Abstract
We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fröhlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons, competing fermion-boson and fermion-fermion interactions, as well as symmetry-protected topological states in fermion and anyon models.
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References
N. Tsuda, K. Nasu, A. Yanase, K. Siratori, Electronic Conduction in Oxides (Springer-Verlag, Berlin, 1991)
A.R. Bishop, B.I. Swanson, Los Alamos Sci. 21, 133 (1993)
S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950)
J.M. Luttinger, J. Math. Phys. 4, 1154 (1963)
A. Luther, V.J. Emery, Phys. Rev. Lett. 33, 589 (1974)
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
N.F. Mott, Metal-Insulator Transitions (Taylor & Francis, London, 1990)
R. Peierls, Quantum Theory of Solids, (Oxford University Press, Oxford, 1955)
J.-P. Pouget, C. R. Phys. 17, 332 (2016)
J.E. Moore, Nature 464, 194 (2010)
M.Z. Hazan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
B.I. Halperin, Phys. Rev. B 25, 2185 (1982)
M. Hohenadler, F.F. Assaad, J. Phys.: Condens. Matter 25, 143201 (2013)
Z.-C. Gu, X.-G. Wen, Phys. Rev. B 80, 155131 (2009)
F. Pollmann, E. Berg, A.M. Turner, M. Oshikawa, Phys. Rev. B 85, 075125 (2012)
X. Chen, Z.-C. Gu, Z.-X. Liu, X.-G. Wen, Phys. Rev. B 87, 155114 (2013)
S. Ryu, Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002)
F.D.M. Haldane, Phys. Rev. Lett. 50, 1153 (1983)
T. Giamarchi, ¿Quantum Physics in One Dimension (Clarendon Press, Oxford, 2004)
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)
J.K. Cullum, R.A. Willoughby, in Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Progress in scientific computing (Birkhäuser, Boston, 1985), Vols. I & II
S.R. White, Phys. Rev. Lett. 69, 2863 (1992)
U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)
E. Jeckelmann, H. Fehske, Riv. Nuovo Cimento 30, 259 (2007)
I.P. McCulloch, https://doi.org/arXiv:0804.2509 (2008)
A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, Phys. Rev. B 72, 035122 (2005)
F.F. Assaad, T.C. Lang, Phys. Rev. B 76, 035116 (2007)
A. Sandvik, R. Singh, D. Campbell, Phys. Rev. B 56, 14510 (1997)
R.T. Clay, R.P. Hardikar, Phys. Rev. Lett. 95, 096401 (2005)
J. Voit, Rep. Prog. Phys. 58, 977 (1995)
T. Holstein, Ann. Phys. 8, 325 (1959)
T. Holstein, Ann. Phys. 8, 343 (1959)
A. Weiße, H. Fehske, Phys. Rev. B 58, 13526 (1998)
M. Capone, W. Stephan, M. Grilli, Phys. Rev. B 56, 4484 (1997)
A. Alvermann, H. Fehske, S.A. Trugman, Phys. Rev. B 81, 165113 (2010)
M. Capone, M. Grilli, W. Stephan, Eur. Phys. J. B 11, 551 (1999)
Q.S. Hu, H. Zheng, Eur. Phys. J. B 28, 255 (2002)
J.E. Hirsch, E. Fradkin, Phys. Rev. B 27, 4302 (1983)
