Ground states and critical temperatures in quasi-one-dimensional systems

Firsov, Yu. A.; Prigodin, V. N.; Seidel, C. F.

doi:10.1016/0370-1573(85)90079-1

Cited by 65 publications

(23 citation statements)

References 150 publications

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“…Its efficiency may therefore be severly reduced if there are only collective excitations. While z(k = t ⊥ /v F ) = 0 in general, we still expect that a reduced quasi-particle residue z(t ⊥ ) ≪ 1 will delay the establishment of 3D coherence in the single-electron dynamics [21,22,222]. Charge-spin separation could also confine particles on their chains because a holon and spinon must tunnel together -yet in general they are separated [223].…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

“…Nonabelian bosonization, retaining manifestly the SU(2)-invariance in the spin sector, is reviewed by Affleck [20]. Firsov, Prigodin, and Seidel [21] and Bourbonnais and Caron [22] more strongly emphasize phase transitions in real materials made of coupled 1D chains, and especially the paper by Bourbonnais and Caron gives a very modern presentation combining functional integral representations with renormalization group. A classical review on the earlier work on organic conductors is by Jérôme and Schulz [15] and the more recent developments have been summarized by Jérôme [23] and Williams et al [24].…”

Section: Purpose and Structure Of This Reviewmentioning

confidence: 99%

“…A description of the system for finite t ⊥ is, however, a difficult task. We only briefly review the major achievements and refer the reader to more extended treatments [21,22,222] for further details.…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

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One-dimensional Fermi liquids

1995

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We review the progress in the theory of one-dimensional (1D) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particlehole bubble producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless one-dimensional quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t − J-or the extended Hubbard model. Also 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.We discuss in detail various solutions of the Luttinger model which emphasize different aspects of the physics of 1D Fermi liquids. Correlation functions are calculated in detail using bosonization, and the relation of this method to other approaches is discussed. The correlation functions decay as non-universal power-laws, and scaling relations between their exponents are parameterized by the effective coupling constant. Charge-spin separation only shows up in dynamical correlations. The Luttinger liquid concept is developed from perturbations of the Luttinger model. Mainly specializing to the 1D Hubbard model, we review a variety of mappings for complicated models of interacting electrons onto Luttinger models, and thereby obtain their correlation functions. We also discuss the generic behaviour of systems not falling into the Luttinger liquid universality class because of gaps in their low-energy spectrum. The Mott transition provides an example for the transition from Luttinger to non-Luttinger behaviour, and recent results on this problem are summarized. Coupling chains by interactions or tunneling allows transverse coherence to establish in the single-or two-particle dynamics, and drives the systems away from a Luttinger liquid. We discuss the influence of charge-spin separation and of the anomalous dimensions on the transverse dynamics of the electrons. The edge states in the quani tum Hall effect provide a realization of a modified, chiral Luttinger liquid whose detailed properties differ...

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Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

Section: Purpose and Structure Of This Reviewmentioning

confidence: 99%

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One-dimensional Fermi liquids

1995

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“…Basic electronic properties of many solids, including phase transitions into symmetry-breaking states like superconducting or charge-density wave (CDW) state, are well described within this One may expect to observe formation of Luttinger liquid in quasi-1D conductors, i. e., highly anisotropic 3D conductors with chain-like structure. However, according to present theoretical point of view, the formation of Luttinger liquid in quasi-1D conductors at low enough temperatures is problematic because of the instability towards 3D behavior in the presence of arbitrarily small inter-chain hopping 4,5,6,7,8,9 . So inter-chain hopping induces a crossover to 3D behavior at low energies, while Luttinger liquid behavior can survive only at high enough energy scale where it is not affected by 3D coupling.…”

Section: Introductionmentioning

confidence: 99%

Low-temperature conductivity of quasi-one-dimensional conductors: Luttinger liquid stabilized by impurities

Artemenko

Remizov

2005

Phys. Rev. B

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A new non-Fermi liquid state of quasi-one-dimensional conductors is suggested in which electronic system exists in a form of collection of bounded Luttinger liquids stabilized by impurities. This state is shown to be stable towards inter-chain electron hopping at low temperatures. Electronic spectrum of the system contains zero modes and collective excitations of the bounded Luttinger liquids in the segments between impurities. Zero modes give rise to randomly distributed localized electronic levels, and long-range interaction generates the Coulomb gap in the density of states at the Fermi energy. Mechanism of conductivity at low temperatures is phonon-assisted hopping via zero-mode states. At higher voltages the excitations of Luttinger liquid are involved into electron transport, and conductivity obeys power-law dependence on voltage. The results are compared with recent experimental data for NbSe 3 and TaS 3 crystals.

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“…Для описания проводимости в 1D-случае на данный момент нет точной модели, но есть точные решения для упрощенных моделей: модель Томонага [3], Латтинже-ра [4], латтинжерова жидкость (LL), о чем подробнее можно узнать в [5]. Общее для этих моделей состоит в следующем:…”

Section: Introductionunclassified

Электронный Транспорт В Нанопроволоках Те

Березовец¹,

Кумзеров²,

Фирсов³

2018

Физика Твердого Тела

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Проведено измерение температурной и магнетополевой зависимости вольтамперных характеристик образцов нанопроволок Те, изготовленных путем внедрения из расплава Те в поры хризотилового асбеста. Измерения проходили в широком интервале температур и магнитных полей. Анализ результатов таких измерений проводился путем сравнения их с предсказаниями теоретических моделей, разработанными для случая одномерных структур. Сделан вывод о том, что полученные зависимости наилучшим образом согласуются с предсказаниями теории о жидкости Латтинжера. Этот результат находится в соответствии с представлениями о том, что основной механизм протекания в таких одномерных нитях не зависит от материала, внедренного в поры, а зависит только от размерности проводящих нитей.Работа частично поддержана программой Президиума РАН.

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Ground states and critical temperatures in quasi-one-dimensional systems

Cited by 65 publications

References 150 publications

One-dimensional Fermi liquids

One-dimensional Fermi liquids

Low-temperature conductivity of quasi-one-dimensional conductors: Luttinger liquid stabilized by impurities

Электронный Транспорт В Нанопроволоках Те

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