Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions

2007 ◽  
Vol 76 (15) ◽  
Author(s):  
M. Khodas ◽  
M. Pustilnik ◽  
A. Kamenev ◽  
L. I. Glazman
Keyword(s):  
Spectral Function ◽  
Luttinger Liquid ◽  
One Dimensional

Threshold singularities in the one-dimensional supersymmetric boson–fermion gas mixture

2018 ◽  
Vol 32 (21) ◽  
pp. 1850221 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Spectral Function ◽  
Bethe Ansatz ◽  
Interaction Strength ◽  
Luttinger Liquid ◽  
Low Energy ◽  
Type Model ◽  
Gas Mixture ◽  
Linear Dispersion ◽  
Energy Excitation ◽  
One Dimensional

A one-dimensional gas mixture consisting of bosons and fermions without spin interacting via a repulsive [Formula: see text]-function potential is considered. The model is integrable and soluble via two nested Bethe ansatz, if all particles are assumed to have equal masses and the interaction strength between the bosons and among the bosons and fermions is the same. The low energy excitation spectrum is a two-component Luttinger liquid and can be parametrized by a conformal field theory with conformal charges c = 1. In the low-energy limit, where the band curvature terms in the dispersion can be neglected, the linear dispersion of a Luttinger liquid is asymptotically exact. The spectral function, however, displays deviations from the Luttinger behavior for higher energy excitations. In the neighborhood of the single-particle (hole) energy, the spectral function is represented by an effective X-ray edge type model. Expressions of the critical exponents for the single-hole Green’s function are obtained using the Bethe ansatz solution in the limit of the bosonic gas. The results could be of relevance in the context of ultracold atoms confined to an elongated optical trap.

scholarly journals Gate-tunable plasmons in mixed-dimensional van der Waals heterostructures

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sheng Wang ◽  
SeokJae Yoo ◽  
Sihan Zhao ◽  
Wenyu Zhao ◽  
Salman Kahn ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Carrier Density ◽  
Electromagnetic Interaction ◽  
Luttinger Liquid ◽  
Fundamental Physics ◽  
Metallic Structures ◽  
One Dimensional ◽  
Figures Of Merit ◽  
Electrostatic Gating ◽  
Plasmon Dispersion

AbstractSurface plasmons, collective electromagnetic excitations coupled to conduction electron oscillations, enable the manipulation of light–matter interactions at the nanoscale. Plasmon dispersion of metallic structures depends sensitively on their dimensionality and has been intensively studied for fundamental physics as well as applied technologies. Here, we report possible evidence for gate-tunable hybrid plasmons from the dimensionally mixed coupling between one-dimensional (1D) carbon nanotubes and two-dimensional (2D) graphene. In contrast to the carrier density-independent 1D Luttinger liquid plasmons in bare metallic carbon nanotubes, plasmon wavelengths in the 1D-2D heterostructure are modulated by 75% via electrostatic gating while retaining the high figures of merit of 1D plasmons. We propose a theoretical model to describe the electromagnetic interaction between plasmons in nanotubes and graphene, suggesting plasmon hybridization as a possible origin for the observed large plasmon modulation. The mixed-dimensional plasmonic heterostructures may enable diverse designs of tunable plasmonic nanodevices.

scholarly journals String orders in the Luttinger liquid phase of one-dimensional spin-1/2 systems

2019 ◽  
Vol 516 ◽  
pp. 212-221
Author(s):  
Hadi Cheraghi ◽  
Majid Jafar Tafreshi ◽  
Saeed Mahdavifar
Keyword(s):  
Liquid Phase ◽  
Luttinger Liquid ◽  
One Dimensional

RENORMALIZATION OF POTENTIAL SCATTERING IN A ONE-DIMENSIONAL NON-LUTTINGER LIQUID: CONDUCTION AND X-RAY FERMI-EDGE SINGULARITY

