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arXiv:1705.04450 · Physical review. B./Physical review. B

Anisotropy crossover in the frustrated Hubbard model on four-chain cylinders

G. Ehlers, Benjamin Lenz, Salvatore R. Manmana, R. M. Noack

Published Jan 10, 2018• 4 citations
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Abstract

Motivated by dimensional crossover in layered organic $\ensuremath{\kappa}$ salts, we determine the phase diagram of a system of four periodically coupled Hubbard chains with frustration at half filling as a function of the interchain hopping ${t}_{\ensuremath{\perp}}/t$ and interaction strength $U/t$ at a fixed ratio of frustration and interchain hopping ${t}^{\ensuremath{'}}/{t}_{\ensuremath{\perp}}=\ensuremath{-}0.5$. We cover the range from the one-dimensional limit of uncoupled chains (${t}_{\ensuremath{\perp}}/t=0.0$) to the isotropic model (${t}_{\ensuremath{\perp}}/t=1.0$). For strong $U/t$, we find an antiferromagnetic insulator; in the weak-to-moderate-interaction regime, the phase diagram features quasi-one-dimensional antiferromagnetic behavior, an incommensurate spin density wave, and a metallic phase as ${t}_{\ensuremath{\perp}}/t$ is increased. We characterize the phases through their magnetic ordering, dielectric response, and dominant static correlations. Our analysis is based primarily on a variant of the density-matrix renormalization-group algorithm based on an efficient hybrid--real-momentum-space formulation, in which we can treat relatively large lattices albeit of a limited width. This is complemented by a variational cluster approximation study with a cluster geometry corresponding to the cylindrical lattice allowing us to directly compare the two methods for this geometry. As an outlook, we make contact with work studying dimensional crossover in the full two-dimensional system.

DOI
10.1103/physrevb.97.035118

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By following the ideas of Emery and Noguera, a recent study revealed the dynamics of the charge sector of a one-dimensional quarter-filled electronic system with extended Hubbard interactions to be that of an effective pseudospin transverse-field Ising model (TFIM) in the strong-coupling limit. With the twin motivations of studying the co-existing charge and spin order found in strongly correlated chain systems and the effects of interchain couplings, we investigate the phase diagram of coupled effective (TFIM) systems. A bosonization and renormalization group (RG) analysis for a two-leg TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and Néel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Kosterlitz-Thouless transitions are found to lead from the gapless phase to either of the charge-ordered phases. A detailed analysis is also carried out for the dimensional crossover physics when many such pseudospin systems are coupled to one another. Importantly, the analysis reveals the key role of critical quantum fluctuations in driving the strong dispersion in the transverse directions, as well as a T = 0 deconfinement transition. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled chain and ladder systems.
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The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength UUU being its parameters. At half-filling, a relation between the staggered magnetization MMM and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small UUU limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at UMott=10t{U}_{\text{Mott}}=10tUMott​=10t. The interaction Uc{U}_{c}Uc​ for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than UMott{U}_{\text{Mott}}UMott​ at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.
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