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Physical review. B, Condensed matter

HubbardU=∞ model in one dimension: The slave-boson method as an alternative bosonization scheme

D. Schmeltzer

Published Apr 1, 1991• 18 citations
Publisher

Abstract

The Hubbard U=\ensuremath{\infty} in one dimension is equivalent to a noninteracting spinless fermion in a gauge field. The gauge field induced by spin fluctuations is described by a gas of instantons. This gas is in the plasma phase, which leads to the decoupling of spin and charge at large distances. These results are used to find the charge-change correlations and the Wowe-renormalization exponent \ensuremath{\theta}.

DOI
10.1103/physrevb.43.8650

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The Hubbard U=\ensuremath{\infty} in one dimension is equivalent to a noninteracting spinless fermion in a gauge field. The gauge field induced by spin fluctuations is described by a gas of instantons. This gas is in the plasma phase, which leads to the decoupling of spin and charge at large distances. These results are used to find the charge-change correlations and the Wowe-renormalization exponent \ensuremath{\theta}.
We present a slave-boson formulation for the Hubbard model that preserves the spin-rotation and particle-hole symmetries of the paramagnetic phase at half filling. Fermion and boson fields are treated on an equal footing in a functional integral formulation. We show that, while in two and three dimensions there is a metal-insulator transition as the interaction U increases, in one dimension our approach always gives an insulating state. Short-range spin-spin correlations are included at the saddle-point level for all values of U, giving a good description of the insulating state. We show that the energy gap in the one-particle spectrum increases from zero as (U-Uc{\mathit{U}}_{\mathit{c}}Uc​${)}^{\mathrm{\ensuremath{\alpha}}}$, where Uc{\mathit{U}}_{\mathit{c}}Uc​ is the critical value of the on-site interaction and the exponent \ensuremath{\alpha} is 1 and 1/2 for 2 and 3 dimensions, respectively. \textcopyright{} 1996 The American Physical Society.
In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott transition and this approach is smoothly connected to the non-interacting limit. As an example, we study the phase diagram of the Kane-Mele-Hubbard model using our current approach. In the absence of the spin-orbit interaction, the Mott transition occurs at Uc 3t1U_c ~ 3 t_1Uc​ 3t1​. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.
We review the slave-boson representations of the Hubbard model. When both spin and charge fermion degrees of freedom are represented by Bose fields, the approach is equivalent at the "self-consistent" saddle point level to the Gutzwiller approximation (GA). We show how the determination of the Lagrange multipliers, introduced to enforce the constraints, involves a Mott-Hubbard gap near half-filling for U > U c (localization edge). The quantum fluctuations are then considered within a renormalized basis of boson fields (restoring the spin-rotation invariance), which brings out two distinct channels, symmetric and antisymmetric. It is remarkable that both spin and charge fluctuations are obtained at the same level of the gaussian fluctuations, as oppossed to the standard 1/N expansion. This provides the microscopic basis for a Fermi liquid theory. Both dynamic effects and extension to finite temperature which were beyond the scope of the variational procedure can now be described by this approach. The physical implications of the model (dynamic correlation functions, T3Ln T term of the specific heat, superfluid instability) are finally considered, all of which reflect the Fermi liquid nature of the system.
In this paper we investigate possible spin disordered phase in the Hubbard model on the honeycomb lattice. Using a slave-particle theory that include the charge fluctuations, we find a meanfield spin disordered phase in a range of on-site repulsion UUU. The spin disordered state is described by gapped fermions coupled to compact U(1) gauge field. We study the confinement/deconfinement problem of the U(1) gauge theory due to the instantons proliferation. We calculate all allowed instanton terms and compute their quantum numbers. It is shown that the meanfield spin disordered phase is unstable. The instantons proliferation induce a translation symmetry breaking.
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and fermionic operators in one dimension. We use these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. We then apply the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension, and transport in clean quantum wires and in the presence of isolated impurities.