scholarly journals Probing Spin-Charge Separation in a Tomonaga-Luttinger Liquid

Science ◽  
2009 ◽  
Vol 325 (5940) ◽  
pp. 597-601 ◽  
Author(s):  
Y. Jompol ◽  
C. J. B. Ford ◽  
J. P. Griffiths ◽  
I. Farrer ◽  
G. A. C. Jones ◽  
...  
Keyword(s):  
Power Law ◽  
Charge Separation ◽  
Luttinger Liquid ◽  
Interaction Effects ◽  
Low Energy ◽  
One Dimensional ◽  
Energy Regime ◽  
Low Energies ◽  
Interacting Electrons

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunneling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.

The electronic structure and spin-charge separation of one-dimensional SrCuO2

2019 ◽  
Vol 33 (02) ◽  
pp. 1950006
Author(s):  
Huaisong Zhao ◽  
Jiasheng Qian ◽  
Sheng Xu ◽  
Feng Yuan
Keyword(s):  
Electronic Structure ◽  
Charge Separation ◽  
Energy Region ◽  
Doping Concentration ◽  
High Energy ◽  
Intermediate Energy ◽  
Low Energy ◽  
One Dimensional ◽  
High Energy Peak ◽  
Energy Peak

Based on the t-J model and slave-boson theory, we have studied the electronic structure in one-dimensional SrCuO2 by calculating the electron spectrum. Our results show that the electron spectra are mainly composed of three parts in one-dimensional SrCuO2, a sharp low-energy peak, a broad intermediate-energy peak and a high-energy peak. The sharp low-energy peak corresponds to the main band (MB) while the broad intermediate-energy peak and high-energy peak are associated with the shadow band (SB) and high-energy band (HB), respectively. From low-energy to intermediate-energy region, a clear two-peak structure (MB and SB) around the momentum [Formula: see text] appears, and the distance between two peaks decreases along the momentum direction from [Formula: see text] to [Formula: see text], then disappears at the critical momentum point [Formula: see text], leaving a single peak above [Formula: see text]. The electron spectral function in one-dimensional SrCuO2 is also the doping and temperature dependent. In particular, in the very low doping concentration, the HB merges into the MB. However, with the increases of the doping concentration, the HB separates from the MB and moves quickly to the high-binding energy region. The HB and MB are the direct results of the spin-charge separation while SB is the result of strong interaction between charge and spin parts. Therefore, our theoretical result predicts that the HB is more likely to be found at the low doping concentration, and it will be drowned in the background when the doping concentration is larger. Then with the temperature increases, the magnitude of the SB decreases, and it disappears at high temperature.

scholarly journals THE LUTTINGER LIQUID AND INTEGRABLE MODELS

2012 ◽  
Vol 26 (22) ◽  
pp. 1244009 ◽  
Author(s):  
J. SIRKER
Keyword(s):  
Luttinger Liquid ◽  
Lattice Models ◽  
Lattice Relaxation ◽  
Integrable Models ◽  
Low Energy ◽  
Spin Lattice Relaxation ◽  
Effective Theory ◽  
Spin Lattice ◽  
Liquid Theory ◽  
Low Energies

Many fundamental one-dimensional lattice models such as the Heisenberg or the Hubbard model are integrable. For these microscopic models, parameters in the Luttinger liquid theory can often be fixed and parameter-free results at low energies for many physical quantities such as dynamical correlation functions obtained where exact results are still out of reach. Quantum integrable models thus provide an important testing ground for low-energy Luttinger liquid physics. They are, furthermore, also very interesting in their own right and show, for example, peculiar transport and thermalization properties. The consequences of the conservation laws leading to integrability for the structure of the low-energy effective theory have, however, not fully been explored yet. I will discuss the connection between integrability and Luttinger liquid theory here, using the anisotropic Heisenberg model as an example. In particular, I will review the methods which allow to fix free parameters in the Luttinger model with the help of the Bethe ansatz solution. As applications, parameter-free results for the susceptibility in the presence of nonmagnetic impurities, for spin transport, and for the spin-lattice relaxation rate are discussed.

scholarly journals TRANSPORT IN QUANTUM WIRES WITH IMPURITIES AT FINITE TEMPERATURE

2003 ◽  
Vol 17 (28) ◽  
pp. 5483-5487
Author(s):  
T. KLEIMANN ◽  
M. SASSETTI ◽  
B. KRAMER
Keyword(s):  
Quantum Dot ◽  
Temperature Dependence ◽  
Power Law ◽  
Finite Temperature ◽  
Coulomb Blockade ◽  
Quantum Wires ◽  
Luttinger Liquid ◽  
Electron Interaction ◽  
One Dimensional ◽  
Liquid Model

The temperature dependence of Coulomb blockade peaks of a one dimensional quantum dot is calculated. The Coulomb interaction is treated microscopically using the Luttinger liquid model. The electron interaction is assumed to be non-homogeneous with a maximum strength near the quantum dot. The conductance peaks show non-analytic power law behaviour induced by the interaction. It is shown that there is a crossover in the power law which is related to the inhomogeneity of the interaction.

