Moreno Segura, Oscar A. (2023) Cálculo de brechas de energía en modelos unidimensionales para fermiones interactuantes / Charge and spin gaps in one-dimensional models for interacting fermions. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
El transporte cuantizado de carga es posible desde un enfoque topológico a partir de la modulación adiabática de los parámetros del sistema. Recientemente, experimentos que estudian este tipo de fenómenos por medio de gases fermiónicos interactuantes han encontrado dificultades para mantener la adiabaticidad del proceso por utilizar trayectorias en el espacio de parámetros que cruzan regiones sin brecha de energía. En este trabajo proponemos una forma de evitar esta situación estudiando la fase de aislante dimerizado espontáneamente (SDI) en el modelo de Hubbard iónico (IHM), el cual describe el sistema en esta región de interés. Para esto, calculamos las brechas de energía de carga y espín para el IHM incluyendo hopping dependiente de la densidad (debido a que favorece la fase SDI). El cierre de estas brechas de energía marcan puntos críticos en los sectores de carga y espín que, a su vez, definen la fase SDI, donde ambas brechas de energía permanecen abiertas. Por lo tanto, en este trabajo nos enfocamos principalmente en dicha legión y en sus transiciones de fase. Con el propósito de lograr lo anterior, desarrollamos un método para calcular la brecha de energía de carga considerando las simetrías de los estados que definen esta cantidad. Para ello, utilizamos sistemas de tamaños finitos en condiciones de contorno open shell y realizamos extrapolaciones al límite termodinámico. En el caso de la brecha de energía de espín hacemos extrapolaciones a partir de sistemas de tamaños finitos en condiciones de contorno abiertas. Para calcular el punto crítico que determina la transición de fase de aislante de Mott a la fase SDI, implementamos un procedimiento combinando el método de niveles excitados de energía utilizado con el método de Lanczos y el grupo de renormalización de la matriz densidad. Proponemos como punto óptimo de cruce para mantener el sistema en condiciones adiabáticas al relacionado con el cruce entre las brechas de energías de carga y espín dentro de la fase SDI. Por otra parte, encontramos que el efecto de considerar el hopping dependiente de la densidad no resulta suficientemente significativo para los casos de interés en el bombeo cuantizado de cargas. Los resultados de este trabajo llevaron a la publicación de un artículo científico, correspondiente a la referencia [1].
Resumen en inglés
The quantized charge transport is possible from a topological approach through the adiabatic modulation of system parameters. Recently, experiments studying such phenomena with interacting fermionic gases have encountered challenges in maintaining adiabaticity due to trajectories in parameter space that cross regions without an energy gap. In this work, we propose a way to avoid this situation by investigating the spontaneously dimerized insulator (SDI) phase in the ionic Hubbard model (IHM), which describes the system in this region of interest. To achieve this, we calculate the charge and spin energy gaps for the IHM, including density-dependent hopping (favoring the SDI phase). The closure of these energy gaps marks critical points in the charge and spin sectors, defining the SDI phase where both energy gaps remain open. Therefore, this work focuses primarily on this region and its phase transitions. With the aim of achieving the aforementioned goals, we developed a method to calculate the charge energy gap, considering the symmetries of the states that define this quantity. For this purpose, we employ finite-sized systems under open-shell boundary conditions and perform extrapolations to the thermodynamic limit. Regarding the spin energy gap, we conduct extrapolations based on finite-sized systems under open boundary conditions. To calculate the critical point determining the phase transition from the Mott insulator to the SDI phase, we implement a procedure that combines the method of crossing of excited energy levels used with the Lanczos method and the density matrix renormalization group. We propose the optimal crossing point to maintain the system under adiabatic conditions is related to the crossing between the charge and spin energy gaps within the SDI phase. On the other hand, we find that considering density-dependent hopping is not significantly impactful for the cases of interest in quantized charge pumping.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
