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Physical review. B, Condensed matter

SU(N) generalization of the Gutzwiller-Jastrow wave function and its critical properties in one dimension

Norio Kawakami

Published Aug 1, 1992• 64 citations
Publisher

Abstract

The SU(N)-generalized Gutzwiller-Jastrow wave function, which includes the effects of smooth-correlation holes, is discussed in one dimension. The long-distance critical properties are analyzed using conformal field theory, and the exact critical exponents of the correlation functions are obtained analytically. The universal scaling relations for SU(N) Luttinger liquids are derived. We also present an exactly solvable model for which the SU(N) Gutzwiller wave function gives the ground state.

DOI
10.1103/physrevb.46.3191

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The SU(N)-generalized Gutzwiller-Jastrow wave function, which includes the effects of smooth-correlation holes, is discussed in one dimension. The long-distance critical properties are analyzed using conformal field theory, and the exact critical exponents of the correlation functions are obtained analytically. The universal scaling relations for SU(N) Luttinger liquids are derived. We also present an exactly solvable model for which the SU(N) Gutzwiller wave function gives the ground state.
Using conformal field theory the exact critical exponents are obtained for the SU(N) generalization of the U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model and the supersymmetric t-J model in one dimension. For the Hubbard model the critical exponent of the momentum distribution function is given as \ensuremath{\theta}=(1-1/N)2{)}^{2})2/2 while for the supersymmetric t-J model \ensuremath{\theta} varies continuously in the range 0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}(1-1/N)2{)}^{2})2/2 depending on the electron concentration. The critical exponents of various correlation functions are shown to satisfy the universal scaling relations. The SU(N) t-J model in the range 0J/t\ensuremath{\le}2 belongs to the SU(N) Luttinger liquid for any finite N.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
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.
Exact critical properties of the one-dimensional SU(N) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary conformal field theory. They are classified into two types, i.e., the exponents for the chiral SU(N) Tomonaga-Luttinger liquid and those related to the orthogonality catastrophe. We discuss a possible application of the results to the photoemission (absorption) in the edge state of the fractional quantum Hall effect. \textcopyright{} 1996 The American Physical Society.