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:1212.1868 · Physical Review B

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

Izak Snyman

Published Apr 26, 2013• 2 citations
arXivHTMLPDF

Abstract

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

DOI
10.1103/physrevb.87.165135

Related papers

Linear response of a one-dimensional conductor coupled to a dynamical impurity with a Fermi edge singularity

Izak Snyman

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport setup in which the impurity can be realized in a double quantum dot. The same Hamiltonian describes tunneling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e., many fermion correlations result in an impurity decay rate with a nontrivial power-law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand and the linear response of the Fermi sea to external perturbations on the other. This results in a power-law singularity in the space and time dependence of the nonlocal polarizability of the Fermi sea, which can be detected in transport experiments.

arXiv:1312.2719•Physical Review B•Feb 18, 2014•1 citation

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

Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States

Jacopo De Nardis, Miłosz Panfil

The singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very difficult in most cold atomic experimental settings. Moreover the presence of a finite temperature destroys another feature of one-dimensional quantum liquids: the real space quasilong-range order in which the spatial correlation functions exhibit power-law decay. We consider a nonequilibrium protocol where two interacting Bose gases are prepared either at different temperatures or chemical potentials and then joined. We show that the nonequilibrium steady state emerging at large times around the junction displays edge singularities in the response function and quasilong-range order.

arXiv:1801.08079•Physical Review Letters•May 25, 2018•40 citations

Singular low energy properties of an impurity model with finite range interactions

Thierry Giamarchi, Chandra Mohan Varma, Andrei E. Ruckenstein +1 more

A resonant-level impurity Hamiltonian with finite range interactions is considered. It is shown that for repulsive interactions above a critical threshold, the model displays scale invariant properties unlike those of a Fermi liquid. The various correlation functions behave as power laws with nonuniversal exponents depending on the interactions. At the transition between the Fermi-liquid and non-Fermi-liquid regimes the resistivity behaves as A+B/ln(T${)}^{2}$, whereas it behaves as A+${\mathit{BT}}^{\ensuremath{\nu}}$ with \ensuremath{\nu}>0 in the latter.

Physical Review Letters•Jun 21, 1993•67 citations

Dynamically induced multichannel Kondo effect

Tatsuya Fujii, Norio Kawakami

We study how the multichannel Kondo effect is dynamically induced to affect the photoemission and the inverse photoemission spectrum when an electron is emitted from (or added to) the completely screened Kondo impurity with spin $S>1/2.$ The spectrum thereby shows a power-law edge singularity characteristic of the multichannel Kondo model. We discuss this anomalous behavior by using the exact solution of the multichannel Kondo model and boundary conformal field theory. The idea is further applied to the photoemission for quantum spin systems, in which the edge singularity is controlled by the dynamically induced overscreening effect with a mobile Kondo impurity.

arXiv:cond-mat/0005495•Physical review. B, Condensed matter•Jan 22, 2001•2 citations

Signatures of the orthogonality catastrophe in a coherently driven impurity

Haydn S. Adlong, Weizhe Edward Liu, Lincoln D. Turner +2 more

We consider a fixed impurity immersed in a Fermi gas at arbitrary temperature. We take the impurity to have two internal spin states where the $\ensuremath{\uparrow}$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, whereas the $\ensuremath{\downarrow}$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states, therefore, allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity Green's functions with a variational approach to treat the Rabi driven dynamics, we find that the system features Rabi oscillations whose frequency scales as a nontrivial power of the Rabi drive at low temperatures. This reflects the power law of the Fermi-edge singularity and, importantly, this behavior is qualitatively different from the case of a mobile impurity quasiparticle where the scaling is linear. We, therefore, argue that the scaling law serves as an experimentally implementable probe of the orthogonality catastrophe. We additionally simulate rf spectroscopy beyond linear response, finding a remarkable agreement with an experiment using heavy impurities [Kohstall et al., Nature 485, 615 (2012)], thus, demonstrating the power of our approach.

arXiv:2107.06102•Physical Review A•Oct 14, 2021•5 citations
We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.
I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport setup in which the impurity can be realized in a double quantum dot. The same Hamiltonian describes tunneling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e., many fermion correlations result in an impurity decay rate with a nontrivial power-law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand and the linear response of the Fermi sea to external perturbations on the other. This results in a power-law singularity in the space and time dependence of the nonlocal polarizability of the Fermi sea, which can be detected in transport experiments.
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 singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very difficult in most cold atomic experimental settings. Moreover the presence of a finite temperature destroys another feature of one-dimensional quantum liquids: the real space quasilong-range order in which the spatial correlation functions exhibit power-law decay. We consider a nonequilibrium protocol where two interacting Bose gases are prepared either at different temperatures or chemical potentials and then joined. We show that the nonequilibrium steady state emerging at large times around the junction displays edge singularities in the response function and quasilong-range order.
A resonant-level impurity Hamiltonian with finite range interactions is considered. It is shown that for repulsive interactions above a critical threshold, the model displays scale invariant properties unlike those of a Fermi liquid. The various correlation functions behave as power laws with nonuniversal exponents depending on the interactions. At the transition between the Fermi-liquid and non-Fermi-liquid regimes the resistivity behaves as A+B/ln(T)2{)}^{2})2, whereas it behaves as A+${\mathit{BT}}^{\ensuremath{\nu}}$ with \ensuremath{\nu}>0 in the latter.
We study how the multichannel Kondo effect is dynamically induced to affect the photoemission and the inverse photoemission spectrum when an electron is emitted from (or added to) the completely screened Kondo impurity with spin S>1/2.S>1/2.S>1/2. The spectrum thereby shows a power-law edge singularity characteristic of the multichannel Kondo model. We discuss this anomalous behavior by using the exact solution of the multichannel Kondo model and boundary conformal field theory. The idea is further applied to the photoemission for quantum spin systems, in which the edge singularity is controlled by the dynamically induced overscreening effect with a mobile Kondo impurity.
We consider a fixed impurity immersed in a Fermi gas at arbitrary temperature. We take the impurity to have two internal spin states where the $\ensuremath{\uparrow}$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, whereas the $\ensuremath{\downarrow}$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states, therefore, allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity Green's functions with a variational approach to treat the Rabi driven dynamics, we find that the system features Rabi oscillations whose frequency scales as a nontrivial power of the Rabi drive at low temperatures. This reflects the power law of the Fermi-edge singularity and, importantly, this behavior is qualitatively different from the case of a mobile impurity quasiparticle where the scaling is linear. We, therefore, argue that the scaling law serves as an experimentally implementable probe of the orthogonality catastrophe. We additionally simulate rf spectroscopy beyond linear response, finding a remarkable agreement with an experiment using heavy impurities [Kohstall et al., Nature 485, 615 (2012)], thus, demonstrating the power of our approach.