Metal-insulator transition of spinless fermions coupled to dispersive optical bosons.
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
05 Aug 2024
05 Aug 2024
Historique:
received:
10
04
2024
accepted:
29
07
2024
medline:
6
8
2024
pubmed:
6
8
2024
entrez:
5
8
2024
Statut:
epublish
Résumé
Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model.
Identifiants
pubmed: 39103429
doi: 10.1038/s41598-024-68811-y
pii: 10.1038/s41598-024-68811-y
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
18050Subventions
Organisme : German federal and state governments
ID : NHR@FAU
Informations de copyright
© 2024. The Author(s).
Références
Peierls, R. Quantum Theory of Solids (Oxford University Press, 1955).
Fröhlich, H. Electrons in lattice fields. Adv. Phys. 3, 325 (1954).
doi: 10.1080/00018735400101213
Grüner, G. Density Waves in Solids (Addison Wesley, 1994).
Pouget, J.-P. The Peierls instability and charge density wave in one-dimensional electronic conductors. C. R. Phys. 17, 332 (2016).
doi: 10.1016/j.crhy.2015.11.008
Jeckelmann, E., Zhang, C. & White, S. R. Metal-insulator transition in the one-dimensional Holstein model at half filling. Phys. Rev. B 60, 7950 (1999).
doi: 10.1103/PhysRevB.60.7950
Hohenadler, M. & Fehske, H. Density waves in strongly correlated quantum chains. Eur. Phys. J. B 91, 204 (2018).
doi: 10.1140/epjb/e2018-90354-7
Costa, N. C., Blommel, T., Chiu, W.-T., Batrouni, G. & Scalettar, R. T. Phonon dispersion and the competition between pairing and charge order. Phys. Rev. Lett. 120, 187003 (2018).
pubmed: 29775370
doi: 10.1103/PhysRevLett.120.187003
Mott, N. F. Metal-Insulator Transitions (Taylor & Francis, 1990).
Holstein, T. Studies of polaron motion. Part I. The molecular-crystal model. Ann. Phys. 8, 325 (1959).
doi: 10.1016/0003-4916(59)90002-8
Hirsch, J. E. & Fradkin, E. Phase diagram of one-dimensional electron-phonon systems. II. The molecular-crystal model. Phys. Rev. B 27, 4302 (1983).
doi: 10.1103/PhysRevB.27.4302
Zhao, S., Han, Z., Kivelson, S. A. & Esterlis, I. One-dimensional Holstein model revisited. Phys. Rev. B 107, 075142 (2023).
doi: 10.1103/PhysRevB.107.075142
Debika, Debnath M. Zahid, Malik Ashok, Chatterjee. A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons Abstract Scientific Reports 11(1) https://doi.org/10.1038/s41598-021-91604-6 (2021).
Weiße, A., Fehske, H., Wellein, G. & Bishop, A. R. Optimized phonon approach for the diagonalization of electron-phonon problems. Phys. Rev. B 62, R747 (2000).
doi: 10.1103/PhysRevB.62.R747
Fehske, H. & Trugman, S. A. Numerical solution of the Holstein polaron problem. In Polarons in Advanced Materials, vol. 103 of Springer Series in Material Sciences (ed Alexandrov, A. S.), 393–461 (Canopus/Springer Publishing, 2007).
Sykora, S., Hübsch, A., Becker, K. W., Wellein, G. & Fehske, H. Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model. Phys. Rev. B 71, 045112 (2005).
doi: 10.1103/PhysRevB.71.045112
Weiße, A., Wellein, G., Alvermann, A. & Fehske, H. The kernel polynomial method. Rev. Mod. Phys. 78, 275 (2006).
doi: 10.1103/RevModPhys.78.275
Mishchenko, A. S., Nagaosa, N. & Prokof’ev, N. Diagrammatic Monte Carlo method for many-polaron problems. Phys. Rev. Lett. 113, 166402 (2014).
pubmed: 25361271
doi: 10.1103/PhysRevLett.113.166402
Hohenadler, M., Fehske, H. & Assaad, F. F. Dynamic charge correlations near the Peierls transition. Phys. Rev. B 83, 115105 (2011).
doi: 10.1103/PhysRevB.83.115105
Weber, M., Assaad, F. F. & Hohenadler, M. Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model. Phys. Rev. B 94, 245138 (2016).
doi: 10.1103/PhysRevB.94.245138
Jeckelmann, E. & Fehske, H. Exact numerical methods for electron-phonon problems. Rivista del Nuovo Cimento 30, 259 (2007).
