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

Scientific Reports

Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity

Ch. Uma Lavanya, I. V. Sankar, Ashok Chatterjee

Published Jun 13, 2017• 13 citations
Publisher

Abstract

The Holstein-Hubbard model with Gaussian phonon anharmonicity is studied in one-dimension at half filling using a variational method based on a series of canonical transformations. A fairly accurate phonon state is chosen to average the transformed Holstein-Hubbard Hamiltonian to obtain an effective Hubbard model which is then solved using the exact Bethe - ansatz following Lieb and Wu to obtain the ground state energy, the average lattice displacement and the renormalized parameters. The Mott-Hubbard criterion, local spin moment and the von Neumann entropy (which is a measure of quantum entanglement) are calculated to determine the ground state phase diagram which shows that the width of the metallic phase flanked by the SDW and CDW phases increases with increasing anharmonicity at low and moderate values of anharmonicity but eventually saturates when the anharmonicity becomes substantially large.

DOI
10.1038/s41598-017-03985-2

Related papers

A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

Debika Debnath, Mohammed Zahid Malik, Ashok Chatterjee

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott-Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron-phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Scientific Reports•Jun 10, 2021•10 citations

The Holstein-Hubbard model with Gaussian anharmonicity in one-dimension at half filling

Ch. Uma Lavanya, Ashok Chatterjee

The Holstein-Hubbard model(HHM) with Gaussian anharmonicityis studied at half filling in one-dimension using a variational method based on a series of canonical transformations. It is shown that the anharmonicityincreases the width of the intermediate metallic phase at the SDW-CDW crossover region.

AIP conference proceedings•Jan 1, 2016•1 citation

An intervening metallic phase at the CDW–SDW transition region in the one-dimensional Holstein-Hubbard model at half filling: a semi-exact solution

Mohammed Zahid Malik, Ashok Chatterjee

Abstract The one-dimensional Holstein–Hubbard model is analyzed at half filling at the CDW-SDW transition region by using a series of unitary transformations. The phonon degrees of freedom are eliminated by averaging the transformed Hamiltonian with respect to a generalized many-phonon state and the resulting effective electronic Hamiltonian is finally solved exactly by employing the Bethe-ansatz technique. The present variational state leads to a lower ground state energy as compared to those obtained from the previous variational calculations and yields a wider intermediate metallic phase at the SDW-CDW transition region confirming the prediction of Takada and Chatterjee.

Journal of Physics Communications•Sep 11, 2020•3 citations

Metallicity of the anharmonic Holstein-Hubbard model in the adiabatic regime

Ch. Uma Lavanya, Ashok Chatterjee

The Holstein-Hubbard Model in one dimension at half filling with the Gaussian anharmonicity is considered in the present work. In order to solve the Hamiltonian a series of transformations have been applied as a part of the variational calculation approach. The ground state energy of the model is calculated and the existence of metallic phase in the adiabatic regime is observed.

AIP conference proceedings•Jan 1, 2018•0 citations

Existence of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the 1-D Hubbard-Holstein model at half filling

Mohammed Zahid Malik, Soma Mukhopadhyay, Ashok Chatterjee

The Holstein–Hubbard model is considered to study the competition between the electron-phonon interaction and the electron-electron interaction in a one-dimensional correlated Fermi system at half-filling. First, a series of canonical transformations that incorporate phonon coherence and correlation effects is performed and then the transformed Hamiltonian is averaged with respect to a zero-phonon state. The resulting effective electronic Hamiltonian is finally solved exactly by the Bethe-ansatz technique. It is shown that the present method suggests the existence of a wider intermediate metallic phase at the SDW-CDW crossover region than the one predicted by the simple variational method of Takada and Chatterjee. The presence of this metallic phase is indeed a favorable situation from the point of view of high temperature superconductivity.

AIP conference proceedings•Jan 1, 2019•0 citations

The Hubbard–Holstein Model with Anharmonic Phonons in One Dimension

Ashok Chatterjee, Yasutami Takada

Effects of cubic and quartic anharmonic phonons on the polaronic properties are investigated in the one-dimensional Hubbard–Holstein model at half filling, using the variable-displacement Lang–Firsov canonical transformation and the exact solution of Lieb and Wu. Although the quartic anharmonicity always reduces the effect of the Coulomb repulsion U , the cubic one mainly responsible for the thermal expansion of lattice brings about the effect of strong asymmetric nature in the sign of the electron–phonon coupling constant g ; it enhances the effect of U for positive g , while it suppresses for negative g . As a result, the overall features of the anharmonic system are basically similar to those in the harmonic one for positive g , but even in the range of the realistic magnitudes for those anharmonicities, they may become qualitatively so different for negative g as to provide a first-order phase transition.

Journal of the Physical Society of Japan•Apr 15, 2004•18 citations
The Holstein-Hubbard model with Gaussian phonon anharmonicity is studied in one-dimension at half filling using a variational method based on a series of canonical transformations. A fairly accurate phonon state is chosen to average the transformed Holstein-Hubbard Hamiltonian to obtain an effective Hubbard model which is then solved using the exact Bethe - ansatz following Lieb and Wu to obtain the ground state energy, the average lattice displacement and the renormalized parameters. The Mott-Hubbard criterion, local spin moment and the von Neumann entropy (which is a measure of quantum entanglement) are calculated to determine the ground state phase diagram which shows that the width of the metallic phase flanked by the SDW and CDW phases increases with increasing anharmonicity at low and moderate values of anharmonicity but eventually saturates when the anharmonicity becomes substantially large.
The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott-Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron-phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.
Abstract The one-dimensional Holstein–Hubbard model is analyzed at half filling at the CDW-SDW transition region by using a series of unitary transformations. The phonon degrees of freedom are eliminated by averaging the transformed Hamiltonian with respect to a generalized many-phonon state and the resulting effective electronic Hamiltonian is finally solved exactly by employing the Bethe-ansatz technique. The present variational state leads to a lower ground state energy as compared to those obtained from the previous variational calculations and yields a wider intermediate metallic phase at the SDW-CDW transition region confirming the prediction of Takada and Chatterjee.
The Holstein–Hubbard model is considered to study the competition between the electron-phonon interaction and the electron-electron interaction in a one-dimensional correlated Fermi system at half-filling. First, a series of canonical transformations that incorporate phonon coherence and correlation effects is performed and then the transformed Hamiltonian is averaged with respect to a zero-phonon state. The resulting effective electronic Hamiltonian is finally solved exactly by the Bethe-ansatz technique. It is shown that the present method suggests the existence of a wider intermediate metallic phase at the SDW-CDW crossover region than the one predicted by the simple variational method of Takada and Chatterjee. The presence of this metallic phase is indeed a favorable situation from the point of view of high temperature superconductivity.
Effects of cubic and quartic anharmonic phonons on the polaronic properties are investigated in the one-dimensional Hubbard–Holstein model at half filling, using the variable-displacement Lang–Firsov canonical transformation and the exact solution of Lieb and Wu. Although the quartic anharmonicity always reduces the effect of the Coulomb repulsion U , the cubic one mainly responsible for the thermal expansion of lattice brings about the effect of strong asymmetric nature in the sign of the electron–phonon coupling constant g ; it enhances the effect of U for positive g , while it suppresses for negative g . As a result, the overall features of the anharmonic system are basically similar to those in the harmonic one for positive g , but even in the range of the realistic magnitudes for those anharmonicities, they may become qualitatively so different for negative g as to provide a first-order phase transition.