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Physical review. B, Condensed matter

Interplay of randomness, electron correlation, and dimensionality effects in quasi-one-dimensional conductors

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Nov 15, 2000• 2 citations
Publisher

Abstract

We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of $d=1+\ensuremath{\epsilon}$ $(\ensuremath{\epsilon}\ensuremath{\ll}1)$ dimensions is also mentioned.

DOI
10.1103/physrevb.62.13323

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We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of d=1+\ensuremathϵd=1+\ensuremath{\epsilon}d=1+\ensuremathϵ (\ensuremathϵ\ensuremath≪1)(\ensuremath{\epsilon}\ensuremath{\ll}1)(\ensuremathϵ\ensuremath≪1) dimensions is also mentioned.
Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one-dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of disorder-averaged charge and fermion two-point correlations, but power-law decay of disorder-averaged spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.
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.
We derive two-loop renormalization group equations for the half filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the ggg-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half filled Hubbard model and obtain constraints on the ggg-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical Bosonization and Fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have $\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry when the interchain hopping exceeds the magnitude of the charge gap.
A one-dimensional interacting electron gas in a random potential exhibits a localized-delocalized transition for increasingly attractive interactions. We develop here a renormalization-group approach to study this transition. Our treatment allows us to obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and the strength of the interactions. For (nearly) spin-isotropic interactions the delocalized phase is dominated by superconducting fluctuations of either singlet or triplet type. The temperature dependence of the conductivity in the delocalized phase is also obtained and a nonuniversal power-law behavior is found. A description of the crossover towards the localized phase is given and the localization length is computed. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions. We suggest a phase diagram with two different localized phases. Finally, we discuss some possible implications of our model for real quasi-one-dimensional metals.
We investigate the effects of quenched disorder on two-chain Hubbard models at half-filling by using bosonization and renormalization-group methods. It is found that the sufficiently strong forward scattering due to impurities and the random gauge field, which is generated by impurity backward scattering, destroy the charge gaps as well as the spin gaps. Random backward scattering due to impurities then drives the resulting massless phase to the Anderson localization phase. For intermediate strength of random forward scattering, however, the spin gaps still survive, and only one of the charge gaps is collapsed. In this parameter region, one of the charge degrees of freedom is in the Anderson localized state, while the other one is still in the massive state.