Phase diagram of the extended Hubbard model in one spatial dimension

Cannon, Joel W.; Fradkin, Eduardo

doi:10.1103/physrevb.41.9435

Cited by 77 publications

(64 citation statements)

References 11 publications

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“…The phase diagram then has a shape very similar to that of the half-filled 1D extended Hubbard model ͑EHM͒. 29,[32][33][34] In the half-filled EHM, as the nearest-neighbor Coulomb repulsion V is increased for fixed U, there is a transition from AFM to CDW order. This transition is continuous for small U and first order for U Ͼ U m .…”

Section: First-order Transitionmentioning

confidence: 89%

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

2007

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The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electronphonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that ͑i͒ as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model.

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Section: First-order Transitionmentioning

confidence: 89%

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

2007

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“…However, these quantities as well as different correlation functions vary smoothly at the transition and it is very difficult to obtain accurate boundaries [52][53][54][55] . Instead, the use of topological numbers as order parameters necessarily leads to sharp transitions.…”

Section: Phase Diagram Obtained From Topological Transitionsmentioning

confidence: 99%

“…There exists a metallic phase (the detailed nature of which will be discussed later) for small values of U and V , which shrinks as t AB → t. When t AB = t (Hubbard limit), several results indicate that there is no M phase, except, eventually, on the second-order transition line between the CDW and SDW phases, that ends at a tricritical point. The position of this point is, to date, not well determined and should be around U ∼ 2V ∼ 4t [52][53][54][55][56] .…”

Section: Introductionmentioning

confidence: 99%

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping

et al. 1998

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We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping for spin up (down) which depends on the total occupation n b of spin down (up) electrons on both sites involved. The hopping parameters are tAA, tAB and tBB for n b = 0, 1, 2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for tAB < tAA = tBB and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences.

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“…For higher V the ground state is a staggered charge-density-wave (CDW), where both the charge and spin excitations are gapped. The transition between the critical SDW and the long-rangeordered CDW has been the subject of numerous studies [3,4,5,6,7,8,9,10,11,12,13,14]. Until recently, it was believed that the SDW-CDW transition occurs for all U > 0 at V > ∼ U/2 and that it is continuous for small U ( < ∼ 5) and first-order for larger U .…”

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confidence: 99%

Ground State Phases of the Half-Filled One-Dimensional Extended Hubbard Model

2004

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Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V . We show that spin frustration stabilizes a bond-ordered (dimerized) state for U ≈ V /2 up to U/t ≈ 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-densitywave state for large V /U is continuous for U < ∼ 5.5 and first-order for higher U . The one-dimensional Hubbard model, which describes electrons on a tight-binding chain with single-particle hopping matrix element t and on-site repulsion U , has a charge-excitation gap for any U > 0 at half-filling [1]. In the spin sector, the low-energy spectrum maps onto that of the S = 1/2 Heisenberg chain; the spin coupling J = 4t 2 /U for U → ∞. The spin spectrum is therefore gapless and the spin-spin correlations decay with distance r as (−1) r /r [2]. Hence, the ground state is a quantum critical staggered spin-density-wave (SDW). In the simplest extended Hubbard model, a nearest-neighbor repulsion V is also included. The Hamiltonian is, in standard notation and with t = 1 hereafter,The low-energy properties for V < ∼ U/2 are similar to those at V = 0. For higher V the ground state is a staggered charge-density-wave (CDW), where both the charge and spin excitations are gapped. The transition between the critical SDW and the long-rangeordered CDW has been the subject of numerous studies [3,4,5,6,7,8,9,10,11,12,13,14]. Until recently, it was believed that the SDW-CDW transition occurs for all U > 0 at V > ∼ U/2 and that it is continuous for small U ( < ∼ 5) and first-order for larger U . However, based on a study of excitation spectra of small chains, Nakamura argued that there is also a bond-order-wave (BOW) phase [10], where the ground state has a staggered modulation of the kinetic energy density (dimerization), in a narrow region between the SDW and CDW phases for U smaller than the value at which the transition changes to first order. Previous studies [6,7,8,9] had indicated an SDW state in this region. Nakamura's BOW-CDW boundary coincides with the previously determined SDW-CDW boundary. The presence of dimerization and the accompanying spin gap were subsequently confirmed using quantum Monte Carlo (QMC) simulations [11,12]. The BOW phase now also has a weak-coupling theory [13].The existence of an extended BOW phase has recently been disputed. Jeckelmann argued, on the basis of density-matrix-renormalization-group (DMRG) calculations, that the BOW exists only on a short segment of the first-order part of the SDW-CDW boundary [14], i.e., that the transition always is SDW-CDW and that BOW order is only induced on part of the coexistence curve. However, QMC calculations demonstrate the existence of BOW order well away from the phase boundary [12].Although several studies agree on the existence of an extended BOW phase [10,11,12,13], the shape of ...

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Phase diagram of the extended Hubbard model in one spatial dimension

Cited by 77 publications

References 11 publications

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping

Ground State Phases of the Half-Filled One-Dimensional Extended Hubbard Model

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