We obtain the quantum phase diagram of the ionic Hubbard model including electron-hole symmetric density-dependent hopping. The boundaries of the phases are determined by crossings of excited levels with particular discrete symmetries, which coincide with jumps of charge and spin Berry phases with a topological meaning. Reducing the magnitude of the hopping terms that do not change the total number of singly occupied sites with respect to the other one, the region of the phase diagram occupied by the fully gapped spontaneously dimerized insulator (which separates the band insulating and Mott insulating phases) is enlarged, particularly for small values of the alternating on-site energy. This result might be relevant for experiments in cold atoms in which topological charge pumping is observed when alternation in the hopping is included.We obtain the quantum phase diagram of the ionic Hubbard model including electron-hole symmetric density-dependent hopping. The boundaries of the phases are determined by crossings of excited levels with particular discrete symmetries, which coincide with jumps of charge and spin Berry phases with a topological meaning. Reducing the magnitude of the hopping terms that do not change the total number of singly occupied sites with respect to the other one, the region of the phase diagram occupied by the fully gapped spontaneously dimerized insulator (which separates the band insulating and Mott insulating phases) is enlarged, particularly for small values of the alternating on-site energy. This result might be relevant for experiments in cold atoms in which topological charge pumping is observed when alternation in the hopping is included.

Physical review. B./Physical review. BSep 15, 20238 citations

Charge and spin gaps in the ionic Hubbard model with density-dependent hopping

Oscar Moreno Segura, K. Hallberg, Armando A. Aligia

We calculate the charge gap $\mathrm{\ensuremath{\Delta}}{E}_{C}$ and the spin gap $\mathrm{\ensuremath{\Delta}}{E}_{S}$ of the ionic Hubbard chain including electron-hole symmetric density-dependent hopping. The vanishing of $\mathrm{\ensuremath{\Delta}}{E}_{C}$ $(\mathrm{\ensuremath{\Delta}}{E}_{S})$ signals a quantum critical point in the charge (spin) sector. Between both critical points, the system is a fully gapped spontaneously dimerized insulator. We focus our study in this region. Including alternation in the hopping, it is possible to perform an adiabatic Thouless pump of one charge per cycle, but with a velocity limited by the size of the gaps.We calculate the charge gap $\mathrm{\ensuremath{\Delta}}{E}_{C}$ and the spin gap $\mathrm{\ensuremath{\Delta}}{E}_{S}$ of the ionic Hubbard chain including electron-hole symmetric density-dependent hopping. The vanishing of $\mathrm{\ensuremath{\Delta}}{E}_{C}$ $(\mathrm{\ensuremath{\Delta}}{E}_{S})$ signals a quantum critical point in the charge (spin) sector. Between both critical points, the system is a fully gapped spontaneously dimerized insulator. We focus our study in this region. Including alternation in the hopping, it is possible to perform an adiabatic Thouless pump of one charge per cycle, but with a velocity limited by the size of the gaps.

arXiv:2309.10126Physical review. B./Physical review. BNov 17, 20236 citations

Phase diagram of the Hubbard chain with symmetric density-dependent hopping

Xin Sun, Weiting Chen, Hanqin Ding

By the bosonization and renormalization-group schemes, a half-filled Hubbard chain with density-dependent hopping is investigated at weak coupling. The model involved has an electron–hole symmetry and an SO(4) symmetry. The phase diagram consists of three different phases divided by a charge transition at on-site repulsion U = U c and a spin transition at U = U s , with U s = − U c = 16 π ( t c − 1 ) , including a Mott insulator with the SDW correlation, a dimerized insulator with the BCDW correlation, and a Luttinger metal with the coexisting TS and BSDW correlations. The effective three-body repulsion ( t c − 1 > 0 ) and attraction ( t c − 1 < 0 ) induce the dimerized and metallic phases, respectively. • We study a 1D Hubbard model with symmetric density-dependent hopping analytically. • We provide a theoretical scheme of realization of the BCDW and TS instabilities. • The results supplement further understanding of quantum properties of 1D correlated systems.By the bosonization and renormalization-group schemes, a half-filled Hubbard chain with density-dependent hopping is investigated at weak coupling. The model involved has an electron–hole symmetry and an SO(4) symmetry. The phase diagram consists of three different phases divided by a charge transition at on-site repulsion U = U c and a spin transition at U = U s , with U s = − U c = 16 π ( t c − 1 ) , including a Mott insulator with the SDW correlation, a dimerized insulator with the BCDW correlation, and a Luttinger metal with the coexisting TS and BSDW correlations. The effective three-body repulsion ( t c − 1 > 0 ) and attraction ( t c − 1 < 0 ) induce the dimerized and metallic phases, respectively. • We study a 1D Hubbard model with symmetric density-dependent hopping analytically. • We provide a theoretical scheme of realization of the BCDW and TS instabilities. • The results supplement further understanding of quantum properties of 1D correlated systems.

Results in PhysicsSep 23, 20241 citation

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.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 SinicaJan 1, 20151 citation

Mean-field ground-state phase diagram of the ${t-t^\prime}$ ionic-Hubbard chainMean-field ground-state phase diagram of the ${t-t^\prime}$ ionic-Hubbard chain

Sekania, Mikheil, Shota Garuchava, Jamal Berakdar +1 more

Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor ( $t$ ) and next-nearest-neighbor ( $t^{\prime}$ ) hopping and a staggered potential ( $Δ$ ) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard ( ${t^{\prime}=0}$ ) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor ($t$) and next-nearest-neighbor ($t^{\prime}$) hopping and a staggered potential ($Δ$) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard (${t^{\prime}=0}$) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.

arXiv:2211.10543Nov 19, 20220 citations

Anderson-Mott transition in a disordered Hubbard chain with correlated hopping

Francesca Battista, Alberto Camjayi, Liliana Arrachea

We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude $t$ . We identify three different phases as functions of the disorder amplitude $W$ and Coulomb interaction strength $U>0$ . When $U<4t$ the system shows a metallic phase: (i) only when no disorder is present $W=0$ or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When $U>4t$ the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude $t$. We identify three different phases as functions of the disorder amplitude $W$ and Coulomb interaction strength $U>0$. When $U<4t$ the system shows a metallic phase: (i) only when no disorder is present $W=0$ or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When $U>4t$ the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.

arXiv:1608.06866Physical review. B./Physical review. BJul 12, 20174 citations

Mean-field ground-state phase diagram of the

{t-t^\prime}

ionic-Hubbard chain

Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor (

t

) and next-nearest-neighbor (

t^{\prime}

) hopping and a staggered potential (

Δ

) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard (

{t^{\prime}=0}

) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.

We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion

U

and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude

t

. We identify three different phases as functions of the disorder amplitude

W

and Coulomb interaction strength

U>0

. When

U<4t

the system shows a metallic phase: (i) only when no disorder is present

W=0

or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When

U>4t

the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.