L.G. Caron, C. Bourbonnais, Phys. Rev. B 29, 4230 (1984)
H. Zheng, D. Feinberg, M. Avignon, Phys. Rev. B 39, 9405 (1989)
R.H. McKenzie, C.J. Hamer, D.W. Murray, Phys. Rev. B 53, 9676 (1996)
R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 80, 5607 (1998)
S. Datta, A. Das, S. Yarlagadda, Phys. Rev. B 71, 235118 (2005)
M. Hohenadler, G. Wellein, A.R. Bishop, A. Alvermann, H. Fehske, Phys. Rev. B 73, 245120 (2006)
M. Weber, F.F. Assaad, M. Hohenadler, Phys. Rev. Lett. 119, 097401 (2017)
F. Guinea, J. Phys. C 16, 4405 (1983)
E. Jeckelmann, C. Zhang, S.R. White, Phys. Rev. B 60, 7950 (1999)
A. Weiße, H. Fehske, G. Wellein, A.R. Bishop, Phys. Rev. B 62, R747 (2000)
Y. Takada, A. Chatterjee, Phys. Rev. B 67, 081102 (2003)
R.P. Hardikar, R.T. Clay, Phys. Rev. B 75, 245103 (2007)
I.P. Bindloss, Phys. Rev. B 71, 205113 (2005)
H. Bakrim, C. Bourbonnais, Phys. Rev. B 76, 195115 (2007)
S. Ejima, H. Fehske, Europhys. Lett. 87, 27001 (2009)
H. Fehske, G. Hager, E. Jeckelmann, Europhys. Lett. 84, 57001 (2008)
S. Ejima, H. Fehske, J. Phys.: Conf. Ser. 200, 012031 (2010)
H. Bakrim, C. Bourbonnais, Phys. Rev. B 91, 085114 (2015)
R. Gersch, C. Honerkamp, D. Rohe, W. Metzner, Eur. Phys. J. B 48, 349 (2005)
J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)
J. Greitemann, S. Hesselmann, S. Wessel, F.F. Assaad, M. Hohenadler, Phys. Rev. B 92, 245132 (2015)
M. Hohenadler, H. Fehske, F.F. Assaad, Phys. Rev. B 83, 115105 (2011)
M. Weber, F.F. Assaad, M. Hohenadler, Phys. Rev. B 94, 245138 (2016)
V. Meden, K. Schönhammer, O. Gunnarsson, Phys. Rev. B 50, 11179 (1994)
J. Voit, L. Perfetti, F. Zwick, H. Berger, G. Margaritondo, G. Grüner, H. Höchst, M. Grioni, Science 290, 501 (2000)
H. Fehske, G. Wellein, G. Hager, A. Weiße, A.R. Bishop, Phys. Rev. B 69, 165115 (2004)
W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)
C.E. Creffield, G. Sangiovanni, M. Capone, Eur. Phys. J. B 44, 175 (2005)
S. Sykora, A. Hübsch, K.W. Becker, G. Wellein, H. Fehske, Phys. Rev. B 71, 045112 (2005)
S. Sykora, A. Hübsch, K.W. Becker, Eur. Phys. J. B 51, 181 (2006)
M. Hohenadler, F.F. Assaad, Phys. Rev. B 87, 075149 (2013)
L. Balents, M.P.A. Fisher, Phys. Rev. B 53, 12133 (1996)
K.-M. Tam, S.-W. Tsai, D.K. Campbell, Phys. Rev. B 84, 165123 (2011)
J. Cardy, Scaling and Renormalization in Statistical Physics, (Cambridge University Press, Cambridge, England, 1996)
J. Voit, Eur. Phys. J. B 5, 505 (1998)
C. Zhang, E. Jeckelmann, S.R. White, Phys. Rev. B 60, 092 (1999)
W.Q. Ning, H. Zhao, C.Q. Wu, H.Q. Lin, Phys. Rev. Lett. 96, 156402 (2006)
M. Hohenadler, F.F. Assaad, H. Fehske, Phys. Rev. Lett. 109, 116407 (2012)
