Correlated electron transport in 1d

Table of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization group for interacting fermions 5. Single impurity in a 1D system: scattering theory for interacting electrons 6. Bosonization solution 7. Transport in quantum wires 7.1 Conductivity and conductance 7.2 Dissipation in a contactless measurement 7.3 Conductance of a wire attached to reservoirs 7.4 Spin component of the conductance 7.5 Thermal conductance: Fabry-Perrot resonances of plasmons 8. AppendicesTable of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization group for interacting fermions 5. Single impurity in a 1D system: scattering theory for interacting electrons 6. Bosonization solution 7. Transport in quantum wires 7.1 Conductivity and conductance 7.2 Dissipation in a contactless measurement 7.3 Conductance of a wire attached to reservoirs 7.4 Spin component of the conductance 7.5 Thermal conductance: Fabry-Perrot resonances of plasmons 8. Appendices

arXiv:cond-mat/0506035Jun 1, 20054 citations

Strongly correlated transport

Lincoln D. Carr, Mark T. Lusk

NatureNov 1, 20121 citation

Absence of ballistic charge transport in the half-filled 1D Hubbard model

J. M. P. Carmelo, Somayyeh Nemati, Tomaž Prosen

Whether in the thermodynamic limit of lattice length L→∞, hole concentration mηz=−2Sηz/L=1−ne→0, nonzero temperature T>0, and U/t>0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. (Here Sηz=−(L−Ne)/2 is the η-spin projection and ne=Ne/L the electronic density.) In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T>0 and U/t>0 it vanishes for mηz→0 within the canonical ensemble in the thermodynamic limit L→∞. Moreover, we show that at high temperature T→∞ the charge stiffness vanishes as well within the grand-canonical ensemble for L→∞ and chemical potential μ→μu where (μ−μu)≥0 and 2μu is the Mott–Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.Whether in the thermodynamic limit of lattice length L→∞, hole concentration mηz=−2Sηz/L=1−ne→0, nonzero temperature T>0, and U/t>0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. (Here Sηz=−(L−Ne)/2 is the η-spin projection and ne=Ne/L the electronic density.) In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T>0 and U/t>0 it vanishes for mηz→0 within the canonical ensemble in the thermodynamic limit L→∞. Moreover, we show that at high temperature T→∞ the charge stiffness vanishes as well within the grand-canonical ensemble for L→∞ and chemical potential μ→μu where (μ−μu)≥0 and 2μu is the Mott–Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.

arXiv:1803.09564Nuclear Physics BMar 28, 201816 citations

Fractional Charge in Transport through a 1D Correlated Insulator of Finite Length

Vadim V. Ponomarenko, Naoto Nagaosa

Transport between two Fermi liquid reservoirs through a one channel wire of length $L$ is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ ( ${v}_{c}$ is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).Transport between two Fermi liquid reservoirs through a one channel wire of length $L$ is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ ( ${v}_{c}$ is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).

arXiv:cond-mat/9806136Physical Review LettersAug 30, 199910 citations

Transport between two Fermi liquid reservoirs through a one channel wire of length

L

is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ (

{v}_{c}

is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).