1995 ◽  
Vol 09 (05) ◽  
pp. 249-269
Author(s):  
DONGXIAO YUE
Keyword(s):  
Luttinger Liquid ◽  
Scattered Wave ◽  
Zeeman Splitting ◽  
Electron System ◽  
Potential Scattering ◽  
Differential Conductance ◽  
One Dimensional ◽  
Edge Singularity ◽  
Fermi Edge ◽  
Fermi Edge Singularity

We review some of our recent results on the potential scattering in a weakly interacting one-dimensional(1D) electron gas. The technique we developed is a poor man's renormalization group procedure in the scattered wave basis. This technique can treat the renormalizations of the scattering on the barrier and the scattering between the electrons in a coherent way, and it allows us to find the scattering amplitudes on a localized potential of arbitrary strength for electrons at any energy. The obtained phase shifts are used to study the Fermi-edge singularity in an interacting 1D electron system, where anomalous exponent of the power-law singularity in the vicinity of the edge is found. The transmission coefficient is directly related to the conductance of a 1D channel by the Landauer formula. Simple formulas that describe the conductance at any temperature are derived. In spin-[Formula: see text] systems, the electron–electron backscattering induces renormalizations of the interaction constants, which causes the low-temperature conductance to deviate from the results of the Luttinger liquid theory. In particular, the temperature dependence of the conductance may become nonmonotonic. In the presence of a magnetic field, backscattering gives rise to a peak in the differential conductance at bias equal to the Zeeman splitting.

Application of the Landau-Luttinger Liquid Formulation to the Study of the Magnetic Properties of the 1-D Hubbard Model

1991 ◽  
Vol 05 (01n02) ◽  
pp. 3-30 ◽  
Author(s):  
J. Carmelo ◽  
P. Horsch ◽  
P.A. Bares ◽  
A.A. Ovchinnikov
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Low Temperature ◽  
Hubbard Model ◽  
Luttinger Liquid ◽  
Liquid Formulation ◽  
One Dimensional ◽  
Spin Excitations ◽  
Arbitrary Strength ◽  
The One

The Landau-Luttinger liquid formulation is used to investigate the physics of the one-dimensional Hubbard model in a magnetic field of arbitrary strength H. The low lying charge and spin excitations are studied. A novel branch of sound wave-like spin excitations arises for H>0. The low temperature thermodynamics is considered in some detail.

scholarly journals A Short Review on One Dimensional Wigner Crystallization

2020 ◽  
Author(s):  
Niccolo Traverso Ziani ◽  
Fabio Cavaliere ◽  
Karina Guerrero Becerra ◽  
Maura Sassetti
Keyword(s):  
Carbon Nanotubes ◽  
Structural Transition ◽  
Luttinger Liquid ◽  
Electronic System ◽  
Short Review ◽  
One Dimensional ◽  
Basic Properties ◽  
Wigner Crystallization ◽  
Liquid Theory ◽  
The One

The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions will be shortly addressed, together with the basic properties of carbon nanotubes that are require. Then, the most relevant properties of Wigner molecules will be addressed, and finally the experiments will be described.

scholarly journals Investigating the roots of the nonlinear Luttinger liquid phenomenology

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Lisa Markhof ◽  
Mikhail Pletyukov ◽  
Volker Meden
Keyword(s):  
Spectral Function ◽  
Power Law ◽  
Single Particle ◽  
Structure Factor ◽  
Particle Interaction ◽  
Luttinger Liquid ◽  
Power Laws ◽  
Second Order ◽  
Dynamical Structure ◽  
Momentum Dependence

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

scholarly journals Tomonaga-Luttinger Liquid Spin Dynamics in the Quasi-One-Dimensional Ising-Like Antiferromagnet BaCo2V2O8

2019 ◽  
Vol 123 (2) ◽  
Author(s):  
Quentin Faure ◽  
Shintaro Takayoshi ◽  
Virginie Simonet ◽  
Béatrice Grenier ◽  
Martin Månsson ◽  
...  
Keyword(s):  
Spin Dynamics ◽  
Luttinger Liquid ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document