M. Weber, F.F. Assaad, M. Hohenadler, Phys. Rev. B 91, 235150 (2015)
J.T. Devreese, A.S. Alexandrov, Rep. Prog. Phys. 72, 066501 (2009)
A.S. Alexandrov, P.E. Kornilovitch, Phys. Rev. Lett. 82, 807 (1999)
S. Barišić, J. Labbé, J. Friedel, Phys. Rev. Lett. 25, 919 (1970)
D. Baeriswyl, D. Campbell, S. Mazumdar, in ¿Conjugated conducting polymers, edited by H. Kiess, Springer Series in Solid-State Sciences (Springer, Berlin, Heidelberg, 1992), Vol. 102, pp. 7–133
W. Barford, Electronic and optical properties of conjugated polymers, (Oxford University Press, 2005)
E. Fradkin, J.E. Hirsch, Phys. Rev. B 27, 1680 (1983)
M. Weber, F.F. Assaad, M. Hohenadler, Phys. Rev. B 91, 245147 (2015)
P. Sengupta, A.W. Sandvik, D.K. Campbell, Phys. Rev. B 67, 245103 (2003)
M. Weber, F.F. Assaad, M. Hohenadler, Phys. Rev. B 94, 155150 (2016)
A.P. Schnyder, S. Ryu, A. Furusaki, A.W.W. Ludwig, Phys. Rev. B 78, 195125 (2008)
M. Nakahara, K. Maki, Phys. Rev. B 25, 7789 (1982)
W. Su, Solid State Commun. 42, 497 (1982)
G.T. Zimanyi, S.A. Kivelson, A. Luther, Phys. Rev. Lett. 60, 2089 1988
W. Barford, R.J. Bursill, Phys. Rev. B 73, 045106 (2006)
M. Hohenadler, Phys. Rev. Lett. 117, 206404 (2016)
S. Kivelson, D. Hone, Phys. Rev. B 28, 4833 (1983)
J. Rossler, D. Gottlieb, J. Phys.: Condens. Matter 2, 3723 (1990)
I.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986)
G.H. Jonker, J.H. van Santen, Physica 16, 337 (1950)
M. Berciu, Physics 2, 55 (2009)
M. Brunner, F.F. Assaad, A. Muramatsu, Eur. Phys. J. B 16, 209 (2000)
D.M. Edwards, Physica B 378, 133 (2006)
A. Alvermann, D.M. Edwards, H. Fehske, Phys. Rev. Lett. 98, 056602 (2007)
G. Wellein, H. Fehske, A. Alvermann, D.M. Edwards, Phys. Rev. Lett. 101, 136402 (2008)
S. Ejima, H. Fehske, Phys. Rev. B 80, 155101 (2009)
S. Ejima, G. Hager, H. Fehske, Phys. Rev. Lett. 102, 106404 (2009)
S. Ejima, S. Sykora, K.W. Becker, H. Fehske, Phys. Rev. B 86, 155149 (2012)
H. Fehske, S. Ejima, G. Wellein, A.R. Bishop, J. Phys.: Conf. Ser. 391, 012152 (2012)
J.W. Bray, H.R. Hart, Jr. L.V. Interrante, I.S. Jacobs, J.S. Kasper, G.D. Watkins, S.H. Wee, J.C. Bonner, Phys. Rev. Lett. 35, 744 (1975)
M. Hase, I. Terasaki, K. Uchinokura, Phys. Rev. Lett. 70, 3651 (1993)
M. Braden, B. Hennion, W. Reichardt, G. Dhalenne, A. Revcolevschi, Phys. Rev. Lett. 80, 3634 (1998)
M. Holicki, H. Fehske, R. Werner, Phys. Rev. B 63, 174417 (2001)
E. Pytte, Phys. Rev. B 10, 4637 (1974)
M.C. Cross, D.S. Fisher, Phys. Rev. B 19, 402 (1979)
B. Büchner, H. Fehske, A.P. Kampf, G. Wellein, Physica B 259, 956 (1999)
G. Wellein, H. Fehske, A.P. Kampf, Phys. Rev. Lett. 81, 3956 (1998)
A. Weiße, G. Wellein, H. Fehske, Phys. Rev. B 60, 6566 (1999)
