Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9909005 · Journal of the Physical Society of Japan

Critical Properties of One-Dimensional Electron Systems with 1/rα-type Long-Range Interactions

Yasumasa Tsukamoto, Norio Kawakami

Published Jan 1, 2000• 32 citations
arXivHTMLPDF

Abstract

We study the critical properties of one-dimensional electron systems with the $1/r^α$-type long-range interaction ($α\ge 1$). Using bosonization methods, we discuss how the 1D system exhibits a crossover from the Tomonaga-Luttinger liquid to the Wigner crystal when $α\to 1$. In particular, a detailed analysis is given to the Fermi-edge singularity phenomena when a {\it mobile} core hole is created suddenly in the valence band. It is found that the effect due to the core-hole motion on the Fermi-edge singularity is gradually suppressed as the system approaches the Wigner crystal, and its critical behavior is dominated by the ordinary impurity forward-scattering inherent in a static hole.

DOI
10.1143/jpsj.69.149

Related papers

Resonance in the Fermi-edge singularity of one-dimensional systems

Yuval Oreg, Alexander M. Finkel’stein

The problem of the Fermi-edge singularity in a one-dimensional Tomonaga-Luttinger liquid is reconsidered. The backward scattering of the conduction band electrons on the impuritylike hole in the valence band is analyzed by mapping the problem onto a Coulomb gas theory. For the case when the electron-electron interaction is repulsive, the obtained exponent of the one-dimensional Fermi-edge singularity appears to be different from the exponent found in previous studies. It is shown that the infrared physics of the Fermi-edge singularity in the presence of backward scattering and electron-electron repulsion resembles the physics of the Kondo problem. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9601021•Physical review. B, Condensed matter•Apr 15, 1996•29 citations

Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions

Hiroshi Otani, Tetsuo Ogawa

Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, ${\ensuremath{\lambda}}_{\mathit{e}}$ and ${\ensuremath{\lambda}}_{\mathit{h}}$, of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\infty} and ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\infty}), the correlation function yields a power-law decay only for a long-time regime, which is determined by the force ranges as t>max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]/${\mathit{v}}_{\mathit{F}}$. Corresponding optical spectrum near the Fermi edge (within an energy range of \ensuremath{\Elzxh}${\mathit{v}}_{\mathit{F}}$/max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\rightarrow}\ensuremath{\infty} and/or ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\rightarrow}\ensuremath{\infty}), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power-law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity. Relations between the spectral shape and a measurement time (frequency resolution) are also clarified. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Aug 15, 1996•18 citations

Critical behavior of Tomonaga-Luttinger liquids with a mobile impurity

Yasumasa Tsukamoto, Tatsuya Fujii, Norio Kawakami

The critical properties of Tomonaga-Luttinger liquids including a mobile impurity are studied by means of the Bethe ansatz method, conformal field theory (CFT), and bosonization. We calculate conformal dimensions by performing the CFT analysis of the energy spectrum for an integrable impurity model, and show that this system is classified as $c=1$ shifted Gaussian CFT. The exact critical exponents of various correlation functions are obtained as functions of the impurity mass and its momentum. Passing to the continuum limit, we then construct an effective field theory in terms of bosonization, and directly calculate some correlation functions. A possible application to the Fermi-edge singularity in quantum wires is also discussed.

Physical review. B, Condensed matter•Aug 15, 1998•36 citations

Fermi-edge singularity with backscattering in the Luttinger-liquid model

Nikolay V. Prokof'ev

We study the response of the interacting electron gas in one-dimension (1D) to a local external potential. In the low-frequency limit the power-law singularities are essentially modified by backscattering effects which, in the case of zero forward scattering, result in the universal critical exponent depending only on the Luttinger-liquid interactions. The results obtained may be used to describe singular responses of the 1D boson chains.

arXiv:cond-mat/9306040•Physical review. B, Condensed matter•Jan 15, 1994•54 citations

Fermi-edge singularity of the Tomonaga-Luttinger liquids with spin-split Fermi points

Hiroshi Otani, Tetsuo Ogawa

Interacting electron systems in one dimension with spin-split Fermi points are studied theoretically with the aid of the Tomonaga-Luttinger bosonization. The spin splitting of the systems considered is classified into three categories: (i) the momentum-dependent spin splitting without the time-reversal symmetry, (ii) the momentum-dependent spin splitting with the time-reversal symmetry, and (iii) the momentum-independent spin splitting. Calculating analytically the current-current correlation functions in the three cases, the critical exponents of the optical Fermi-edge singularity (FES) are obtained by using the forward-scattering Tomonaga-Luttinger model. The phase diagrams for the sign of the FES exponent are drawn to clarify the relation between the shape of optical edge spectra and the electron-electron or the electron-hole interactions. Response to circularly polarized incident light is also revealed. In the case of the momentum-dependent spin splitting, the power-law divergence of the edge spectra is possible even for repulsive electron-hole interactions. This is in striking contrast to the FES in spin-degenerate (no spin splitting) electron systems. The FES in a spin-split chiral Luttinger liquid is also discussed. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 15, 1996•11 citations

Transport properties of a quantum wire in the presence of impurities and long-range Coulomb forces

