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Journal of the Physical Society of Japan

Non-Tomonaga-Luttinger-Liquid Behavior of the Ground State of Model One-Dimensional Electron Systems

D. Yoshioka, Masao Ogata

Published Sep 15, 1993• 2 citations
Publisher

Abstract

An asymptotically exact ground-state wave function is obtained for one-dimensional electrons of a model Hamiltonian. The Hamiltonian has an arbitrary parameter. Tomonaga-Luttinger (TL)-liquid-like behavior for a small value of the parameter changes gradually into non-TL-liquid behavior as the parameter is increased. Parameter dependence of the momentum distribution function and the structure factor are investigated numerically for small systems.

DOI
10.1143/jpsj.62.2990

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An asymptotically exact ground-state wave function is obtained for one-dimensional electrons of a model Hamiltonian. The Hamiltonian has an arbitrary parameter. Tomonaga-Luttinger (TL)-liquid-like behavior for a small value of the parameter changes gradually into non-TL-liquid behavior as the parameter is increased. Parameter dependence of the momentum distribution function and the structure factor are investigated numerically for small systems.
The spin, charge and pairing correlation functions for the ground state of two-dimensional t−Jt-Jt−J model are calculated by using the power method which projects out the ground state from a variational wave function. ``Exact'' results are obtained for 10×1010\times1010×10 and 8×88\times88×8 lattices with low particle densities. The results are surprisingly similar to that of one-dimensional t−Jt-Jt−J model. The phenomenology is almost perfectly correlated with the concept of Tomonaga-Luttinger liquid and it is incompatible with traditional Fermi liquid theory.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.
The eect of electronic many-body interactions in one-dimensional (1D) systems is drastically enhanced compared to higher dimensions due to the restricted phasespace, often leading to strong electronic correlations. It can be shown that due to a breakdown of the Fermi liquid theory, the ground state at low temperatures becomes a Tomonaga-Luttinger liquid (TLL). In a TLL, the strength of electronic correlations is characterized by the Luttinger parameter K, ranging between K = 0 and K = 1, where K = 1 describes non-interacting electrons. Various systems, such as single-walled carbon nanotubes, 1D atomic metal chains, and MoS 2 mirror twin boundaries, have been reported to host TLLs, in which spin-degeneracy is intact.
The one-particle Green's function for the two-chain Tomonaga–Luttinger (TL) model coupled by interchain hopping including spin degrees of freedom is calculated as a function of distance and time by the higher-dimensional bosonization method. In the short distance and time region, the one-dimensional TL liquid behavior is reproduced, while the long distance and time behavior is different from that for either TL or Fermi liquid. As the interaction becomes stronger, the behavior of Green's function becomes closer to that for the one-dimensional TL liquid, showing that the one-dimensionality is enhanced for stronger electron interaction, and is interpreted as the precursor of the “confinement”.