Tomonaga, S. Remarks on Bloch’s method of sound waves applied to many-fermion problems. Prog. Theor. Phys. 5, 544 (1950).
doi: 10.1143/ptp/5.4.544
Luttinger, J. M. An exactly soluble model of a many-fermion system. J. Math. Phys. 4, 1154 (1963).
doi: 10.1063/1.1704046
Zheng, H., Feinberg, D. & Avignon, M. Effect of quantum fluctuations on the Peierls dimerization in the one-dimensional molecular-crystal model. Phys. Rev. B 39, 9405 (1989).
doi: 10.1103/PhysRevB.39.9405
Weiße, A. & Fehske, H. Peierls instability and optical response in the one-dimensional half-filled Holstein model of spinless fermions. Phys. Rev. B 58, 13526 (1998).
doi: 10.1103/PhysRevB.58.13526
McKenzie, R. H., Hamer, C. J. & Murray, D. W. Quantum Monte Carlo study of the one-dimensional Holstein model of spinless fermions. Phys. Rev. B 53, 9676 (1996).
doi: 10.1103/PhysRevB.53.9676
Bursill, R. J., McKenzie, R. H. & Hamer, C. J. Phase diagram of the one-dimensional Holstein model of spinless fermions. Phys. Rev. Lett. 80, 5607 (1998).
doi: 10.1103/PhysRevLett.80.5607
Hohenadler, M., Wellein, G., Bishop, A. R., Alvermann, A. & Fehske, H. Spectral signatures of the Luttinger liquid to the charge-density-wave transition. Phys. Rev. B 73, 245120 (2006).
doi: 10.1103/PhysRevB.73.245120
Ejima, S. & Fehske, H. Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approach. Europhys. Lett. 87, 27001 (2009).
doi: 10.1209/0295-5075/87/27001
Alexandrov, A. S. & Kornilovitch, P. E. Mobile small polaron. Phys. Rev. Lett. 82, 807 (1999).
doi: 10.1103/PhysRevLett.82.807
Fehske, H., Loos, J. & Wellein, G. Lattice polaron formation: Effects of non-screened electron-phonon interaction. Phys. Rev. B 61, 8016 (2000).
doi: 10.1103/PhysRevB.61.8016
Hohenadler, M. Interplay of site and bond electron-phonon coupling in one dimension. Phys. Rev. Lett. 117, 206404 (2016).
pubmed: 27886491
doi: 10.1103/PhysRevLett.117.206404
Marchand, D. J. J. & Berciu, M. Effect of dispersive optical phonons on the behavior of a Holstein polaron. Phys. Rev. B 88, 060301 (2013).
doi: 10.1103/PhysRevB.88.060301
Bonča, J. & Trugman, S. A. Dynamic properties of a polaron coupled to dispersive optical phonons. Phys. Rev. B 103, 054304 (2021).
doi: 10.1103/PhysRevB.103.054304
Bonča, J. & Trugman, S. A. Electron removal spectral function of a polaron coupled to dispersive optical phonons. Phys. Rev. B 106, 174303 (2022).
doi: 10.1103/PhysRevB.106.174303
Jansen, D., Bonča, J. & Heidrich-Meisner, F. Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons. Phys. Rev. B 106, 155129 (2022).
doi: 10.1103/PhysRevB.106.155129
Chakraborty, M. & Fehske, H. Quantum transport in an environment parametrized by dispersive bosons. Phys. Rev. B 109, 085125 (2024).
doi: 10.1103/PhysRevB.109.085125
Kovač, K. & Bonča, J. Light bipolarons in a system of electrons coupled to dispersive optical phonons. Phys. Rev. B 109, 064304 (2024).
doi: 10.1103/PhysRevB.109.064304
Edwards, D. M. A quantum phase transition in a model with boson-controlled hopping. Physica B 378–380, 133 (2006).
doi: 10.1016/j.physb.2006.01.307
Alvermann, A., Edwards, D. M. & Fehske, H. Boson-controlled quantum transport. Phys. Rev. Lett. 98, 056602 (2007).
pubmed: 17358879
doi: 10.1103/PhysRevLett.98.056602
Wellein, G., Fehske, H., Alvermann, A. & Edwards, D. M. Correlation-induced metal insulator transition in a two-channel fermion-boson model. Phys. Rev. Lett. 101, 136402 (2008).
pubmed: 18851468
doi: 10.1103/PhysRevLett.101.136402
Ejima, S., Hager, G. & Fehske, H. Quantum phase transition in a 1D transport model with boson affected hopping: Luttinger liquid versus charge-density-wave behavior. Phys. Rev. Lett. 102, 106404 (2009).
pubmed: 19392136
doi: 10.1103/PhysRevLett.102.106404
Lange, F., Wellein, G. & Fehske, H. Charge-order melting in the one-dimensional Edwards model. Phys. Rev. Res. 6, L022007 (2024).
doi: 10.1103/PhysRevResearch.6.L022007
Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326, 96–192 (2011).
