Abstract
We study the existence of a chiral spin ordered state in one-dimensional antiferromagnetic Heisenberg models. We prove that when the coupling constants are short-ranged no quantum vector-spin-chirality order appears at zero temperature for integer spin chains.
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08 October 2019
Reference [39] is corrected to:
<Emphasis Type="Bold">Reference</Emphasis>
39. C. Noce, Phys. Rep. <Emphasis Type="Bold">431</Emphasis>, 173 (2006)
08 October 2019
Reference [39] is corrected to:
References
V. Kalmeyer, R.B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987)
X.G. Wen, F. Wilczek, A. Zee, Phys. Rev. B 39, 11413 (1989)
H. Ishizuka, N. Nagaosa, Sci. Adv. 4, eaap9962 (2018)
Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, Y. Tokura, Science 291, 2573 (2001)
P.A. Lee, N. Nagaosa, X.-G. Wen, Rev. Mod. Phys. 78, 17 (2006)
H. Kawamura, J. Phys. Soc. Jpn. 79, 011007 (2010)
K. Ohgushi, S. Murakami, N. Nagaosa, Phys. Rev. B 62, R6065 (2000)
M. dos Santos Dias, J. Bouaziz, M. Bouhassoune, S. Blügel, S. Lounis, Nat. Commun. 7, 13613 (2016)
C. Franz, F. Freimuth, A. Bauer, R. Ritz, C. Schnarr, C. Duvinage, T. Adams, S. Blügel, A. Rosch, Y. Mokrousov, C. Pfleiderer, Phys. Rev. Lett. 112, 186601 (2014)
K. Everschor-Sitte, M. Sitte, J. Appl. Phys. 115, 172602 (2014)
D. Xiao, M.C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959 (2010)
G. Tatara, N. Garcia, Phys. Rev. Lett. 91, 076806 (2003)
S. Furukawa, M. Sato, Y. Saiga, S. Onoda, J. Phys. Soc. Jpn. 77, 123712 (2008)
S. Furukawa, M. Sato, S. Onoda, Phys. Rev. Lett. 105, 257205 (2010)
T. Hikihara, L. Kecke, T. Momoi, A. Furusaki, Phys. Rev. B 78, 144404 (2008)
F. Buccheri, R. Egger, R.G. Pereira, F.B. Ramos, Phys. Rev. B 97, 220402(R) (2018)
F. Buccheri, R. Egger, R.G. Pereira, F.B. Ramos, Nucl. Phys. B 941, 794 (2019)
G. Ferraz, F.B. Ramos, R. Egger, R.G. Pereira, arXiv:1906.00807
I.P. McCulloch, R. Kube, M. Kurz, A. Kleine, U. Schollwöck, A.K. Kolezhuk, Phys. Rev. B 77, 094404 (2008)
A.A. Nersesyan, A.O. Gogolin, F.H.L. Essler, Phys. Rev. Lett. 81, 910 (1998)
P. Lecheminant, T. Jolicoeur, P. Azaria, Phys. Rev. B 63, 174426 (2001)
T. Hikihara, M. Kaburagi, H. Kawamura, Phys. Rev. B 63, 174430 (2001)
H. Ueda, S. Onoda, Phys. Rev. B 89, 024407 (2014)
N.N. Bogoliubov, Phys. Abhandl. Sowjetunion 6, 1 (1962)
N.N. Bogoliubov, Phys. Abhandl. Sowjetunion 6, 113 (1962)
N.N. Bogoliubov, Phys. Abhandl. Sowjetunion 6, 229 (1962)
P.C. Hohenberg, Phys. Rev. 158, 383 (1967)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
D.K. Ghosh, Phys. Rev. Lett. 27, 1584 (1971)
C. Proetto, A. Lopez, J. Phys. Lett. 44, 635 (1983)
C. Noce, M. Cuoco, Phys. Rev. B 59, 7409 (1999)
A. Gelfert, W. Nolting, J. Phys.: Condens. Matter 13, R505 (2001)
A.B. Harris, T. Yildirim, A. Aharony, O. Entin-Wohlman, I.Ya. Korenblit, Phys. Rev. Lett. 91, 087206 (2003)
C. Noce, New J. Phys. 9, 238 (2007)
D. Loss, F.L. Pedrocchi, A.J. Leggett, Phys. Rev. Lett. 107, 107201 (2011)
G. Guarnaccia, C. Noce, Phys. Rev. B 86, 064409 (2012)
A. Auerbach,Itinerant Electrons and Quantum Magnetism (Springer-Verlag, 1994)
G. Su, A. Schadschneider, J. Zittartz, Phys. Lett. A 230, 99 (1997)
C. Noce, Phys. Rep. 71, 092506 (2006)
J. Wojtkiewicz, W. Pusz, P. Stachura, Rep. Math. Phys. 80, 233 (2017)
C. Noce, Phys. Rev. B 71, 092506 (2005)
G. Su, M. Suzuki, Phys. Rev. B 58, 117 (1998)
F.D.M. Haldane, Phys. Lett. A 95, 464 (1983)
F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)
E. Lieb, T.D. Schultz, D.C. Mattis, Ann. Phys. 16, 407 (1961)
G. Gomez-Santos, Phys. Rev. Lett. 63, 790 (1989)
M.P. Nightingale, H.W.J. Blote, Phys. Rev. B 33, 659(R) (1990)
W.J.L. Buyers, R.M. Morra, R.L. Armstrong, M.J. Hogan, P. Gerlach, K. Hirakawa, Phys. Rev. Lett. 56, 371 (1986)
M. Steiner, K. Kakurai, J. Appl. Phys. 61, 3953 (1987)
K. Katsumata, H. Hori, T. Takeuchi, M. Date, A. Yamagishi, J.P. Renard, Phys. Rev. Lett. 63, 86 (1989)
T. Koma, J. Math. Phys. 48, 023303 (2007)
T. Kawarabayashi, M. Suzuki, Phys. Lett. A 143, 17 (1990)
T. Kawarabayashi, M. Suzuki, J. Magn. Magn. Mat. 104 –107, 929 (1992)
J.M. Kosterliz, D.J. Thouless, J. Phys. C 6, 1181 (1973)
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CN planned the research proposal, GG performed all the calculations and GG and CN wrote the paper.
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Guarnaccia, G., Noce, C. Quantum disordered vector-spin-chirality state in one dimensional Heisenberg model. Eur. Phys. J. B 92, 212 (2019). https://doi.org/10.1140/epjb/e2019-100322-8
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DOI: https://doi.org/10.1140/epjb/e2019-100322-8