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:1601.01251 · Physical review. B./Physical review. B

Mobile impurity approach to the optical conductivity in the Hubbard chain

Thomas Veness, Fabian H. L. Eßler

Published May 2, 2016• 9 citations
arXivHTMLPDF

Abstract

We consider the optical conductivity in the one-dimensional Hubbard model in the metallic phase close to half-filling. In this regime, most of the spectral weight is located at frequencies above an energy scale ${E}_{\mathrm{opt}}$ that tends towards the optical gap in the Mott insulating phase for vanishing doping. Using the Bethe ansatz, we relate ${E}_{\mathrm{opt}}$ to thresholds of particular kinds of excitations in the Hubbard model. We then employ a mobile impurity model to analyze the optical conductivity for frequencies slightly above these thresholds. This entails generalizing mobile impurity models to excited states that are not the highest weight with regards to the SU(2) symmetries of the Hubbard chain, and that occur at a maximum of the impurity dispersion.

DOI
10.1103/physrevb.93.205101

Related papers

Optical conductivity of the Hubbard chain away from half filling

Alexander C. Tiegel, Thomas Veness, Piet E. Dargel +4 more

We consider the optical conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ is computed for a range of interaction strengths and dopings. We identify an energy scale ${E}_{\mathrm{opt}}$ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ for frequencies just above ${E}_{\mathrm{opt}}$ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.

arXiv:1601.00648•Physical review. B./Physical review. B•Mar 3, 2016•11 citations

Optical conductivity of a Hubbard ring with an impurity

Schuster, Cosima, Brune, Philipp

We investigate the optical conductivity of a Hubbard ring in presence of an impurity by means of exact diagonalization using the Lanczos algorithm. We concentrate thereby on the first excited, open shell state, i.e. on twisted boundary conditions. In the metallic phase a substantial part of the spectral weight lies in the Drude peak, $σ(ω) = Dδ(ω)+ σ_{\rm reg}$. In the non-interacting system, the Drude peak can be visualized in our calculations at $ω= 0$ even for finite chain lengths. Adding the impurity, the main peak is shifted to finite frequencies proportional to the impurity strength. The shift indicates the energy gap of the disturbed finite size system, also in the interacting system. Thus, we can pursue in the optical conductivity for finite metallic systems the energy gap. However, due to level crossing, the impurity-induced peak arises in the interacting system first when a certain impurity strength is exceeded. In the Mott insulating phase, the impurity leads to an impurity state within the gap.

arXiv:cond-mat/0507053•Jul 2, 2005•0 citations

Finite-size effects on the optical conductivity of a half-filled Hubbard ring

Charles Allen Stafford, Andrew J. Millis, B. Sriram Shastry

We use the Bethe-ansatz equations to calculate the total and zero-frequency spectral weight in the optical conductivity of the half-filled one-dimensional Hubbard model as a function of the lattice size L and the on-site repulsion U. The zero-frequency spectral weight \ensuremath{\pi}D scales as ${\mathit{L}}^{1/2}$exp(-L/\ensuremath{\xi}) as L\ensuremath{\rightarrow}\ensuremath{\infty}. Near U=0, \ensuremath{\xi} varies as the inverse of the Lieb-Wu charge gap. In the strongly correlated regime (U\ensuremath{\gg}t), ${\ensuremath{\xi}}^{\mathrm{\ensuremath{-}}1}$=ln(U/t)-1.48. $D--- is negative when L is a multiple of 4, corresponding to a negative inductance. We give a physical explanation of our results in terms of a simple model of ring exchange. The finite-size corrections to the total spectral weight scale as ${\mathit{L}}^{\mathrm{\ensuremath{-}}2}$. We discuss the implications of our results for exact diagonalization calculations of the optical conductivity.

