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:1810.13106 · Journal of the Physical Society of Japan

Dynamical Charge Structure Factor of a One-Dimensional Ionic Hubbard Model in the Low-Energy Region

Yuhei Komaki, Yuma Iwase, Shogo Yanagimatsu, Yoshiyuki Muta, Nobuya Maeshima, Ken-ichi Hino

Published Apr 22, 2019• 1 citation
arXivHTMLPDF

Abstract

We present a numerical study of the charge dynamical structure factor N(k,omega) of a one-dimensional (1D) ionic Hubbard model in the Mott insulator phase. We show that the low-energy spectrum of N(k,omega) is expressed in terms of the spin operators for the spin degrees of freedom. Numerical results of N(k,omega) for the spin degrees of freedom, obtained by the Lanczos diagonalization method, well reproduce the low-energy spectrum of N(k,omega) of the 1D ionic Hubbard model. In addition, we show that these spectral peaks probe the dispersion of the spin-singlet excitations of the system and are observed in the wide parameter region of the MI phase.

DOI
10.7566/jpsj.88.054709

Related papers

Dynamics in the one-dimensional extended ionic Hubbard model

Mohsen Hafez, Mohammad Reza Abolhassani

We investigate single-particle spectral densities and dynamical charge and spin structure factors of the one-dimensional extended ionic Hubbard model in the band insulator regime by using the perturbative continuous unitary transformations method. The one-body staggered potential is considered as the unperturbed part and the hopping term, on-site electron-electron interaction, and the nearest-neighbor repulsive interaction are treated as the perturbations. The excitation spectrum of this model was determined in a previous work (Hafez and Jafari 2010 Eur. Phys. J. B 78 323). It was shown that when the intersite interaction is off, there are two antibound state modes and one bound state mode in the singlet channel and two bound state modes in the triplet channel, while for finite values of intersite interaction two bound state modes were found in each channel. Our results for dynamical charge and spin structure factors indicate that only one of two bound/antibound state modes can be probed by electron-energy-loss spectroscopy and inelastic neutron scattering experiments.

Journal of Physics Condensed Matter•Jun 1, 2011•6 citations

Phase diagram of the one-dimensional extended ionic Hubbard model

Zhao Hong-Xia, Hui Zhao, Chen Yu-Guang +1 more

We use a density-matrix renormalization group method to study quantitatively the phase diagram of the half-filled one-dimensional (1D) extended Hubbard model in the presence of a staggered ionic potential Δ. An extensive finite-size scaling analysis is carried out on the relevant structure factors and localization operator to characterize the Mott-insulator (MI)-bond-ordered insulator (BOI)-band-insulator (BI) transitions. The intermediate BOI phase occupies a small region of the phase diagram, and this region is enlarged in the presence of Δ. In addition, the phase diagram of ionic Hubbard (the nearest-neighbor electron-electron interaction V=0) is also given.

Acta Physica Sinica•Jan 1, 2015•1 citation

Nature of the insulating phases in the half-filled ionic Hubbard model

A. P. Kampf, Michael Sekania, G. I. Japaridze +1 more

We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.

arXiv:cond-mat/0304697•Journal of Physics Condensed Matter•Aug 15, 2003•76 citations

Magnetic excitation spectra of strongly correlated quasi-one-dimensional systems: Heisenberg versus Hubbard-like behavior

Alberto Nocera, N. D. Patel, Jaime A. Fernandez-Baca +2 more

We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing $U/t$ converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of $U/t$ of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

arXiv:1608.07717•Physical review. B./Physical review. B•Nov 28, 2016•18 citations

One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields

J. M. P. Carmelo, Tilen Čadež, Pedro D Sacramento

Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-$1/2$ atom systems is discussed.

arXiv:2105.06721•Physical review. B./Physical review. B•May 13, 2021•9 citations

Excitation spectrum and quantum phase transitions in the one-dimensional ionic Hubbard model

Mohsen Hafez-Torbati

Strongly correlated electron systems are one of the most fascinating problems in current physics. The strong electron-electron interaction in these materials leads to the emergence of nontrivial elementary excitations (quasiparticles, QPs) above the ground state ranging from fractional spins in quasi-one-dimensional materials to magnetic monopole in the pyrochlore lattice. The condensation of these quasiparticles upon changing some external parameters may stabilize new exotic states of matter. Experimental measurements such as inelastic neutron scattering provide us with valuable information about the excitation spectrum of such systems which require microscopic models to be described. This thesis is devoted to a detailed analysis of the excitation spectrum and of the quantum phase transitions in the one-dimensional (1D) ionic Hubbard model (IHM). The IHM consists of a nearest-neighbor (n.n.) hopping, onsite Hubbard interaction, and an ionic (staggered) potential separating the odd and even sites energetically. The model exhibits two continuous phase transitions on increasing the Hubbard interaction identified by a low-energy effective field theory and confirmed by a rigorous density matrix renormalization group (DMRG) analysis after several attempts. The first transition occurs from band insulator (BI) phase to the 2-fold degenerate spontaneously dimerized insulator (SDI) phase. The transition is in the Ising universality class as is plausible from symmetry considerations. The SDI phase becomes unstable towards a quasi-long-range order Mott insulator (MI) phase at a second transition point resembling the Kosterlitz-Thouless (KT) transition in the frustrated Heisenberg chain. We employ continuous unitary transformations (CUT) to systematically map the IHM to effective Hamiltonians (almost) conserving the number of QPs in the system. Using an analysis in the BI regime where electrons and holes define QPs, the low-energy excitation spectrum of the model is quantitatively determined in the BI phase almost up to the first transition point. The transition from the BI to the SDI phase is signaled by the vanishing of an S=0 exciton mode at the total momentum K=\pi. The condensation of these excitons beyond the first transition point is described by a BCS-type-theory showing the stabilization of the SDI phase. The mean-field solution indicates no second phase transition to the quasi-long-range order MI phase. This is interpreted as the effect of strong quantum fluctuations in one dimension. We consider the IHM in the dimer limit where the uniform chain is separated into independent dimers. The different phases of the IHM are studied by increasing the interdimer hopping and reaching the uniform limit. This dimer limit satisfactorily produces the excitation spectrum of the BI phase confirming the vanishing of an S=0 exciton mode at the first transition point. It is found that the SDI-to-MI transition takes place by softening of a magnetic S=1 excitation, i.e., a triplon. We report rigorous results for the gapless triplon dispersion in the MI phase and discuss the binding effects in the 2-triplon sector.

