Abstract
We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value − 1. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of 104 or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.
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References
K. Schönhammer,Interacting Electrons in Low Dimensions, edited by D. Baeriswyl (Kluwer Academic Publishers, Dordrecht, 2005), https://arXiv:cond-mat/0305035
T. Giamarchi,Quantum Physics in One Dimension (Oxford University Press, New York, 2003)
F.D.M. Haldane, J. Phys. C 14, 2585 (1981)
M. Fabrizio, A.O. Gogolin, Phys. Rev. B 51, 17827 (1995)
R. Egger, H. Grabert, Phys. Rev. Lett. 75, 3505 (1995)
F.D.M. Haldane, Phys. Rev. Lett. 45, 1358 (1980)
V. Meden, W. Metzner, U. Schollwöck, O. Schneider, T. Stauber, K. Schönhammer, Eur. Phys. J. B 16, 631 (2000)
O. Gunnarsson, K. Schönhammer, Phys. Rev. Lett. 56, 1968 (1986)
K. Schönhammer, O. Gunnarsson, R.M. Noack, Phys. Rev. B 52, 2504 (1995)
N.A. Lima, M.F. Silva, L.N. Oliveira, K. Capelle, Phys. Rev. Lett. 90, 146402 (2003)
P. Schmitteckert, F. Evers, Phys. Rev. Lett. 100, 086401 (2008)
P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
S. Schenk, M. Dzierzawa, P. Schwab, U. Eckern, Phys. Rev. B 78, 165102 (2008)
A. Luther, I. Peschel, Phys. Rev. B 9, 2911 (1974)
W. Apel, T.M. Rice, Phys. Rev. B 26, 7063 (1982)
C.L. Kane, M.P.A. Fisher, Phys. Rev. B 46, 15233 (1992)
P. Schmitteckert, Phys. Chem. Chem. Phys. 20, 27600 (2018)
S. Andergassen, T. Enss, V. Meden, W. Metzner, U. Schollwöck, K. Schönhammer, Phys. Rev. B 70, 075102 (2004)
J. Sólyom, Adv. Phys. 28, 201 (1979)
S. Andergassen, T. Enss, V. Meden, W. Metzner, U. Schollwöck, K. Schönhammer, Phys. Rev. B 73, 045125 (2006)
S.A. Söffing, I. Schneider, S. Eggert, EPL 101, 56006 (2013)
N. Kitanine, K.K. Kozlowski, J.M. Maillet, G. Niccoli, N.A. Slavnov, V. Terras, J. Stat. Mech. 2008, P07010 (2008)
C. Karrasch, J.E. Moore, Phys. Rev. B 86, 155156 (2012)
P. Schmitteckert, U. Eckern, Phys. Rev. B 53, 15397 (1996)
L.J. Sham, W. Kohn, Phys. Rev. 145, 561 (1966)
J. Odavić, Ph.D. thesis, RWTH Aachen University, 2019
V. Meden, W. Metzner, U. Schollwöck, K. Schönhammer, J. Low Temp. Phys. 126, 1147 (2002)
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Odavić, J., Helbig, N. & Meden, V. Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory. Eur. Phys. J. B 93, 103 (2020). https://doi.org/10.1140/epjb/e2020-10127-1
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DOI: https://doi.org/10.1140/epjb/e2020-10127-1