Variational cluster approximation study of the one-dimensional Holstein-Hubbard model at half filling

Payeur, A.; Sénéchal, David

doi:10.1103/physrevb.83.033104

Cited by 23 publications

(11 citation statements)

References 21 publications

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“…It is well known that the HH model is extremely complicated and impossible to solve analytically. Its phase diagram and ground-state static properties 23,[25][26][27][28][29][30][31][32][33][34][35] have been thoroughly studied in the literature, using different numerical techniques, including the DMRG [36][37][38] . The main difficulty consists of handling the phononic degrees of freedom, that need to be described in principle by an infinite dimensional Hilbert space at every lattice site.…”

Section: The 1d Hubbard-holstein Modelmentioning

confidence: 99%

Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model

et al. 2014

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We calculate the spectral function of the one dimensional Hubbard-Holstein model using the time dependent Density Matrix Renormalization Group (tDMRG), focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave-function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.

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Section: The 1d Hubbard-holstein Modelmentioning

confidence: 99%

Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model

et al. 2014

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“…The presence of such a state was more recently supported by density matrix renormalization group (DMRG) and variational methods 14,15 . Its origin was thereafter extensively discussed from various approaches [16][17][18][19][20][21] . In particular, quantum Monte Carlo (QMC) 16,18,22 and further DMRG 23 calculations have corroborated its existence over a definite, ω 0 −dependent region of the (U, g ph ) plane.…”

Section: Introductionmentioning

confidence: 99%

Nature of ground states in one-dimensional electron-phonon Hubbard models at half filling

Bakrim

Bourbonnais

2015

Phys. Rev. B

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The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the (U, g ph ) plane for the phonon-mediated interaction g ph and the Coulomb interaction U . The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency ω0. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical U * ≈ g * ph , followed at larger U ∼ g ph by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on U . For the Peierls-Hubbard model, the region of the (U, g ph ) plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency ωD decreases. A power law dependence g ph ∼ U 2η is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term V is added to the Hubbard interaction.

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“…Perhaps the most important opportunity enabled by CPT+DQMC is the possibility to study models that are not well suited to ED. For instance, strongly electronphonon coupled system involves huge Hilbert space and cannot be solved by pure ED [36][37][38][39][40]. However, both the Hilbert-space issue and the fermion-sign issue are absent for DQMC in the electron-phonon systems.…”

Section: The Spectral Function Is Extracted From the Relationmentioning

confidence: 99%

Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory

Huang¹,

Wang²

2021

Preprint

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Cluster Perturbation Theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intra-cluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce Determinantal Quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT+DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT+ED simulations.

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Variational cluster approximation study of the one-dimensional Holstein-Hubbard model at half filling

Cited by 23 publications

References 21 publications

Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model

Interplay of charge, spin, and lattice degrees of freedom in the spectral properties of the one-dimensional Hubbard-Holstein model

Nature of ground states in one-dimensional electron-phonon Hubbard models at half filling

Determinantal Quantum Monte Carlo solver for Cluster Perturbation Theory

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