Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

Nélisse, Hugues; Bourbonnais, C.; Touchette, Hugo; Vilk, Y. M.; Tremblay, A.–M. S.

doi:10.1007/s100510051016

Cited by 33 publications

(39 citation statements)

References 22 publications

(56 reference statements)

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“…The result for the Hubbard model (U = 2t) given by the plot (i) is quantitatively consistent with χ(T ) calculated by the quantum Monte Carlo (QMC) simulations. 5 The value at T = 0, χ(0)t = 0.58, agrees well with the exact solution, χ exact (0)t = 0.57, for U = 2t. 4 Near zero temperature, χ(T ) decreases as dχ/dT → ∞ for plots (i) and (ii), which has also been pointed out in the context of the Heisenberg spin chain.…”

Section: (C) and (D) Respectively] Given Bysupporting

confidence: 69%

Effect of Intersite Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter Filling

et al. 2005

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The temperature dependence of the magnetic susceptibility, χ(T ), is investigated for one-dimensional interacting electron systems at quarter-filling within the Kadanoff-Wilson renormalization-group method. The forward scattering on the same branch (the g4-process) is examined together with the backward (g1) and forward (g2) scattering amplitudes on opposite branches. In connection with lattice models, we show that χ(T ) is strongly enhanced by the nearest-neighbor interaction, an enhancement that surpasses one of the next-nearest-neighbor interaction. A connection between our predictions for χ(T ) and experimental results for χ(T ) in quasi-one-dimensional organic conductors is presented.KEYWORDS: magnetic susceptibility, renormalization group, long-range Coulomb interaction, extendedHubbard model, quarter-filling, one-dimension, (TMTTF)2X, (TMTSF)2XIn low dimensional conductors, the influence of longrange Coulomb interactions, or the off-site interaction V 's are known to lead to various interesting ordered states, such as charge ordering 1 and spin-density wave (SDW) state coexisting with charge-density wave (CDW).2, 3 At the present stage, however, the effect of V 's is not clearly understood compared with that of the on-site repulsion U . The purpose of this letter is to analyze the effect of V 's on the quasi-one-dimensional conductor in the normal state by calculating the temperature dependence of the magnetic susceptibility χ(T ) for the one-dimensional system at quarter-filling. The results shed some light on the magnetic properties of both normal and ordered states in these kinds of materials.A lot of studies of χ(T ) were devoted to the onedimensional (1D) Hubbard model, i.e., for V 's = 0. The Bethe ansatz gives us an exact solution, but χ only at T = 0 is available for the 1D Hubbard model. 4 The temperature dependence of χ can be extracted from numerical simulations but only at high temperatures.5 For U smaller than the bandwidth, the renormalization-group (RG) approach gives results that quantitatively agree with both the exact solution at T = 0 and the numerical solutions at high temperatures.5 In the presence of V 's, however, there is no exact solution, and the size of numerical simulations becomes exceedingly large. These techniques are then of limited use to investigate the effect of V 's.In this letter, we use the RG technique to calculate χ(T ) for the full temperature range from zero to the bandwidth E 0 in the presence of V 's (> 0). Considering the possible interactions for branches of right and left going electrons in the continuum limit, we take into account the forward scattering on the same branch (SB), denoted as the g 4 -process, with the backward (g 1 ) and forward (g 2 ) scattering processes on opposite branches. This is the first derivation of the RG flows of the sets of coupling constants and χ(T ) at the one-loop level in- * E-mail address: fuseya@slab.phys.nagoya-u.ac.jp.cluding the non-logarithmic channels for particles on the SB, which become important at finite-temperature...

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Section: (C) and (D) Respectively] Given Bysupporting

confidence: 69%

Effect of Intersite Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter Filling

et al. 2005

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“…In this section we study the uniform spin susceptibility and the NMR relaxation rate at finite temperature from two different approaches by extending previous calculations on the single chain 55,56 or on the undoped Heisenberg ladder. 57,58,59,60 One approach is the random-phase approximation (RPA) combined with the renormalization group method and another is direct calculation in terms of the low-energy effective Hamiltonian (3.7).…”

Section: Spin Susceptibility and Nmr Relaxation Ratementioning

confidence: 99%

“…We note that the same result would be derived from the path integral formalism. 56 The explicit forms for the susceptibility are given by…”

Section: A Uniform Spin Susceptibilitymentioning

confidence: 99%

Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

Tsuchiizu

Suzumura

2005

Phys. Rev. B

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We have investigated quantum critical behavior in the doped two-leg extended Hubbard ladder, by using a weak-coupling bosonization method. In the ground state, the dominant fluctuation changes from the conventional d-wave-like superconducting (SCd) state into density-wave states, with increasing nearest-neighbor repulsions and/or decreasing doping rate. The competition between the SCd state and the charge-density-wave state coexisting with the p-density-wave state becomes noticeable on the critical point, at which the gap for magnetic excitations vanishes. Based on the Majorana-fermion description of the effective theory, we calculate the temperature dependence of the magnetic response such as the spin susceptibility and the NMR relaxation rate, which exhibit unusual properties due to two kinds of spin excitation modes. On the quantum critical point, the spin susceptibility shows paramagnetic behavior with logarithmic corrections and the NMR relaxation rate also exhibits anomalous power-law behavior. We discuss the commensurability effect due to the umklapp scattering and relevance to the two-leg ladder compounds Sr14−xCaxCu24O41.

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“…The present procedure is explained in detail in [21]. The spin susceptibility χ σ (T ) [30,31] and the resistivity ρ(T ) [32,33] are respectively written by the T dependent parameters as Figure 5. The spin susceptibility is enhanced below T CO without any steep singularity at T = T CO .…”

Section: Quantities Across T Comentioning

confidence: 99%

Theoretical Studies on Phase Transitions in Quasi-One-Dimensional Molecular Conductors

2012

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A review is given for recent theoretical studies on phase transitions in quasi-one-dimensional molecular conductors with a quarter-filled band. By lowering temperature, charge transfer salts exhibit a variety of transitions accompanying symmetry breaking, such as charge ordering, lattice dimerization, antiferromagnetic transition, spin-Peierls distortion, and so on. Analyses on microscopic quasi-one-dimensional models provide their systematic understandings, by the complementary use of different analytical and numerical techniques; they can reproduce finite-temperature phase transitions, whose results can be directly compared with experiments and give feedbacks to material design.

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Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

Abstract: PACS. 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 75.40.Mg Numerical simulation studies,

Cited by 33 publications

References 22 publications

Effect of Intersite Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter Filling

Effect of Intersite Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter Filling

Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

Theoretical Studies on Phase Transitions in Quasi-One-Dimensional Molecular Conductors

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