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

José M. P. Carmelo (Author), S. Nemati (Author), Tomaž Prosen (Author)

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.

Keywords

termodinamika;fizika kondenzirane snovi;Hubbardov model;thermodynamics;condensed matter physics;Hubbard model;

Data

Language:	English
Year of publishing:	2018
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	536.7
COBISS:	3193444
ISSN:	0550-3213
Views:	761
Downloads:	656
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	termodinamika;fizika kondenzirane snovi;Hubbardov model;
Pages:	str. 418-498
Issue:	ǂVol. ǂ930
Chronology:	2018
DOI:	10.1016/j.nuclphysb.2018.03.011
ID:	10922067