doi: 10.1016/j.aop.2010.09.012
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863 (1992).
pubmed: 10046608
doi: 10.1103/PhysRevLett.69.2863
Zauner-Stauber, V., Vanderstraeten, L., Fishman, M. T., Verstraete, F. & Haegeman, J. Variational optimization algorithms for uniform matrix product states. Phys. Rev. B 97, 045145 (2018).
doi: 10.1103/PhysRevB.97.045145
Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016).
doi: 10.1103/PhysRevB.94.165116
Gleis, A., Li, J.-W. & von Delft, J. Controlled bond expansion for density matrix renormalization group ground state search at single-site costs. Phys. Rev. Lett. 130, 246402 (2023).
pubmed: 37390431
doi: 10.1103/PhysRevLett.130.246402
Li, J.-W., Gleis, A. & von Delft, J. Time-dependent variational principle with controlled bond expansion for matrix product states (2022). arXiv:2208.10972 .
Phien, H. N., Vidal, G. & McCulloch, I. P. Infinite boundary conditions for matrix product state calculations. Phys. Rev. B 86, 245107 (2012).
doi: 10.1103/PhysRevB.86.245107
Milsted, A., Haegeman, J., Osborne, T. J. & Verstraete, F. Variational matrix product ansatz for nonuniform dynamics in the thermodynamic limit. Phys. Rev. B 88, 155116 (2013).
doi: 10.1103/PhysRevB.88.155116
Zauner, V., Ganahl, M., Evertz, H. G. & Nishino, T. Time evolution within a comoving window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains. J. Phys. Condens. Matter 27, 425602 (2015).
pubmed: 26444495
doi: 10.1088/0953-8984/27/42/425602
Stolpp, J. et al. Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without U(1) symmetry. Comput. Phys. Commun. 269, 108106 (2021).
doi: 10.1016/j.cpc.2021.108106
Jeckelmann, E. & White, S. R. Density-matrix renormalization-group study of the polaron problem in the Holstein model. Phys. Rev. B 57, 6376 (1998).
doi: 10.1103/PhysRevB.57.6376
Lang, I. G. & Firsov, Y. A. Kinetic theory of semiconductors with low mobility. Zh. Eksp. Teor. Fiz. 43, 1843 (1962).
Datta, S., Das, A. & Yarlagadda, S. Many-polaron effects in the Holstein model. PRB 71, 235118 (2005).
doi: 10.1103/PhysRevB.71.235118
Giamarchi, T. Quantum Physics in One Dimension (Clerendon Press, 2003).
doi: 10.1093/acprof:oso/9780198525004.001.0001
Kane, C. L. & Fisher, M. P. A. Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas. Phys. Rev. B 46, 15233 (1992).
doi: 10.1103/PhysRevB.46.15233
Kang, Y.-T., Lo, C.-Y., Oshikawa, M., Kao, Y.-J. & Chen, P. Two-wire junction of inequivalent Tomonaga-Luttinger liquids. Phys. Rev. B 104, 235142 (2021).
doi: 10.1103/PhysRevB.104.235142
Giamarchi, T. & Schulz, H. J. Correlation functions of one-dimensional quantum systems. Phys. Rev. B 39, 4620 (1989).
doi: 10.1103/PhysRevB.39.4620
Ejima, S., Gebhard, F. & Nishimoto, S. Tomonaga-Luttinger parameters for doped Mott insulators. Europhys. Lett. 70, 492 (2005).
doi: 10.1209/epl/i2005-10020-8
Karrasch, C. & Moore, J. E. Luttinger liquid physics from the infinite-system density matrix renormalization group. Phys. Rev. B 86, 155156 (2012).
doi: 10.1103/PhysRevB.86.155156
Hohenadler, M., Assaad, F. F. & Fehske, H. Effect of electron-phonon interaction range for a half-filled band in one dimension. Phys. Rev. Lett. 109, 116407 (2012).
pubmed: 23005659
doi: 10.1103/PhysRevLett.109.116407
Ogata, M., Luchini, M. U., Sorella, S. & Assaad, F. F. Phase diagram of the one-dimensional t-j model. Phys. Rev. Lett. 66, 2388 (1991).
pubmed: 10043472
doi: 10.1103/PhysRevLett.66.2388
Ejima, S., Sykora, S., Becker, K. W. & Fehske, H. Phase separation in the Edwards model. Phys. Rev. B 86, 155149 (2012).
doi: 10.1103/PhysRevB.86.155149
Gotta, L., Mazza, L., Simon, P. & Roux, G. Two-fluid coexistence in a spinless fermions chain with pair hopping. Phys. Rev. Lett. 126, 206805 (2021).
pubmed: 34110210
doi: 10.1103/PhysRevLett.126.206805
Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022).
Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022).