R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 83, 408 (1999)
K. Okamoto, K. Nomura, Phys. Lett. A 169, 433 (1992)
G.S. Uhrig, Phys. Rev. B 57, R14004 (1998)
A. Weiße, G. Hager, A.R. Bishop, H. Fehske, Phys. Rev. B 74, 214426 (2006)
I. Affleck, D. Gepner, H.J. Schulz, T. Ziman, J. Phys. A 22, 511 (1989)
F. Michel, H.G. Evertz, https://doi.org/arXiv:0705.0799 (2007)
Z. Cai, U. Schollwöck, L. Pollet, Phys. Rev. Lett. 113, 260403 (2014)
J. Hubbard, Proc. R. Soc. Lond. 276, 238 (1963)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
H.J. Schulz, Phys. Rev. Lett 64, 2831 (1990)
H. Fehske, A.P. Kampf, M. Sekania, G. Wellein, Eur. Phys. J. B 31, 11 (2003)
Y. Takada, A. Chatterjee, Phys. Rev. B 67, 081102(R) (2003)
M. Tezuka, R. Arita, H. Aoki, Phys. Rev. Lett. 95, 226401 (2005)
M. Tezuka, R. Arita, H. Aoki, Phys. Rev. B 76, 155114 (2007)
H. Benthien, E. Jeckelmann, Phys. Rev. B 75, 205128 (2007)
H. Matsueda, S. Sota, T. Tohyama, S. Maekawa, J. Phys. Soc. Jpn 81, 013701 (2012)
K. Yonemitsu, N. Maeshima, Phys. Rev. B 79, 125118 (2009)
J.D. Lee, P. Moon, M. Hase, Phys. Rev. B 84, 195109 (2011)
E.A. Nowadnick, S. Johnston, B. Moritz, R.T. Scalettar, T.P. Devereaux, Phys. Rev. Lett. 109, 246404 (2012)
G. De Filippis, V. Cataudella, E.A. Nowadnick, T.P. Devereaux, A.S. Mishchenko, N. Nagaosa, Phys. Rev. Lett. 109, 176402 (2012)
Y. Wang, B. Moritz, C.-C. Chen, C.J. Jia, M. van Veenendaal, T.P. Devereaux, Phys. Rev. Lett. 116, 086401 (2016)
E. Jeckelmann, Phys. Rev. B 57, 11838 (1998)
C.J. Pearson, W. Barford, R.J. Bursill, Phys. Rev. B 83, 195105 (2011)
S. Kivelson, D.E. Heim, Phys. Rev. B 26, 4278 (1982)
S. Mazumdar, S.N. Dixit, Phys. Rev. Lett. 51, 292 (1983)
J.E. Hirsch, Phys. Rev. Lett. 51, 296 (1983)
J. Voit, Phys. Rev. Lett. 62, 1053 (1989)
R. Lyzwa, Z. Doma ński, Phys. Rev. B 50, 11381 (1994)
P. Farka šovský, Phys. Rev. B 77, 085110 (2008)
Z.G. Wang, Y.G. Chen, S.J. Gu, Phys. Rev. B 75, 165111 (2007)
C.D. Batista, Phys. Rev. Lett. 89, 166403 (2002)
W.-G. Yin, W.N. Mei, C.-G. Duan, H.-Q. Lin, J.R. Hardy, Phys. Rev. B 68, 075111 (2003)
D. Ihle, M. Pfafferott, E. Burovski, F.X. Bronold, H. Fehske, Phys. Rev. B 78, 193103 (2008)
E.A. Winograd, R. Chitra, M.J. Rozenberg, Phys. Rev. B 86, 195118 (2012)
B. Zenker, D. Ihle, F.X. Bronold, H. Fehske, Phys. Rev. B 85, 121102R (2012)
J. Kuneš, J. Phys.: Condens. Matter 27, 333201 (2015)
L.M. Falicov, J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969)
V. Subrahmanyam, M. Barma, J. Phys. C 21, L19 (1988)
D. Jérome, T.M. Rice, W. Kohn, Phys. Rev. 158, 462 (1967)
S. Ejima, T. Kaneko, Y. Ohta, H. Fehske, Phys. Rev. Lett. 112, 026401 (2014)
