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arXiv:1802.07282 · Physical review. B./Physical review. B

Phase diagram of the Hubbard-Holstein model on a four-leg tube system at quarter filling

Sahinur Reja, Satoshi Nishimoto

Published Jun 7, 2018• 2 citations
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Abstract

We derive an effective electronic Hamiltonian for the square lattice Hubbard-Holstein model (HHM) in the strong electron-electron $(e\text{\ensuremath{-}}e)$ and electron-phonon $(e\text{\ensuremath{-}}ph)$ coupling regime and under nonadiabatic conditions $(t/{\ensuremath{\omega}}_{0}\ensuremath{\le}1)$, $t$ and ${\ensuremath{\omega}}_{0}$ being the electron hopping and phonon frequency respectively. Using the density matrix renormalization-group method, we simulate this effective electronic model on a four-leg cylinder system at quarter filling and present a phase diagram in the $g\text{\ensuremath{-}}U$ plane where $g$ and $U$ are the $e\text{\ensuremath{-}}ph$ coupling constant and Hubbard on-site interaction respectively. For larger $g$, we find that a cluster of spins, i.e., phase separation (PS), gives way to a charge density wave (CDW) phase made of nearest-neighbor singlets which abruptly goes to another CDW phase as we increase $U$. But for smaller $g$, we find a metallic phase sandwiched between PS and the singlet CDW phase. This phase is characterized by a vanishing charge gap but a finite spin gap, suggesting a singlet superconducting phase.

DOI
10.1103/physrevb.97.245108

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We derive an effective electronic Hamiltonian for the square lattice Hubbard-Holstein model (HHM) in the strong electron-electron (e\ensuremath-e)(e\text{\ensuremath{-}}e)(e\ensuremath-e) and electron-phonon (e\ensuremath-ph)(e\text{\ensuremath{-}}ph)(e\ensuremath-ph) coupling regime and under nonadiabatic conditions (t/\ensuremathω0\ensuremath≤1)(t/{\ensuremath{\omega}}_{0}\ensuremath{\le}1)(t/\ensuremathω0​\ensuremath≤1), ttt and \ensuremathω0{\ensuremath{\omega}}_{0}\ensuremathω0​ being the electron hopping and phonon frequency respectively. Using the density matrix renormalization-group method, we simulate this effective electronic model on a four-leg cylinder system at quarter filling and present a phase diagram in the g\ensuremath-Ug\text{\ensuremath{-}}Ug\ensuremath-U plane where ggg and UUU are the e\ensuremath-phe\text{\ensuremath{-}}phe\ensuremath-ph coupling constant and Hubbard on-site interaction respectively. For larger ggg, we find that a cluster of spins, i.e., phase separation (PS), gives way to a charge density wave (CDW) phase made of nearest-neighbor singlets which abruptly goes to another CDW phase as we increase UUU. But for smaller ggg, we find a metallic phase sandwiched between PS and the singlet CDW phase. This phase is characterized by a vanishing charge gap but a finite spin gap, suggesting a singlet superconducting phase.
Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of sss-wave pairing between charge and magnetic orders
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) sss-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
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Abstract The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping ttt, the on-site electron-electron interaction UUU, the phonon energy ${\ensuremath{\omega}}_{0}$, and the electron-phonon coupling ggg. At half filling, the ground state is an antiferromagnetic insulator for $U\ensuremath{\gtrsim}2{g}^{2}/{\ensuremath{\omega}}_{0}$, while it is a charge-density-wave (or bipolaronic) insulator for $U\ensuremath{\lesssim}2{g}^{2}/{\ensuremath{\omega}}_{0}$. In addition to these phases, we find a superconducting phase that intrudes between them. For ${\ensuremath{\omega}}_{0}/t=1$, superconductivity emerges when both U/tU/tU/t and $2{g}^{2}/t{\ensuremath{\omega}}_{0}$ are small; then, by increasing the value of the phonon energy ${\ensuremath{\omega}}_{0}$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.
The authors employ the density-matrix renormalization group to investigate the doped Hubbard model on six-leg square cylinders. It uncovers a rich quantum phase diagram, intricately sensitive to next-nearest-neighbor electron hopping ($t\ensuremath{'}$). The positive-ttt\ensuremath{'} region shows a robust ddd-wave superconducting phase with intertwined superconducting and charge-density-wave orders. In contrast, the negative-ttt\ensuremath{'} side remains insulating, where doped holes form either long-range charge stripe order at small ttt\ensuremath{'} or a holon Wigner crystal with one doped hole per emergent unit cell and short-range spin correlations at larger ttt'.
We analyze the global ground-state (quantum) phase diagram of the one-dimensional spinful Holstein model at half filling as a function of the strength of the electron-phonon coupling (represented by the strength of the phonon-induced attraction, UUU) and the phonon frequency ${\ensuremath{\omega}}_{0}$. In addition to reanalyzing the various asymptotic regimes, we carry out density-matrix renormalization group simulations to correct previous inferences concerning the antiadiabatic (large ${\ensuremath{\omega}}_{0}$) and strong-coupling (large UUU) regimes. There are two distinct phases---a fully gapped commensurate charge-density-wave phase and a spin-gapped Luther-Emery phase with a gapless charge mode---separated by a phase boundary, with a shape that reflects different microscopic physics in the weak- and strong-coupling limits.