Abstract.
We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior of the phonon dynamics gives a clear signal of the transition to a charge-ordered phase, and the phase diagram obtained in this way is in excellent agreement with previous DMRG results. By analyzing the phonon propagator we extract the renormalized phonon frequency, and study how it first softens as the transition is approached and then subsequently hardens in the charge-ordered phase. We then show how anharmonic features develop in the phonon propagator, and how the interaction induces a sizable dispersion of the dressed phonon in the non-adiabatic regime.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.M. De Teresa, M.R. Ibarra, P.A. Algarabel, C. Ritter, C. Marquina, J. Blasco, J. Garcia, A. del Moral, Z. Arnold, Nature 386, 256 (1997); A.J. Millis, Nature 392, 147 (1998); M.B. Salamon, M. Jaime, Rev. Mod. Phys. 73, 583 (2001)
Organic Conductors edited by J.-P. Farges (Marcel Dekker, New York, 1994)
M. Matus, H. Kuzmany, E. Sohmen, Phys. Rev. Lett. 68, 2822 (1992); K. Harigaya, Phys. Rev. B 45, 13676 (1992); B. Friedman, Phys. Rev. B 45, 1454 (1992); W.M. You, C.L. Wang, F.C. Zhang, Z.B. Su, Phys. Rev. B 47, 4765 (1993)
Guo-Meng-Zhao, M.B. Hunt, H. Keller, K.A. Muller, Nature 385, 236 (1997); A. Lanzara, P.V. Bogdanov, X.J. Zhou, S.A. Kellar, D.L. Feng, E.D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, Z.-X. Shen, Nature 412, 510 (2001); R.J. McQueeney, J.L. Sarrao, P.G. Pagliuso, P.W. Stephens, R. Osborn, Phys. Rev. Lett. 87, 77001 (2001)
J. Kortus, I.I. Mazin, K.D. Belashchenko, V.P. Antropov, L.L. Boyer, Phys. Rev. Lett. 86, 4656 (2001); P. Postorino, A. Congeduti, P. Dore, A. Nucara, A. Bianconi, D. Di Castro, S. De Negri, A. Saccone, Phys. Rev. B 65, 020507R (2002)
M. Capone, W. Stephan, M. Grilli, Phys. Rev. B 56, 4484 (1997)
R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 80, 5607 (1998)
J.E. Hirsch, E. Fradkin, Phys. Rev. B 27, 4302 (1983)
A. Weiße, H. Fehske, Phys. Rev. B 58, 13526 (1998)
R.H. McKenzie, C.J. Hamer, D.W. Murray, Phys. Rev. B 53, 9676 (1996)
Zhiguo Lü, Qin Wang, Hang Zheng, Phys. Rev. B 69, 134304 (2004)
C.A. Perroni, V. Cataudella, G. De Filippis, G. Iadonisi, V. Marigliano Ramaglia, F. Ventriglia, Phys. Rev. B 67, 214301 (2003)
S. Sykora, A. Huebsch, K.W. Becker, G. Wellein, H. Fehske, Phys. Rev. B 71, 045112 (2005)
M. Hohenadler, M. Aichhorn, W. von der Linden, Phys. Rev. B 68, 184304 (2003)
R. Blankenbecler, D.J. Scalapino, R.L. Sugar, Phys. Rev. D 24, 2278 (1981)
J.E. Gubernatis, M. Jarrell, R.N. Silver, D.S. Sivia, Phys. Rev. B 44, 6011 (1991)
R.K. Bryan, Eur. Bio. J. 18, 165 (1990)
C.E. Creffield, E.G. Klepfish, E.R. Pike, S. Sarkar, Phys. Rev. Lett. 75, 517 (1995)
L. Boeri, G.B. Bachelet, E. Cappelluti, L. Pietronero, Phys. Rev. B 65, 214501 (2002)
A.S. Alexandrov, V.V. Kabanov, D.K. Ray, Phys. Rev. B 49, 9915 (1994)
As we do not use an explicitly symmetric form for the electron-phonon interaction term in equation (1) (i.e. we use g q n instead of \(g q \left( n - \langle n \rangle \right)\)), this bimodal distribution is not symmetric about the origin, instead having an overall shift of -q0
M. Capone, S. Ciuchi, Phys. Rev. B 65, 104409 (2002)
M. Capone, S. Ciuchi, Phys. Rev. Lett. 91, 186405 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Creffield, C., Sangiovanni, G. & Capone, M. Phonon softening and dispersion in the 1D Holstein model of spinless fermions. Eur. Phys. J. B 44, 175–181 (2005). https://doi.org/10.1140/epjb/e2005-00112-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2005-00112-9