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Physical Review Letters

Two-particle spectral properties of generalized Landau liquids

J. M. P. Carmelo, Peter Horsch

Published Feb 10, 1992• 40 citations
Publisher

Abstract

The matrix elements of the up-spin and down-spin electronic density fluctuations taken between the ground state and the gapless elementary excitations of the Hubbard chain in a magnetic field are obtained. The small-\ensuremath{\omega} charge and spin conductivity spectra are derived. Our results clarify the physical character of the pseudoparticles of the new Landau liquid theory, and identify them as the transport carriers. A generalized adiabatic continuity principle concerning the elementary excitations at finite magnetic field in the limit where momentum and frequency tend to zero is established.

DOI
10.1103/physrevlett.68.871

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We use the Landau-liquid character of the low-energy eigenstate spectrum of the Hubbard chain in a magnetic field to investigate its two-particle spectral properties. The picture that emerges is that of a gas of two coupled fluids of pseudoparticles. The kinetic equations that govern the flow of pseudoparticles are derived. The macroscopic currents are expressed in terms of the elementary pseudoparticle currents. As a central result we evaluate in the limit of zero momentum the wave function for the electronic excitations obtained by applying the up-spin and down-spin density-fluctuation operators on the ground state. This wave function is calculated on the basis of the pseudoparticle single-pair eigenstates. It is defined by the microscopic two-particle matrix elements of the corresponding fluctuations taken between the ground state and the elementary excitations. The on-site interaction U, electronic density n, and magnetic field H dependence of these matrix elements, which play a major role in the two-particle spectral functions, provide relevant information on the microscopic foundation of the one-dimensional Landau-liquid theory. This leads to the introduction of an adiabatic continuity principle, which is valid in the Hilbert subspace of the pseudoparticle single-pair eigenstates of lowest energy and momentum. The non-Landau-liquid character of the zero-magnetic-field L\"uttinger phase, where such an adiabatic continuity principle is not valid, is explained.Exact expressions for the two-pseudoparticle forward-scattering amplitudes and for the charge-charge and spin-spin correlation functions at small momentum and low frequency are obtained. The dependence of the charge and spin stiffnesses of the conductivity spectra on U, n, and H, which is determined by the pseudoparticle transport masses, is investigated in detail. The study of these masses and of the effective charge and spin projection of the pseudoparticles gives information on their structure in the electronic representation. It is shown that the decoupling that characterizes the low-energy excitation spectrum does not correspond in the case of finite magnetic fields to a real charge-spin separation. Our results provide a method for the study of the low-frequency dynamics of interacting systems solvable with the Bethe ansatz, and we identify the spectral parameters that control the nonclassical critical exponents with microscopic two-electron matrix elements.

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Magnetic-field and chemical-potential effects on the low-energy separation of the Hubbard chain