Physical review. B, Condensed matter•Jun 1, 1991•78 citations

Exact diagonalization study of optical conductivity in the two-dimensional Hubbard model

Takami Tohyama, Y. Inoue, K. Tsutsui +1 more

The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ sites. Spectral-weight distributions at half-filling and their doping dependence in the 20-site cluster are found to be similar to those in a $\sqrt{18}\ifmmode\times\else\texttimes\fi{}\sqrt{18}$ cluster, but different from $4\ifmmode\times\else\texttimes\fi{}4$ results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.

arXiv:cond-mat/0505404•Physical Review B•Jul 11, 2005•37 citations

Drude weight, optical conductivity, and flux properties of one-dimensional Hubbard rings

Richard M. Fye, Marcio Jose Martins, Douglas J. Scalapino +2 more

We study the Drude weight, optical conductivity, and flux-periodicity properties of one-dimensional Hubbard chains using Bethe-ansatz, Lanczos, and exact-diagonalization techniques. We find that the Drude weight D is unexpectedly negative for half-filled Hubbard rings with N=4n sites reflecting a strong paramagnetic response, while it is positive (diamagnetic) for half-filled rings of N=4n+2 sites. In both cases at half filling, D vanishes exponentially with N on a length scale set by the inverse of the gap for small U/t. Near half filling, we find that D approaches a constant, positive, diamagnetic value as N increases, indicating metallic behavior. Combining Bethe-ansatz results near half filling with the known U=0 and U=\ensuremath{\infty} limits and Lanczos finite-size extrapolations, we obtain a general picture of D in the thermodynamic limit as a function of band filling and the ratio U/t. We note similarities with the low-frequency integrated spectral weight of certain hole-doped and electron-doped high-${\mathit{T}}_{\mathit{c}}$ compounds. We investigate the finite-frequency optical conductivity, finding structure at \ensuremath{\omega}\ensuremath{\approxeq}U and, for one hole off half filling, at \ensuremath{\omega}\ensuremath{\propto}${\mathit{t}}^{2}$/U. We find that minima in the energy of a Hubbard ring enclosing a flux \ensuremath{\Phi} occur with changes of half a flux quantum rather than a full flux quantum when the Coulomb repulsion is turned on. Lastly, we discuss the relationship of the Drude weight computed from open chains to that obtained from rings, and also the effect of arbitrary phases at the ring boundary.

Physical review. B, Condensed matter•Oct 1, 1991•164 citations

Photoinduced Metallic Properties of One-Dimensional Strongly Correlated Electron Systems

Nobuya Maeshima, Kenji Yonemitsu

We study photoinduced optical responses of one-dimensional strongly correlated electron systems. The optical conductivity spectra are calculated for the ground state and a photoexcited state in the one-dimensional Hubbard model at half filling by using the exact diagonalization method. It is found that, in the Mott insulator phase, the photoexcited state has large spectral weights including the Drude weight below the optical gap. As a consequence, the spectral weight above the optical gap is largely reduced. These results imply that a metallic state is induced by photoexcitation. Comparison between the photoexcited and hole-doped states shows that the photoexcitation is similar to chemical doping.