H. Maurey, Thierry Giamarchi

One-dimensional electron systems interacting with long-range Coulomb forces (quantum wires) show a Wigner crystal structure. We investigate in this paper the transport properties of such a Wigner crystal in the presence of impurities. Contrary to what happens when only short-range interactions are included, the system is dominated by 4${\mathit{k}}_{\mathit{F}}$ scattering on the impurities. There are two important length scales in such a problem: one is the pinning length above which the (quasi-)long-range order of the Wigner crystal is destroyed by disorder. The other length, ${\ensuremath{\xi}}_{\mathrm{cr}}$, is the length below which Coulomb interactions are not important and the system is behaving as a standard Luttinger liquid with short-range interactions. We obtain the frequency and temperature dependence of the conductivity. We show that such a system is very similar to a classical charge density wave pinned by impurities, but with important differences due to quantum fluctuations and long-range Coulomb interactions. Finally, we discuss our results in comparison with experimental systems.

arXiv:cond-mat/9408094•Physical review. B, Condensed matter•Apr 15, 1995•47 citations
We study the critical properties of one-dimensional electron systems with the 1/rα1/r^α1/rα-type long-range interaction (α≥1α\ge 1α≥1). Using bosonization methods, we discuss how the 1D system exhibits a crossover from the Tomonaga-Luttinger liquid to the Wigner crystal when α→1α\to 1α→1. In particular, a detailed analysis is given to the Fermi-edge singularity phenomena when a {\it mobile} core hole is created suddenly in the valence band. It is found that the effect due to the core-hole motion on the Fermi-edge singularity is gradually suppressed as the system approaches the Wigner crystal, and its critical behavior is dominated by the ordinary impurity forward-scattering inherent in a static hole.
The problem of the Fermi-edge singularity in a one-dimensional Tomonaga-Luttinger liquid is reconsidered. The backward scattering of the conduction band electrons on the impuritylike hole in the valence band is analyzed by mapping the problem onto a Coulomb gas theory. For the case when the electron-electron interaction is repulsive, the obtained exponent of the one-dimensional Fermi-edge singularity appears to be different from the exponent found in previous studies. It is shown that the infrared physics of the Fermi-edge singularity in the presence of backward scattering and electron-electron repulsion resembles the physics of the Kondo problem. \textcopyright{} 1996 The American Physical Society.
Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, ${\ensuremath{\lambda}}_{\mathit{e}}$ and ${\ensuremath{\lambda}}_{\mathit{h}}$, of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\infty} and ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\infty}), the correlation function yields a power-law decay only for a long-time regime, which is determined by the force ranges as t>max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]/vF{\mathit{v}}_{\mathit{F}}vF​. Corresponding optical spectrum near the Fermi edge (within an energy range of \ensuremath{\Elzxh}vF{\mathit{v}}_{\mathit{F}}vF​/max[${\ensuremath{\lambda}}_{\mathit{e}}$,${\ensuremath{\lambda}}_{\mathit{h}}$]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the ${\mathit{x}}^{\mathrm{\ensuremath{-}}1}$ type (i.e., ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\rightarrow}\ensuremath{\infty} and/or ${\ensuremath{\lambda}}_{\mathit{h}}$\ensuremath{\rightarrow}\ensuremath{\infty}), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power-law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity. Relations between the spectral shape and a measurement time (frequency resolution) are also clarified. \textcopyright{} 1996 The American Physical Society.
The critical properties of Tomonaga-Luttinger liquids including a mobile impurity are studied by means of the Bethe ansatz method, conformal field theory (CFT), and bosonization. We calculate conformal dimensions by performing the CFT analysis of the energy spectrum for an integrable impurity model, and show that this system is classified as c=1c=1c=1 shifted Gaussian CFT. The exact critical exponents of various correlation functions are obtained as functions of the impurity mass and its momentum. Passing to the continuum limit, we then construct an effective field theory in terms of bosonization, and directly calculate some correlation functions. A possible application to the Fermi-edge singularity in quantum wires is also discussed.
Interacting electron systems in one dimension with spin-split Fermi points are studied theoretically with the aid of the Tomonaga-Luttinger bosonization. The spin splitting of the systems considered is classified into three categories: (i) the momentum-dependent spin splitting without the time-reversal symmetry, (ii) the momentum-dependent spin splitting with the time-reversal symmetry, and (iii) the momentum-independent spin splitting. Calculating analytically the current-current correlation functions in the three cases, the critical exponents of the optical Fermi-edge singularity (FES) are obtained by using the forward-scattering Tomonaga-Luttinger model. The phase diagrams for the sign of the FES exponent are drawn to clarify the relation between the shape of optical edge spectra and the electron-electron or the electron-hole interactions. Response to circularly polarized incident light is also revealed. In the case of the momentum-dependent spin splitting, the power-law divergence of the edge spectra is possible even for repulsive electron-hole interactions. This is in striking contrast to the FES in spin-degenerate (no spin splitting) electron systems. The FES in a spin-split chiral Luttinger liquid is also discussed. \textcopyright{} 1996 The American Physical Society.
One-dimensional electron systems interacting with long-range Coulomb forces (quantum wires) show a Wigner crystal structure. We investigate in this paper the transport properties of such a Wigner crystal in the presence of impurities. Contrary to what happens when only short-range interactions are included, the system is dominated by 4kF{\mathit{k}}_{\mathit{F}}kF​ scattering on the impurities. There are two important length scales in such a problem: one is the pinning length above which the (quasi-)long-range order of the Wigner crystal is destroyed by disorder. The other length, ${\ensuremath{\xi}}_{\mathrm{cr}}$, is the length below which Coulomb interactions are not important and the system is behaving as a standard Luttinger liquid with short-range interactions. We obtain the frequency and temperature dependence of the conductivity. We show that such a system is very similar to a classical charge density wave pinned by impurities, but with important differences due to quantum fluctuations and long-range Coulomb interactions. Finally, we discuss our results in comparison with experimental systems.