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Physica B Condensed Matter

Correlated one-dimensional electron systems: Luttinger liquid properties and deviations at finite temperature

Guido Jüttner, Andreas Klümper, Junji Suzuki

Published Jan 1, 1999• 3 citations
Publisher
DOI
10.1016/s0921-4526(98)01045-x

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Ann Elisabet Mattsson

Strongly correlated systems show a variety of intriguing properties and have been extensively studied over the years. In this thesis two strongly correlated systems are discussed: the two-dimensional antiferromagnet and the Luttinger liquid. The Luttinger liquid has attracted much interest as a paradigm of non-Fermi liquid behavior. In the first part of the thesis, basic properties of Fermi liquids are briefly described while those of Luttinger liquids are considered in more detail. The differences in spectral properties of Luttinger liquids and Fermi liquids are discussed, as are the consequences for photoemission experiments. In this context Luttinger liquids with boundaries, treated in Papers I, II, and III, are introduced. The exact single-electron Green's function at finite temperature is calculated with bosonization methods, for both periodic and finite open-boundary systems. The corresponding local spectral density is analyzed. For a system with open boundaries, the well-known zero temperature bulk behavior always crosses over to a boundary dominated regime for small energies, while at finite temperature the low energy behavior becomes quadratic. For a periodic finite-size system we also calculate the Coulomb-blockade-like oscillations and study their dependence on interaction and temperature. The two-dimensional antiferromagnet has attracted much attention due to its connection to the undoped phase of the ceramic high-temperature superconductors. In the second part of the thesis including Papers IV and V, the two-dimensional Heisenberg antiferromagnet defined on the triangular and the honeycomb lattices is studied. We use the Schwinger-boson mean-field theory to investigate the stability of the ground state with respect to frustration. For the honeycomb lattice model we find an increased Néel stability as compared to the classical case. The dynamic structure factor is considered for various temperatures and the spin-wave velocity and the susceptibility are presented as functions of frustration for spin S=1/2. In the case of the intrinsically frustrated triangular lattice model we obtain, in the limit of infinite spin, results in complete agreement with the linear spin-wave theory. In contrast to the latter, however, two of the three modes acquire a mass for finite spin. The origin of this effect is discussed.

•Jan 1, 1997•0 citations
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.
The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang theory, path integral quantum Monte-Carlo calculations, and Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Tomonaga-Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms.
Strongly correlated systems show a variety of intriguing properties and have been extensively studied over the years. In this thesis two strongly correlated systems are discussed: the two-dimensional antiferromagnet and the Luttinger liquid. The Luttinger liquid has attracted much interest as a paradigm of non-Fermi liquid behavior. In the first part of the thesis, basic properties of Fermi liquids are briefly described while those of Luttinger liquids are considered in more detail. The differences in spectral properties of Luttinger liquids and Fermi liquids are discussed, as are the consequences for photoemission experiments. In this context Luttinger liquids with boundaries, treated in Papers I, II, and III, are introduced. The exact single-electron Green's function at finite temperature is calculated with bosonization methods, for both periodic and finite open-boundary systems. The corresponding local spectral density is analyzed. For a system with open boundaries, the well-known zero temperature bulk behavior always crosses over to a boundary dominated regime for small energies, while at finite temperature the low energy behavior becomes quadratic. For a periodic finite-size system we also calculate the Coulomb-blockade-like oscillations and study their dependence on interaction and temperature. The two-dimensional antiferromagnet has attracted much attention due to its connection to the undoped phase of the ceramic high-temperature superconductors. In the second part of the thesis including Papers IV and V, the two-dimensional Heisenberg antiferromagnet defined on the triangular and the honeycomb lattices is studied. We use the Schwinger-boson mean-field theory to investigate the stability of the ground state with respect to frustration. For the honeycomb lattice model we find an increased Néel stability as compared to the classical case. The dynamic structure factor is considered for various temperatures and the spin-wave velocity and the susceptibility are presented as functions of frustration for spin S=1/2. In the case of the intrinsically frustrated triangular lattice model we obtain, in the limit of infinite spin, results in complete agreement with the linear spin-wave theory. In contrast to the latter, however, two of the three modes acquire a mass for finite spin. The origin of this effect is discussed.