scholarly journals Doped Kondo chain, a heavy Luttinger liquid

2018 ◽  
Vol 115 (20) ◽  
pp. 5140-5144 ◽  
Author(s):  
Ilia Khait ◽  
Patrick Azaria ◽  
Claudius Hubig ◽  
Ulrich Schollwöck ◽  
Assa Auerbach
Keyword(s):  
Conduction Band ◽  
Power Law ◽  
Wave Vector ◽  
Luttinger Liquid ◽  
Magnetic Ordering ◽  
Kondo Lattice ◽  
Low Energy ◽  
Fermi Velocity ◽  
Large N ◽  
Fermi Wave Vector

The doped 1D Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave vector-dependent charge and spin susceptibilities give insights into its low-energy properties. Similar to the prediction of the large N approximation, gapless spin and charge modes appear at the large Fermi wave vector. The highly suppressed spin velocity is a manifestation of “heavy” Luttinger liquid quasiparticles. A low-energy hybridization gap is detected at the small (conduction band) Fermi wave vector. In contrast to the exponential suppression of the Fermi velocity in the large-N approximation, we fit the spin velocity by a density-dependent power law of the Kondo coupling. The differences between the large-N theory and our numerical results are associated with the emergent magnetic Ruderman–Kittel–Kasuya–Yosida interactions.

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.

ELECTROSTATIC SCREENING IN FULLERENE COMPOUNDS

1994 ◽  
Vol 08 (23) ◽  
pp. 1437-1446
Author(s):  
J. GONZÁLEZ ◽  
F. GUINEA ◽  
M.A.H. VOZMEDIANO
Keyword(s):  
Field Theory ◽  
Electric Charge ◽  
Quantum Electrodynamics ◽  
Luttinger Liquid ◽  
Coulomb Interactions ◽  
Standard Quantum ◽  
One Dimensional ◽  
Close Analogy ◽  
Low Energies ◽  
The One

We study the Coulomb interactions in fullerene compounds within a continuum formalism. The model gives rise to a renormalizable field theory, which has many similarities to standard quantum electrodynamics. The effective electric charge at low energies is reduced by screening processes. The associated renormalization of the one-electron Green’s function leads to the vanishing of the quasiparticle pole. It implies the disappearance of coherent one-particle excitations, in close analogy to the one-dimensional Luttinger liquid. The relevance of these results for C 60 and related molecules is discussed.

QUANTUM HALL EDGE PHYSICS AND ITS ONE-DIMENSIONAL LUTTINGER LIQUID DESCRIPTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1244001 ◽  
Author(s):  
ORION CIFTJA
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Quantum Hall ◽  
Luttinger Liquid ◽  
Edge States ◽  
One Dimensional ◽  
Liquid Model ◽  
Experimental Values ◽  
The One ◽  
The Relationship

We describe the relationship between quantum Hall edge states and the one-dimensional Luttinger liquid model. The Luttinger liquid model originated from studies of one-dimensional Fermi systems, however, it results that many ideas inspired by such a model can find applications to phenomena occurring even in higher dimensions. Quantum Hall systems which essentially are correlated two-dimensional electronic systems in a strong perpendicular magnetic field have an edge. It turns out that the quantum Hall edge states can be described by a one-dimensional Luttinger model. In this work, we give a general background of the quantum Hall and Luttinger liquid physics and then point out the relationship between the quantum Hall edge states and its one-dimensional Luttinger liquid representation. Such a description is very useful given that the Luttinger liquid model has the property that it can be bosonized and solved. The fact that we can introduce a simpler model of noninteracting bosons, even if the quantum Hall edge states of electrons are interacting, allows one to calculate exactly various quantities of interest. One such quantity is the correlation function which, in the asymptotic limit, is predicted to have a power law form. The Luttinger liquid model also suggests that such a power law exponent should have a universal value. A large number of experiments have found the quantum Hall edge states to show behavior consistent with a Luttinger liquid description. However, while a power law dependence of the correlation function has been observed, the experimental values of the exponent appear not to be universal. This discrepancy might be due to various correlation effects between electrons that sometimes are not easy to incorporate within a standard Luttinger liquid model.

scholarly journals INTERACTIONS IN QUASICRYSTALS

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1329-1337 ◽  
Author(s):  
JULIEN VIDAL ◽  
DOMINIQUE MOUHANNA ◽  
THIERRY GIAMARCHI
Keyword(s):  
Solid State ◽  
Transport Properties ◽  
Fermi Liquid ◽  
Electron Gas ◽  
Three Dimensional ◽  
Luttinger Liquid ◽  
Dimensional Model ◽  
One Dimensional ◽  
Interacting Electrons ◽  
The One

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in periodic crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in quasicrystalline structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.

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