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| Palabras Clave: | [Thouless pump; Bomba de Thouless; Cold atoms; Átomos fríos; Berry phase; Fase de Berry] |
| Referencias: | [1] Moreno Segura, O. A., Hallberg, K., Aligia, A. A. Charge and spin gaps in the ionic hubbard model with density-dependent hopping. Phys. Rev. B, 108, 195135, Nov 2023. URL https://link.aps.org/doi/10.1103/PhysRevB.108.195135. vii [2] Thouless, D. J. Quantization of particle transport. Phys. Rev. B, 27, 6083–6087, May 1983. URL https://link.aps.org/doi/10.1103/PhysRevB.27.6083. 1, 19 [3] Lohse, M., Schweizer, C., Zilberberg, O., Aidelsburger, M., Bloch, I. A thouless quantum pump with ultracold bosonic atoms in an optical superlattice. Nature Physics, 12 (4), 350–354, 2016. URL https://doi.org/10.1038/nphys3584. 1 [4] Nakajima, S., Tomita, T., Taie, S., Ichinose, T., Ozawa, H., Wang, L., et al. Topological thouless pumping of ultracold fermions. Nature Physics, 12 (4), 296–300, 2016. URL https://doi.org/10.1038/nphys3622. 1 [5] Walter, A.-S., Zhu, Z., Gachter, M., Minguzzi, J., Roschinski, S., Sandholzer, K., et al. Quantization and its breakdown in a hubbard–thouless pump. Nature Physics, 19 (10), 1471–1475, 2023. URL https://doi.org/10.1038/s41567-023-02145-w. [6] Viebahn, K., Walter, A.-S., Bertok, E., Zhu, Z., Gachter, M., Aligia, A. A., et al. Interaction-induced charge pumping in a topological many-body system. arXiv preprint arXiv:2308.03756, 2023. 1, 24, 25 [7] Rice, M. J., Mele, E. J. Elementary excitations of a linearly conjugated diatomic polymer. Phys. Rev. Lett., 49, 1455–1459, Nov 1982. URL https://link.aps.org/doi/10.1103/PhysRevLett.49.1455. 1, 19 [8] Bertok, E., Heidrich-Meisner, F., Aligia, A. A. Splitting of topological charge pumping in an interacting two-component fermionic rice-mele hubbard model. Phys. Rev. B, 106, 045141, Jul 2022. URL https://link.aps.org/doi/10.1103/PhysRevB.106.045141. 1, 23, 24 [9] Nagaosa, N., Takimoto, J. Theory of neutral-ionic transition in organic crystals. i. monte carlo simulation of modified hubbard model. Journal of the Physical Society of Japan, 55 (8), 2735–2744, 1986. URL https://doi.org/10.1143/JPSJ.55.2735. 2 [10] Hubbard, J., Torrance, J. B. Model of the neutral-ionic phase transformation. Phys. Rev. Lett., 47, 1750–1754, Dec 1981. URL https://link.aps.org/doi/10.1103/PhysRevLett.47.1750. 2 [11] Egami, T., Ishihara, S., Tachiki, M. Lattice effect of strong electron correlation: Implication for ferroelectricity and superconductivity. Science, 261 (5126), 1307–1310, 1993. URL https://www.science.org/doi/abs/10.1126/science.261.5126.1307. 2 [12] Fabrizio, M., Gogolin, A. O., Nersesyan, A. A. From band insulator to mott insulator in one dimension. Phys. Rev. Lett., 83, 2014–2017, Sep 1999. URL https://link.aps.org/doi/10.1103/PhysRevLett.83.2014. 2, 28 [13] Torio, M. E., Aligia, A. A., Ceccatto, H. A. Phase diagram of the hubbard chain with two atoms per cell. Phys. Rev. B, 64, 121105, Sep 2001. URL https://link.aps.org/doi/10.1103/PhysRevB.64.121105. 2, 22, 23, 27 [14] Manmana, S. R., Meden, V., Noack, R. M., Schonhammer, K. Quantum critical behavior of the one-dimensional ionic hubbard model. Phys. Rev. B, 70, 155115, Oct 2004. URL https://link.aps.org/doi/10.1103/PhysRevB.70.155115. 