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 crossing 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.
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.
We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong-coupling phase can only partly be understood in terms of the strong-coupling behavior of the ordinary Hubbard model.
A repulsive Hubbard model with both spin-asymmetric hopping $({t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}})$ and a staggered potential (of strength $\mathrm{\ensuremath{\Delta}})$ is studied in one dimension. The model is a compound of the mass-imbalanced $({t}_{\ensuremath{\uparrow}}\ensuremath{\ne}{t}_{\ensuremath{\downarrow}},\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}=0)$ and ionic $({t}_{\ensuremath{\uparrow}}={t}_{\ensuremath{\downarrow}},\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}>0)$ Hubbard models, and may be realized by cold atoms in engineered optical lattices. We use mostly mean-field theory to determine the phases and phase transitions in the ground state for a half-filled band (one particle per site). We find that a period-two modulation of the particle (or charge) density and an alternating spin density coexist for arbitrary Hubbard interaction strength, $U\ensuremath{\ge}0$. The amplitude of the charge modulation is largest at
U=0, decreases with increasing
U and tends to zero for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. The amplitude for spin alternation increases with
U and tends to saturation for $U\ensuremath{\rightarrow}\ensuremath{\infty}$. Charge order dominates below a value
Uc, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\uparrow}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\downarrow}}$, which have to be determined self-consistently. For
U<Uc both parameters are positive, for
U>Uc they have different signs, and for
U=Uc one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at
Uc can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.
A Thouless pump transports an integer amount of charge when pumping adiabatically around a singularity. We study the splitting of such a critical point into two separate critical points by adding a Hubbard interaction. Furthermore, we consider extensions to a spinful Rice-Mele model, namely, a staggered magnetic field or an Ising-type spin coupling, further reducing the spin symmetry. The resulting models additionally allow for the transport of a single charge in a two-component system of spinful fermions, whereas in the absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric case, the ionic Hubbard model is visited once along pump cycles that enclose a single singularity. Adding a staggered magnetic field additionally transports an integer amount of spin while the Ising term realizes a pure charge pump. We employ real-time simulations in finite and infinite systems to calculate the adiabatic charge and spin transport, complemented by the analysis of gaps and the many-body polarization to confirm the adiabatic nature of the pump. The resulting charge pumps are expected to be measurable in finite-pumping speed experiments in ultracold atomic gases for which the
SU(2) invariant version is the most promising path. We discuss the implications of our results for a related quantum-gas experiment by Walter et al. [arXiv:2204.06561].