arXiv:cond-mat/0507674•Journal of the Physical Society of Japan•Oct 1, 2005•47 citations
We consider the optical conductivity in the one-dimensional Hubbard model in the metallic phase close to half-filling. In this regime, most of the spectral weight is located at frequencies above an energy scale Eopt{E}_{\mathrm{opt}}Eopt​ that tends towards the optical gap in the Mott insulating phase for vanishing doping. Using the Bethe ansatz, we relate Eopt{E}_{\mathrm{opt}}Eopt​ to thresholds of particular kinds of excitations in the Hubbard model. We then employ a mobile impurity model to analyze the optical conductivity for frequencies slightly above these thresholds. This entails generalizing mobile impurity models to excited states that are not the highest weight with regards to the SU(2) symmetries of the Hubbard chain, and that occur at a maximum of the impurity dispersion.
We consider the optical conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ is computed for a range of interaction strengths and dopings. We identify an energy scale Eopt{E}_{\mathrm{opt}}Eopt​ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ for frequencies just above Eopt{E}_{\mathrm{opt}}Eopt​ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.
We investigate the optical conductivity of a Hubbard ring in presence of an impurity by means of exact diagonalization using the Lanczos algorithm. We concentrate thereby on the first excited, open shell state, i.e. on twisted boundary conditions. In the metallic phase a substantial part of the spectral weight lies in the Drude peak, σ(ω)=Dδ(ω)+σregσ(ω) = Dδ(ω)+ σ_{\rm reg}σ(ω)=Dδ(ω)+σreg​. In the non-interacting system, the Drude peak can be visualized in our calculations at ω=0ω= 0ω=0 even for finite chain lengths. Adding the impurity, the main peak is shifted to finite frequencies proportional to the impurity strength. The shift indicates the energy gap of the disturbed finite size system, also in the interacting system. Thus, we can pursue in the optical conductivity for finite metallic systems the energy gap. However, due to level crossing, the impurity-induced peak arises in the interacting system first when a certain impurity strength is exceeded. In the Mott insulating phase, the impurity leads to an impurity state within the gap.
We use the Bethe-ansatz equations to calculate the total and zero-frequency spectral weight in the optical conductivity of the half-filled one-dimensional Hubbard model as a function of the lattice size L and the on-site repulsion U. The zero-frequency spectral weight \ensuremath{\pi}D scales as L1/2{\mathit{L}}^{1/2}L1/2exp(-L/\ensuremath{\xi}) as L\ensuremath{\rightarrow}\ensuremath{\infty}. Near U=0, \ensuremath{\xi} varies as the inverse of the Lieb-Wu charge gap. In the strongly correlated regime (U\ensuremath{\gg}t), ${\ensuremath{\xi}}^{\mathrm{\ensuremath{-}}1}$=ln(U/t)-1.48. $D--- is negative when L is a multiple of 4, corresponding to a negative inductance. We give a physical explanation of our results in terms of a simple model of ring exchange. The finite-size corrections to the total spectral weight scale as ${\mathit{L}}^{\mathrm{\ensuremath{-}}2}$. We discuss the implications of our results for exact diagonalization calculations of the optical conductivity.
The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ sites. Spectral-weight distributions at half-filling and their doping dependence in the 20-site cluster are found to be similar to those in a $\sqrt{18}\ifmmode\times\else\texttimes\fi{}\sqrt{18}$ cluster, but different from $4\ifmmode\times\else\texttimes\fi{}4$ results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.
We study the Drude weight, optical conductivity, and flux-periodicity properties of one-dimensional Hubbard chains using Bethe-ansatz, Lanczos, and exact-diagonalization techniques. We find that the Drude weight D is unexpectedly negative for half-filled Hubbard rings with N=4n sites reflecting a strong paramagnetic response, while it is positive (diamagnetic) for half-filled rings of N=4n+2 sites. In both cases at half filling, D vanishes exponentially with N on a length scale set by the inverse of the gap for small U/t. Near half filling, we find that D approaches a constant, positive, diamagnetic value as N increases, indicating metallic behavior. Combining Bethe-ansatz results near half filling with the known U=0 and U=\ensuremath{\infty} limits and Lanczos finite-size extrapolations, we obtain a general picture of D in the thermodynamic limit as a function of band filling and the ratio U/t. We note similarities with the low-frequency integrated spectral weight of certain hole-doped and electron-doped high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compounds. We investigate the finite-frequency optical conductivity, finding structure at \ensuremath{\omega}\ensuremath{\approxeq}U and, for one hole off half filling, at \ensuremath{\omega}\ensuremath{\propto}t2{\mathit{t}}^{2}t2/U. We find that minima in the energy of a Hubbard ring enclosing a flux \ensuremath{\Phi} occur with changes of half a flux quantum rather than a full flux quantum when the Coulomb repulsion is turned on. Lastly, we discuss the relationship of the Drude weight computed from open chains to that obtained from rings, and also the effect of arbitrary phases at the ring boundary.
We study photoinduced optical responses of one-dimensional strongly correlated electron systems. The optical conductivity spectra are calculated for the ground state and a photoexcited state in the one-dimensional Hubbard model at half filling by using the exact diagonalization method. It is found that, in the Mott insulator phase, the photoexcited state has large spectral weights including the Drude weight below the optical gap. As a consequence, the spectral weight above the optical gap is largely reduced. These results imply that a metallic state is induced by photoexcitation. Comparison between the photoexcited and hole-doped states shows that the photoexcitation is similar to chemical doping.