2, 24, 35 [15] Aligia, A. A. Charge dynamics in the mott insulating phase of the ionic hubbard model. Phys. Rev. B, 69, 041101, Jan 2004. URL https://link.aps.org/doi/10.1103/PhysRevB.69.041101. [16] Batista, C. D., Aligia, A. A. Exact bond ordered ground state for the transition between the band and the mott insulator. Phys. Rev. Lett., 92, 246405, Jun 2004. URL https://link.aps.org/doi/10.1103/PhysRevLett.92.246405. 15 [17] Aligia, A. A., Batista, C. D. Dimerized phase of ionic hubbard models. Phys. Rev. B, 71, 125110, Mar 2005. URL https://link.aps.org/doi/10.1103/PhysRevB.71.125110. 15 [18] Tincani, L., Noack, R. M., Baeriswyl, D. Critical properties of the band-insulatorto-mott-insulator transition in the strong-coupling limit of the ionic hubbard model. Phys. Rev. B, 79, 165109, Apr 2009. URL https://link.aps.org/doi/10.1103/PhysRevB.79.165109. [19] Hosseinzadeh, A., Jafari, S. A. Quantum integrability of 1d ionic hubbard model. Annalen der Physik, 532 (3), 1900601, 2020. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.201900601. [20] Hosseinzadeh, A., Jafari, S. Generalization of lieb–wu wave function inspired by one-dimensional ionic hubbard model. Annals of Physics, 414, 168075, 2020. URL https://www.sciencedirect.com/science/article/pii/S0003491620300087. 2 [21] Nomura, K., Okamoto, K. Critical properties of s= 1/2 antiferromagnetic xxz chain with next-nearest-neighbour interactions. Journal of Physics A: Mathematical and General, 27 (17), 5773, sep 1994. URL https://dx.doi.org/10.1088/0305-4470/27/17/012. 2, 27, 35 [22] Nakamura, M., Nomura, K., Kitazawa, A. Renormalization group analysis of the spin-gap phase in the one-dimensional t - J model. Phys. Rev. Lett., 79, 3214–3217, Oct 1997. URL https://link.aps.org/doi/10.1103/PhysRevLett.79.3214. [23] Somma, R. D., Aligia, A. A. Phase diagram of the xxz chain with next-nearestneighbor interactions. Phys. Rev. B, 64, 024410, Jun 2001. URL https://link.aps.org/doi/10.1103/PhysRevB.64.024410. [24] Nakamura, M. Tricritical behavior in the extended hubbard chains. Phys. Rev. B, 61, 16377–16392, Jun 2000. URL https://link.aps.org/doi/10.1103/PhysRevB.61.16377. [25] Nakamura, M. Mechanism of cdw-sdw transition in one dimension. Journal of the Physical Society of Japan, 68 (10), 3123–3126, 1999. URL https://doi.org/10.1143/JPSJ.68.3123. 2 [26] Roura-Bas, P., Aligia, A. A. Phase diagram of the ionic hubbard model with density-dependent hopping. Phys. Rev. B, 108, 115132, Sep 2023. URL https: //link.aps.org/doi/10.1103/PhysRevB.108.115132. 2, 16, 24, 27, 28, 29, 30,38 [27] Aligia, A. A., Hallberg, K., Batista, C. D., Ortiz, G. Phase diagrams from topological transitions: The hubbard chain with correlated hopping. Phys. Rev. B, 61, 7883–7886, Mar 2000. URL https://link.aps.org/doi/10.1103/PhysRevB. 61.7883. 2 [28] Peschel, I., Kaulke, M., Wang, X., Hallberg, K. Density-Matrix Renormalization - A New Numerical Method in Physics. Springer Berlin, Heidelberg, 1999. URL https://doi.org/10.1007/BFb0106062. 5 [29] Hallberg, K. A. New trends in density matrix renormalization. Advances in Physics, 55 (5-6), 477–526, 2006. URL https://doi.org/10.1080/00018730600766432. [30] Schollwock, U. The density-matrix renormalization group. Rev. Mod. Phys., 77, 259–315, Apr 2005. URL https://link.aps.org/doi/10.1103/RevModPhys.77.259. 5 [31] Schollwock, U. The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 326 (1), 96–192, 2011. URL https://www.sciencedirect.com/science/article/pii/S0003491610001752, january 2011 Special Issue. 5, 6, 7 [32] Dalmonte, M., Montangero, S. Lattice gauge theory simulations in the quantum information era. Contemporary Physics, 57 (3), 388–412, 2016. URL https://doi.org/10.1080/00107514.2016.1151199. 5, 6 [33] Fishman, M., White, S. R., Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases, pag. 4, 2022. URL https://scipost.org/10.21468/SciPostPhysCodeb.4. 14 [34] Torio, M. E., Aligia, A. A., Japaridze, G. I., Normand, B. Quantum phase diagram of the generalized ionic hubbard model for abn chains. Phys. Rev. B, 73, 115109, Mar 2006. URL https://link.aps.org/doi/10.1103/PhysRevB.73.115109. 