T. Kaneko, B. Zenker, H. Fehske, Y. Ohta, Phys. Rev. B 92, 115106 (2015)
J. Voit, Phys. Rev. B 45, 4027 (1992)
M. Nakamura, J. Phys. Soc. Jpn. 68, 10, 3123 (1999)
M. Tsuchiizu, A. Furusaki, Phys. Rev. Lett. 88, 056402 (2002)
K.-M. Tam, S.-W. Tsai, D.K. Campbell, Phys. Rev. Lett. 96, 036408 (2006)
G.I. Japaridze, S. Sarkar, Eur. Phys. J. B 28, 139 (2002)
H.Q. Ding, J. Zhang, Eur. Phys. J. B 85, 200 (2012)
J.E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984)
E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)
A.W. Sandvik, L. Balents, D.K. Campbell, Phys. Rev. Lett. 92, 236401 (2004)
M. Aichhorn, H.G. Evertz, W. von der Linden M. Potthoff, Phys. Rev. B 70, 235107 (2004)
S. Ejima, S. Nishimoto, Phys. Rev. Lett. 99, 216403 (2007)
E. Jeckelmann, Phys. Rev. B 67, 075106 (2003)
G. Barcza, W. Barford, F. Gebhard, O. Legeza, Phys. Rev. B 87, 245116 (2013)
M. Timár, G. Barcza, F. Gebhard, O. Legeza, Phys. Rev. B 95, 085150 (2017)
F. Lange, S. Ejima, H. Fehske, Phys. Rev. B 92, 041120 (2015)
M. Tsuchiizu, A. Furusaki, Phys. Rev. B 69, 035103 (2004)
H. Benthien, F.H.L. Essler, A. Grage, Phys. Rev. B 73, 085105 (2006)
S.R. Manmana, A.M. Essin, R.M. Noack, V. Gurarie, Phys. Rev. B 86, 205119 (2012)
S. Ejima, F.H.L. Essler, F. Lange, H. Fehske, Phys. Rev. B 93, 235118 (2016)
A.O. Gogolin, A.A. Nersesyuan, A.M. Tsvelik, Bosonization and strongly correlated systems, (Cambridge University Press, Cambridge, 1999)
S. Ejima, F. Lange, H. Fehske, Phys. Rev. Lett. 113, 020401 (2014)
S. Ejima, H. Fehske, Phys. Rev. B 91, 045121 (2015)
P. Calabrese, J. Cardy, J. Stat. Mech. P06002 (2004)
S. Nishimoto, Phys. Rev. B 84, 195108 (2011)
J.M. Leinaas, J. Myrheim, Nuovo Cimento B 37, 1 (1977)
F. Wilczek, Phys. Rev. Lett. 49, 957 (1982)
F.D.M. Haldane, Phys. Rev. Lett. 67, 937 (1991)
E.G. Dalla Torre, E. Berg, E. Altman, Phys. Rev. Lett. 97, 260401 (2006)
T. Keilmann, S. Lanzmich, I.P. McCulloch, M. Roncaglia, Nat. Commun. 2, 361 (2011)
F. Lange, S. Ejima, H. Fehske, Phys. Rev. Lett. 118, 120401 (2017)
E. Berg, E.G. Dalla Torre, T. Giamarchi, E. Altman, Phys. Rev. B 77, 245119 (2008)
H. Li, F.D.M. Haldane, Phys. Rev. Lett. 101, 010504 (2008)
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Contribution to the Topical Issue “Coexistence of Long-Range Orders in Low-dimensional Systems”, edited by Sudhakar Yarlagadda and Peter B. Littlewood.
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Hohenadler, M., Fehske, H. Density waves in strongly correlated quantum chains. Eur. Phys. J. B 91, 204 (2018). https://doi.org/10.1140/epjb/e2018-90354-7
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DOI: https://doi.org/10.1140/epjb/e2018-90354-7