Spin-Charge Separation and Localization in One Dimension

Auslaender, Ophir M.; Steinberg, Hadar; Yacoby, Amir; Tserkovnyak, Yaroslav; Halperin, B. I.; Baldwin, K. W.; Pfeiffer, L. N.; West, K. W.

doi:10.1126/science.1107821

Cited by 388 publications

(413 citation statements)

References 28 publications

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“…At low energies these systems are well described by the Luttinger Liquid (LL) theory 2 that predicts two independent excitations carrying either only charge (holons) or only spin (spinons) and propagating with different velocities, and hence, spin-charge separation. Experimental evidences of its existence have been observed in quasi-1D organic conductors 3 , semiconductor quantum wires 4 , and quantum chains on semiconductor surfaces 5 . The LL theory also predicts the fractionalization of injected charge into two chiral modes (leftand right-going) [6][7][8][9][10] , a phenomenon recently confirmed experimentally 11 .…”

Section: Introductionmentioning

confidence: 99%

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

2013

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It is well established that at low energies one-dimensional (1D) fermionic systems are described by the Luttinger liquid (LL) theory, that predicts phenomena like spin-charge separation, and charge fractionalization into chiral modes. Here we show through the time evolution of an electron injected into a 1D t-J model, obtained with time-dependent density matrix renormalization group, that a further fractionalization of both charge and spin takes place beyond the hydrodynamic limit. Its dynamics can be understood at the supersymmetric point (J = 2t) in terms of the excitations of the Bethe-Ansatz solution. Furthermore we show that fractionalization with similar characteristics extends to the whole region corresponding to a repulsive LL.

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Section: Introductionmentioning

confidence: 99%

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

2013

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“…3 A peculiarity of a one-dimensional world is that such systems can be explained not by the conventional Landau theory of normal Fermi liquids but, rather, by an effective low-energy Luttinger liquid description, 4 generalizable to long-range Coulomb interactions. 5 A number of approaches of increasing accuracy (random-phase approximation, SingwiTosi-Land-Sjölander scheme, density functional theory) have been devised to study energetic and structural properties.…”

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confidence: 99%

Exact ground-state properties of a one-dimensional Coulomb gas

Astrakharchik

Girardeau

2011

Phys. Rev. B

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The ground-state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground-state wave function which permits solution of the Fermi sign problem in the following respects: (i) the nodal surface is known, permitting exact calculations; and (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system and, thus, allowing simulation of a large number of fermions. Due to the mapping, the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground-state energy is calculated in homogeneous and trapped geometries using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the high-density ideal Fermi gas/Tonks-Girardeau limit, where low-lying excitations are phonons. Exact density profiles are compared to the ones calculated within the local density approximation, which predicts a change from a semicircular to an inverted parabolic shape of the density profile as the value of the charge is increased. The recent progress in nanoscale technology has made it possible to realize clean one-dimensional quantum gases, such as ultracold atoms confined in elongated traps 1 and electrons in single-well carbon nanotubes 2 and in semiconductor quantum wires. 3 A peculiarity of a one-dimensional world is that such systems can be explained not by the conventional Landau theory of normal Fermi liquids but, rather, by an effective low-energy Luttinger liquid description, 4 generalizable to long-range Coulomb interactions. 5 A number of approaches of increasing accuracy (random-phase approximation, SingwiTosi-Land-Sjölander scheme, density functional theory) have been devised to study energetic and structural properties. 6 The most precise calculations of energy have been obtained by the Monte Carlo technique as in Ref. 7, where a quasi-onedimensional geometry with a finite width of the transverse confinement is studied. The purpose of the present work is to carry out exact calculations in a strictly one-dimensional geometry.In this paper we use the Bose-Fermi mapping to find the ground-state energy of a one-dimensional single-component Coulomb system exactly within statistical precision. The mapping applies to both homogeneous and trapped geometries.We consider a single-component system of N particles (bosons or fermions) of charge e and mass m in a onedimensional box of length L. Periodic boundary conditions are applied and the Coulomb potential is truncated for interparticle distances larger than L/2. The Hamiltonian readŝNatural length scales in a homogeneous system are defined by atomic units, that is, the Bohr radius a 0 =h 2 /me 2 for length and the Rydberg number Ry = e 2 /2a 0 for energy. The system properties are governed by a single parameter, fixed by the ratio of Bohr a 0 radius and Wigner-Seitz r s = 1/2n radius or, equiva...

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“…M ost studies of collective excitations in one-dimensional (1D) systems performed so far have focused on nonchiral quantum wires [1][2][3] . In these systems, the collective excitations carrying the charge and the spin propagate at different velocities, leading to the separation of the charge and spin degrees of freedom.…”

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confidence: 99%

Separation of neutral and charge modes in one-dimensional chiral edge channels

et al. 2013

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Coulomb interactions have a major role in one-dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in one dimension. Here we report the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor 2. Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3-mm propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that result from the phase shift between the fast charge and slow neutral eigenmodes. We measure the dispersion relation and dissipation of the neutral mode from which we deduce quantitative information on the interaction range and parameters.

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Spin-Charge Separation and Localization in One Dimension

Cited by 388 publications

References 28 publications

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

Exact ground-state properties of a one-dimensional Coulomb gas

Separation of neutral and charge modes in one-dimensional chiral edge channels

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