15 [35] Stenzel, L., Hayward, A. L. C., Hubig, C., Schollwock, U., Heidrich-Meisner, F. Quantum phases and topological properties of interacting fermions in onedimensional superlattices. Phys. Rev. A, 99, 053614, May 2019. URL https://link.aps.org/doi/10.1103/PhysRevA.99.053614. 15 [36] Ma, R., Tai, M. E., Preiss, P. M., Bakr, W. S., Simon, J., Greiner, M. Photonassisted tunneling in a biased strongly correlated bose gas. Phys. Rev. Lett., 107, 095301, Aug 2011. URL https://link.aps.org/doi/10.1103/PhysRevLett.107.095301. 16 [37] Meinert, F., Mark, M. J., Lauber, K., Daley, A. J., Nagerl, H.-C. Floquet engineering of correlated tunneling in the bose-hubbard model with ultracold atoms. Phys. Rev. Lett., 116, 205301, May 2016. URL https://link.aps.org/doi/10.1103/PhysRevLett.116.205301. [38] Gorg, F., Messer, M., Sandholzer, K., Jotzu, G., Desbuquois, R., Esslinger, T. Enhancement and sign change of magnetic correlations in a driven quantum manybody system. Nature, 553 (7689), 481–485, 2018. URL https://doi.org/10.1038/nature25135. [39] Messer, M., Sandholzer, K., Gorg, F., Minguzzi, J., Desbuquois, R., Esslinger, T. Floquet dynamics in driven fermi-hubbard systems. Phys. Rev. Lett., 121, 233603, Dec 2018. URL https://link.aps.org/doi/10.1103/PhysRevLett. 121.233603. [40] Gorg, F., Sandholzer, K., Minguzzi, J., Desbuquois, R., Messer, M., Esslinger, T. Realization of density-dependent peierls phases to engineer quantized gauge fields coupled to ultracold matter. Nature Physics, 15 (11), 1161–1167, 2019. URL https://doi.org/10.1038/s41567-019-0615-4. 16 [41] Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 392 (1802), 45–57, 1984. URL https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1984.0023. 17 [42] Bernevig, B. A. Topological insulators and topological superconductors. Princeton University Press, 2013. 17 [43] Vanderbilt, D. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators. Cambridge University Press, 2018. 18, 19 [44] Xiao, D., Chang, M.-C., Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys., 82, 1959–2007, Jul 2010. URL https://link.aps.org/doi/10.1103/RevModPhys.82.1959. [45] Resta, R. Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Rev. Mod. Phys., 66, 899–915, Jul 1994. URL https://link.aps.org/doi/10.1103/RevModPhys.66.899. [46] Ortiz, G., Martin, R. M. Macroscopic polarization as a geometric quantum phase: Many-body formulation. Phys. Rev. B, 49, 14202–14210, May 1994. URL https://link.aps.org/doi/10.1103/PhysRevB.49.14202. [47] Resta, R., Sorella, S. Many-body effects on polarization and dynamical charges in a partly covalent polar insulator. Phys. Rev. Lett., 74, 4738–4741, Jun 1995. URL https://link.aps.org/doi/10.1103/PhysRevLett.74.4738. [48] Ortiz, G., Ordejon, P., Martin, R. M., Chiappe, G. Quantum phase transitions involving a change in polarization. Phys. Rev. B, 54, 13515–13528, Nov 1996. URL https://link.aps.org/doi/10.1103/PhysRevB.54.13515. [49] Song, X.-Y., He, Y.-C., Vishwanath, A., Wang, C. Electric polarization as a nonquantized topological response and boundary luttinger theorem. Phys. Rev. Res., 3, 023011, Apr 2021. URL https://link.aps.org/doi/10.1103/ PhysRevResearch.3.023011. 19 [50] Asboth, J. K., Oroszlany, L., Palyi, A. A short course on topological insulators. Lecture notes in physics, 919, 166, 2016. 21 [51] Aligia, A. A. Berry phases in superconducting transitions. Europhysics Letters, 45 (4), 411, feb 1999. URL https://dx.doi.org/10.1209/epl/i1999-00181-4. 22 [52] Aligia, A. A. Topological invariants based on generalized position operators and application to the interacting rice-mele model. Phys. Rev. B, 107, 075153, Feb 2023. URL https://link.aps.org/doi/10.1103/PhysRevB.107.075153. 22, 23 |
| Materias: | Física > Materia condensada |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Materia condensada > Teoría de sólidos |
| Código ID: | 1244 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 12 Sep 2024 14:58 |
| Última Modificación: | 12 Sep 2024 14:58 |
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