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Spectral microscopic mechanisms and quantum phase transitions in a 1D correlated problem

J. M. P. Carmelo, Karlo Penc

Published Jan 1, 2005• 4 citations
OpenAlex

Abstract

Abstract. In this paper we study the dominant microscopic processes that generate nearly the whole one-electron removal and addition spectral weight of the onedimensional Hubbard model for all values of the on-site repulsion U. We find that for the doped Mott-Hubbard insulator there is a competition between the microscopic processes that generate the one-electron upper-Hubbard band spectral-weight distributions of the Mott-Hubbard insulating phase and finite-doping-concentration metallic phase, respectively. The spectral-weight distributions generated by the nonperturbative processes studied here are shown elsewhere to agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in quasi-one-dimensional compounds. PACS numbers: 71.20.-b, 71.10.Pm, 72.15.Nj, 71.27.+aSpectral microscopic mechanisms and... 2 1.

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Spectral microscopic mechanisms and quantum phase transitions in a 1D correlated problem

J. M. P. Carmelo, Karlo Penc

In this paper we study the dominant microscopic processes that generate nearly the whole one-electron removal and addition spectral weight of the one-dimensional Hubbard model for all values of the on-site repulsion U . We find that for the doped Mott–Hubbard insulator there is a competition between the microscopic processes that generate the one-electron upper-Hubbard-band spectral-weight distributions of the Mott–Hubbard insulating phase and finite-doping-concentration metallic phase, respectively. The spectral-weight distributions generated by the non-perturbative processes studied here are shown elsewhere to agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in quasi-one-dimensional compounds.

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One-electron singular branch lines of the Hubbard chain

J. M. P. Carmelo, Karlo Penc, Luís Miguel Martelo +5 more

The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U . To achieve this goal, we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.

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Finite-Energy Pseudoparticle Theory for the 1D Hubbard Model II: Holon and Spinon Dominant Processes for the Few-Electron Spectral Weight Properties

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In the first paper of this series it was found that the $η$-spin 1/2 holons, spin 1/2 spinons, and $c$ pseudoparticles whose occupancy configurations describe the energy eigenstates of the one-dimensional Hubbard model emerge from the electron - rotated-electron unitary transformation. In this second paper we discuss and clarify how the relation of the electrons to the above objects can be used in a program for evaluation of finite-energy few-electron spectral functions. As a first step, here we characterize the dominant holon and spinon microscopic physical processes that originate more than 99% of the few-electron spectral weight. These dominant processes are related to exact selection rules for the values of the number of holons and spinons generated or annihilated by application onto a ground state of rotated-electron operators. We also generalize the concepts of a lower Hubbard band and upper Hubbard bands to all values of on-site Coulombian repulsion.

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Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-$1/2$ atom systems is discussed.

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In this paper we use the pseudofermion dynamical theory (PDT) in the study of the one-electron removal singular spectral features the one-dimensional Hubbard model. The PDT reveals that in the whole $(k, ω)$-plane such features are of power-law type and correspond to well defined lines of three types: the charge singular branch lines, the spin singular branch lines, and the border lines. One of our goals is the study of the momentum and energy dependence of the spectral-weight distribution in the vicinity of such lines. We find that the charge and spin branch lines correspond to the main tetracyanoquinodimethane (TCNQ) peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ). Our expressions refer to all values of the electronic density and on-site repulsion $U$. The weight distribution in the vicinity of the singular spectral lines is fully controlled by the overall pseudofermion phase shifts. Moreover, the shape of these lines is determined by the bare-momentum dependence of the pseudofermion energy dispersions.

arXiv:cond-mat/0307602•Jul 24, 2003•0 citations

Dynamical functions of a 1D correlated quantum liquid

J. M. P. Carmelo, D. Bozi, Karlo Penc

We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.

arXiv:0808.3001•Journal of Physics Condensed Matter•Sep 5, 2008•27 citations
Abstract. In this paper we study the dominant microscopic processes that generate nearly the whole one-electron removal and addition spectral weight of the onedimensional Hubbard model for all values of the on-site repulsion U. We find that for the doped Mott-Hubbard insulator there is a competition between the microscopic processes that generate the one-electron upper-Hubbard band spectral-weight distributions of the Mott-Hubbard insulating phase and finite-doping-concentration metallic phase, respectively. The spectral-weight distributions generated by the nonperturbative processes studied here are shown elsewhere to agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in quasi-one-dimensional compounds. PACS numbers: 71.20.-b, 71.10.Pm, 72.15.Nj, 71.27.+aSpectral microscopic mechanisms and... 2 1.
In this paper we study the dominant microscopic processes that generate nearly the whole one-electron removal and addition spectral weight of the one-dimensional Hubbard model for all values of the on-site repulsion U . We find that for the doped Mott–Hubbard insulator there is a competition between the microscopic processes that generate the one-electron upper-Hubbard-band spectral-weight distributions of the Mott–Hubbard insulating phase and finite-doping-concentration metallic phase, respectively. The spectral-weight distributions generated by the non-perturbative processes studied here are shown elsewhere to agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in quasi-one-dimensional compounds.
The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U . To achieve this goal, we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.
In the first paper of this series it was found that the ηηη-spin 1/2 holons, spin 1/2 spinons, and ccc pseudoparticles whose occupancy configurations describe the energy eigenstates of the one-dimensional Hubbard model emerge from the electron - rotated-electron unitary transformation. In this second paper we discuss and clarify how the relation of the electrons to the above objects can be used in a program for evaluation of finite-energy few-electron spectral functions. As a first step, here we characterize the dominant holon and spinon microscopic physical processes that originate more than 99% of the few-electron spectral weight. These dominant processes are related to exact selection rules for the values of the number of holons and spinons generated or annihilated by application onto a ground state of rotated-electron operators. We also generalize the concepts of a lower Hubbard band and upper Hubbard bands to all values of on-site Coulombian repulsion.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/21/21/2 atom systems is discussed.
In this paper we use the pseudofermion dynamical theory (PDT) in the study of the one-electron removal singular spectral features the one-dimensional Hubbard model. The PDT reveals that in the whole (k,ω)(k, ω)(k,ω)-plane such features are of power-law type and correspond to well defined lines of three types: the charge singular branch lines, the spin singular branch lines, and the border lines. One of our goals is the study of the momentum and energy dependence of the spectral-weight distribution in the vicinity of such lines. We find that the charge and spin branch lines correspond to the main tetracyanoquinodimethane (TCNQ) peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ). Our expressions refer to all values of the electronic density and on-site repulsion UUU. The weight distribution in the vicinity of the singular spectral lines is fully controlled by the overall pseudofermion phase shifts. Moreover, the shape of these lines is determined by the bare-momentum dependence of the pseudofermion energy dispersions.
We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.