Absence of ballistic charge transport in the half-filled 1D Hubbard model
Carmelo, José M. P. (Author), Nemati, S. (Author), Prosen, Tomaž (Author)

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Abstract
Whether in the thermodynamic limit of lattice length $L\to \infty$, hole concentration $m^z_\eta =-2S^z_\eta / L =1-n_e \to 0$, 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 $S^z_\eta =-(L-N_e)/2$ is the $\eta$-spin projection and $n_e=N_e/L$ 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 $m^z_\eta \to 0$ within the canonical ensemble in the thermodynamic limit $L \to \infty$. Moreover, we show that at high temperature $T \to \infty$ the charge stiffness vanishes as well within the grand-canonical ensemble for $L \to \infty$ and chemical potential $\mu \to \mu_u$ where $(\mu-\mu_u)\geq 0$ and $2\mu_u$ 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.

Language: English thermodynamics, condensed matter physics, Hubbard model 1.01 - Original Scientific Article FMF - Faculty of Mathematics and Physics 2018 Str. 418-498 Vol. 930 536.7 0550-3213 10.1016/j.nuclphysb.2018.03.011 3193444 639 607 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Nuclear physics. Section B. Nucl. phys, Sect. B North-Holland 0550-3213 26042624

## Document is financed by a project

Funder: EC - European Commission H2020 694544 Open many-body non-equilibrium systems OMNES

## Licences

License: CC BY 4.0, Creative Commons Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author. 05.04.2018

## Secondary language

Language: Slovenian termodinamika, fizika kondenzirane snovi, Hubbardov model