specifically the wave function describes a Tomonaga-Luttinger liquid at low Jit, a phase-separated state at large Jit, and a stable state with infinite compressibility between these phases at low densities.

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Composite-fermion theory for the strongly correlated Hubbard model

Cited by 21 publications

References 22 publications

One-dimensional Fermi liquids

One-dimensional Fermi liquids

Variational state based on the Bethe-ansatz solution and a correlated singlet liquid state in the one-dimensionalt-Jmodel

Phase diagram of the one-dimensional t-J model from variational theory

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