•Jan 1, 2014•0 citations
We present a numerical study of the charge dynamical structure factor N(k,omega) of a one-dimensional (1D) ionic Hubbard model in the Mott insulator phase. We show that the low-energy spectrum of N(k,omega) is expressed in terms of the spin operators for the spin degrees of freedom. Numerical results of N(k,omega) for the spin degrees of freedom, obtained by the Lanczos diagonalization method, well reproduce the low-energy spectrum of N(k,omega) of the 1D ionic Hubbard model. In addition, we show that these spectral peaks probe the dispersion of the spin-singlet excitations of the system and are observed in the wide parameter region of the MI phase.
We investigate single-particle spectral densities and dynamical charge and spin structure factors of the one-dimensional extended ionic Hubbard model in the band insulator regime by using the perturbative continuous unitary transformations method. The one-body staggered potential is considered as the unperturbed part and the hopping term, on-site electron-electron interaction, and the nearest-neighbor repulsive interaction are treated as the perturbations. The excitation spectrum of this model was determined in a previous work (Hafez and Jafari 2010 Eur. Phys. J. B 78 323). It was shown that when the intersite interaction is off, there are two antibound state modes and one bound state mode in the singlet channel and two bound state modes in the triplet channel, while for finite values of intersite interaction two bound state modes were found in each channel. Our results for dynamical charge and spin structure factors indicate that only one of two bound/antibound state modes can be probed by electron-energy-loss spectroscopy and inelastic neutron scattering experiments.
We use a density-matrix renormalization group method to study quantitatively the phase diagram of the half-filled one-dimensional (1D) extended Hubbard model in the presence of a staggered ionic potential Δ. An extensive finite-size scaling analysis is carried out on the relevant structure factors and localization operator to characterize the Mott-insulator (MI)-bond-ordered insulator (BOI)-band-insulator (BI) transitions. The intermediate BOI phase occupies a small region of the phase diagram, and this region is enlarged in the presence of Δ. In addition, the phase diagram of ionic Hubbard (the nearest-neighbor electron-electron interaction V=0) is also given.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/21/21/2 atom systems is discussed.
Strongly correlated electron systems are one of the most fascinating problems in current physics. The strong electron-electron interaction in these materials leads to the emergence of nontrivial elementary excitations (quasiparticles, QPs) above the ground state ranging from fractional spins in quasi-one-dimensional materials to magnetic monopole in the pyrochlore lattice. The condensation of these quasiparticles upon changing some external parameters may stabilize new exotic states of matter. Experimental measurements such as inelastic neutron scattering provide us with valuable information about the excitation spectrum of such systems which require microscopic models to be described. This thesis is devoted to a detailed analysis of the excitation spectrum and of the quantum phase transitions in the one-dimensional (1D) ionic Hubbard model (IHM). The IHM consists of a nearest-neighbor (n.n.) hopping, onsite Hubbard interaction, and an ionic (staggered) potential separating the odd and even sites energetically. The model exhibits two continuous phase transitions on increasing the Hubbard interaction identified by a low-energy effective field theory and confirmed by a rigorous density matrix renormalization group (DMRG) analysis after several attempts. The first transition occurs from band insulator (BI) phase to the 2-fold degenerate spontaneously dimerized insulator (SDI) phase. The transition is in the Ising universality class as is plausible from symmetry considerations. The SDI phase becomes unstable towards a quasi-long-range order Mott insulator (MI) phase at a second transition point resembling the Kosterlitz-Thouless (KT) transition in the frustrated Heisenberg chain. We employ continuous unitary transformations (CUT) to systematically map the IHM to effective Hamiltonians (almost) conserving the number of QPs in the system. Using an analysis in the BI regime where electrons and holes define QPs, the low-energy excitation spectrum of the model is quantitatively determined in the BI phase almost up to the first transition point. The transition from the BI to the SDI phase is signaled by the vanishing of an S=0 exciton mode at the total momentum K=\pi. The condensation of these excitons beyond the first transition point is described by a BCS-type-theory showing the stabilization of the SDI phase. The mean-field solution indicates no second phase transition to the quasi-long-range order MI phase. This is interpreted as the effect of strong quantum fluctuations in one dimension. We consider the IHM in the dimer limit where the uniform chain is separated into independent dimers. The different phases of the IHM are studied by increasing the interdimer hopping and reaching the uniform limit. This dimer limit satisfactorily produces the excitation spectrum of the BI phase confirming the vanishing of an S=0 exciton mode at the first transition point. It is found that the SDI-to-MI transition takes place by softening of a magnetic S=1 excitation, i.e., a triplon. We report rigorous results for the gapless triplon dispersion in the MI phase and discuss the binding effects in the 2-triplon sector.