arXiv:cond-mat/0402298 · Physical Review B

Dynamical density matrix renormalization group study of photoexcited states in one-dimensional Mott insulators

Hiroaki Matsueda, Takami Tohyama, Sadamichi Maekawa

Published Jul 9, 2004• 25 citations

Abstract

One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, $U$ and $V$, respectively. We find that the lowest optically allowed and forbidden excited states across the Mott gap, which have odd and even parities, respectively, are degenerate for $V∕t\ensuremath{\lesssim}2$ with $t$ being the hopping integral of an electron between nearest neighbor sites. For $V∕t\ensuremath{\gtrsim}2$, the bound states with odd and even parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.

DOI: 10.1103/physrevb.70.033102

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arXiv:cond-mat/0402298 · Physical Review B

Dynamical density matrix renormalization group study of photoexcited states in one-dimensional Mott insulators

Hiroaki Matsueda, Takami Tohyama, Sadamichi Maekawa

Published Jul 9, 2004• 25 citations

arXiv HTML PDF

Abstract

U

and

V

, respectively. We find that the lowest optically allowed and forbidden excited states across the Mott gap, which have odd and even parities, respectively, are degenerate for

V∕t\ensuremath{\lesssim}2

with

t

being the hopping integral of an electron between nearest neighbor sites. For

V∕t\ensuremath{\gtrsim}2

, the bound states with odd and even parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.

DOI: 10.1103/physrevb.70.033102

Related papers

Dynamical DMRG study of photoexcited states in one-dimensional Mott insulators

Hiroaki Matsueda, Takami Tohyama, Sadamichi Maekawa

One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group (DMRG) method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, $U$ and $V$ , respectively. We find that the lowest optically-allowed and forbidden excited states, which have odd and even parities, respectively, are degenerate for $V/t\ltsim 2$ with $t$ being the hopping integral of an electron between nearest neighbor sites. For $V/t\gtsim 2$, the bound states with even and odd parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group (DMRG) method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, $U$ and $V$, respectively. We find that the lowest optically-allowed and forbidden excited states, which have odd and even parities, respectively, are degenerate for $V/t\ltsim 2$ with $t$ being the hopping integral of an electron between nearest neighbor sites. For $V/t\gtsim 2$, the bound states with even and odd parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.

Feb 11, 20040 citations

Density-matrix renormalization group study of optical conductivity of the Mott insulator for two-dimensional clusters

Kazuya Shinjo, Yoshiki Tamaki, Shigetoshi Sota +1 more

The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$ , we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}$, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.

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The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).

arXiv:cond-mat/0208480Physical review. B, Condensed matterFeb 14, 200382 citations

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Kazuya Shinjo, Yoshiki Tamaki, Shigetoshi Sota +1 more

The real part of optical conductivity, $\text{Re}\sigma(\omega)$ , of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\sigma(\omega)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\sigma(\omega)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in $\text{Re}\sigma(\omega)$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\sigma(\omega)$ on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\sigma(\omega)$ by modeling the electron-phonon coupling present in La $_{2}$ CuO $_{4}$ and Nd $_{2}$ CuO $_{4}$ , we obtain $\text{Re}\sigma(\omega)$ comparable with experiments.The real part of optical conductivity, $\text{Re}\sigma(\omega)$, of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\sigma(\omega)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\sigma(\omega)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in $\text{Re}\sigma(\omega)$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\sigma(\omega)$ on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\sigma(\omega)$ by modeling the electron-phonon coupling present in La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$, we obtain $\text{Re}\sigma(\omega)$ comparable with experiments.

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Density-Matrix Renormalization Group Study of Third Harmonic Generation in One-Dimensional Mott Insulator Coupled with Phonon

Shigetoshi Sota, Seiji Yunoki, Takami Tohyama

We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr $_2$ CuO $_3$ . The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr$_2$CuO$_3$. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.

arXiv:1411.4767Journal of the Physical Society of JapanApr 16, 20153 citations

Nonequilibrium optical response of a one-dimensional Mott insulator

Julián Rincón, Adrian E. Feiguin

We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.

arXiv:2012.15652Physical review. B./Physical review. BAug 13, 202114 citations

U

and

V

, respectively. We find that the lowest optically allowed and forbidden excited states across the Mott gap, which have odd and even parities, respectively, are degenerate for

V∕t\ensuremath{\lesssim}2

with

t

being the hopping integral of an electron between nearest neighbor sites. For

V∕t\ensuremath{\gtrsim}2

, the bound states with odd and even parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.

U

and

V

, respectively. We find that the lowest optically-allowed and forbidden excited states, which have odd and even parities, respectively, are degenerate for $V/t\ltsim 2$ with

t

being the hopping integral of an electron between nearest neighbor sites. For $V/t\gtsim 2$, the bound states with even and odd parities occur and are not degenerate. The nature of the degeneracy and its effect on the optical response are examined.

{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}

and

{\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}

, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.

The real part of optical conductivity,

\text{Re}\sigma(\omega)

, of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study

\text{Re}\sigma(\omega)

of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of

\text{Re}\sigma(\omega)

not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in

\text{Re}\sigma(\omega)

implies the formation of a spin polaron. Examining the dependence of

\text{Re}\sigma(\omega)

on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in

\text{Re}\sigma(\omega)

by modeling the electron-phonon coupling present in La

_{2}

CuO

_{4}

and Nd

_{2}

CuO

_{4}

, we obtain

\text{Re}\sigma(\omega)

comparable with experiments.

_2

CuO

_3

. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.