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arXiv:cond-mat/9701094•Physical review. B, Condensed matter•Aug 15, 1997•16 citations
The matrix elements of the up-spin and down-spin electronic density fluctuations taken between the ground state and the gapless elementary excitations of the Hubbard chain in a magnetic field are obtained. The small-\ensuremath{\omega} charge and spin conductivity spectra are derived. Our results clarify the physical character of the pseudoparticles of the new Landau liquid theory, and identify them as the transport carriers. A generalized adiabatic continuity principle concerning the elementary excitations at finite magnetic field in the limit where momentum and frequency tend to zero is established.
We use the Landau-liquid character of the low-energy eigenstate spectrum of the Hubbard chain in a magnetic field to investigate its two-particle spectral properties. The picture that emerges is that of a gas of two coupled fluids of pseudoparticles. The kinetic equations that govern the flow of pseudoparticles are derived. The macroscopic currents are expressed in terms of the elementary pseudoparticle currents. As a central result we evaluate in the limit of zero momentum the wave function for the electronic excitations obtained by applying the up-spin and down-spin density-fluctuation operators on the ground state. This wave function is calculated on the basis of the pseudoparticle single-pair eigenstates. It is defined by the microscopic two-particle matrix elements of the corresponding fluctuations taken between the ground state and the elementary excitations. The on-site interaction U, electronic density n, and magnetic field H dependence of these matrix elements, which play a major role in the two-particle spectral functions, provide relevant information on the microscopic foundation of the one-dimensional Landau-liquid theory. This leads to the introduction of an adiabatic continuity principle, which is valid in the Hilbert subspace of the pseudoparticle single-pair eigenstates of lowest energy and momentum. The non-Landau-liquid character of the zero-magnetic-field L\"uttinger phase, where such an adiabatic continuity principle is not valid, is explained.Exact expressions for the two-pseudoparticle forward-scattering amplitudes and for the charge-charge and spin-spin correlation functions at small momentum and low frequency are obtained. The dependence of the charge and spin stiffnesses of the conductivity spectra on U, n, and H, which is determined by the pseudoparticle transport masses, is investigated in detail. The study of these masses and of the effective charge and spin projection of the pseudoparticles gives information on their structure in the electronic representation. It is shown that the decoupling that characterizes the low-energy excitation spectrum does not correspond in the case of finite magnetic fields to a real charge-spin separation. Our results provide a method for the study of the low-frequency dynamics of interacting systems solvable with the Bethe ansatz, and we identify the spectral parameters that control the nonclassical critical exponents with microscopic two-electron matrix elements.
In this paper we consider the one-dimensional Hubbard model and study the deviations from the ground-state values of double occupation which result from creation or annihilation of holons, spinons, and pseudoparticles. These quantum objects are such that all energy eigenstates are described by their occupancy configurations. The band-momentum dependence of the obtained double-occupation spectra provides important information on the degree of localization/delocalization of the real-space lattice electron site distribution configurations associated with the pseudoparticles. We also study the band momentum, on-site electronic repulsion, and electronic density dependence of the pseudoparticle energy bands. The shape of these bands plays an important role in the finite-energy spectral properties of the model. Such a shape defines the form of the lines in the momentum-energy/frequency plane where the peaks and edges of the one-electron and two-electron spectral weight of physical operators are located. Our findings are useful for the study of the one-electron and two-electron spectral-weight distribution of physical operators.
We show that in the presence of a magnetic field the usual low-energy separation of the Hubbard chain is replaced by a c and s separation. Here c and s refer to small-momentum and low-energy independent excitation modes which couple both to charge and spin. Importantly, we find the exact generators of these excitations in both the electronic and pseudoparticle bases. In the limit of zero magnetic field these generators become the usual charge and spin fluctuation operators. The c and s elementary excitations are associated with the c and s pseudoparticles, respectively. We also study the separate pseudoparticle left and right conservation laws. In the presence of the magnetic field the small-momentum and low-energy excitations can be bosonized. However, the suitable bosonization corresponds to the c and s pseudoparticle modes and not to the usual charge and spin fluctuations. We evaluate exactly the commutator between the electronic-density operators. Its spin-dependent factor is in general nondiagonal and depends on the interaction. The associate bosonic commutation relations characterize the present unconventional low-energy separation. \textcopyright{} 1996 The American Physical Society.
The transport of charge and spin at finite energies is studied for the Hubbard chain in a magnetic field by means of the pseudoparticle perturbation theory. In the general case, this involves the solution of an infinite set of Bethe-ansatz equations with a flux. Our results refer to all densities and magnetizations. We express the charge and the spin-diffusion currents in terms of elementary currents associated with the charge and spin carriers. We show that these are the α,γpseudoparticles (with α=c,s and γ=0,1,2,3,...) and we find their couplings to charge and spin. We also study the ratios of the pseudoparticle charge and spin transport masses over the corresponding static mass. These ratios provide valuable information on the effects of electronic correlations in the transport properties of the quantum system. We show that the transport of charge and spin in the Hubbard chain can, alternatively, be described by means of pseudoparticle kinetic equations. This follows from the occurrence of only forward-scattering pseudoparticle interactions at all energies.
We introduce the pseudohole and heavy-pseudoparticle operator algebra that generates all Hubbard-chain eigenstates from a single reference vacuum. In addition to the pseudoholes already introduced for the description of the low-energy physics, this involves the heavy pseudoparticles associated with Hamiltonian eigenstates whose energy spectrum has a gap relative to the many-electron ground state. We introduce a generalized pseudoparticle perturbation theory that describes the relevant finite-energy ground-state transitions. In the present basis these excitations refer to a small density of excited pseudoparticles. Our operator basis goes beyond the Bethe-ansatz solution and it is the suitable and correct starting point for the study of the finite-frequency properties, which are of great relevance for the understanding of the unusual spectral properties detected in low-dimensional novel materials.