Quantum dynamics and phase transitions in low-dimensional systems

dc.contributorRodríguez Dueñas, Ferney Javier
dc.contributorQuiroga Puello, Luis
dc.contributorGrupo de Fisica Teorica de la Materia Condensada
dc.creatorHiguera Quintero, Santiago
dc.date.accessioned2023-08-01T19:03:54Z
dc.date.accessioned2023-09-07T02:32:26Z
dc.date.available2023-08-01T19:03:54Z
dc.date.available2023-09-07T02:32:26Z
dc.date.created2023-08-01T19:03:54Z
dc.date.issued2023-06-06
dc.identifierhttp://hdl.handle.net/1992/68998
dc.identifierinstname:Universidad de los Andes
dc.identifierreponame:Repositorio Institucional Séneca
dc.identifierrepourl:https://repositorio.uniandes.edu.co/
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8729451
dc.description.abstractLow-dimensional systems have attracted a main interest in current condensed matter physics due to novel quantum phenomena arising from their characteristic confinement. In this work we will review the quantum dynamics of two reduced dimensional systems: a zero-dimensional quantum dot under a Landau-Zener (LZ) Hamiltonian and the Wannier-Stark (WS) model of a one-dimensional chain. The purpose of this work will be to probe equilibrium quantum phase transitions through non-equilibrium dynamical processes. For the first system, the connection between the LZ dynamics and Kibble-Zurek mechanism (KZM) for continuous phase transitions is presented. In addition, experimental quantum simulations on digital quantum computers are shown that validate the link. Then, the equilibrium quantum phases of the WS model are characterized and a study of the Loschmidt echo is presented through numerical simulations of sudden quenches.
dc.description.abstractLos sistemas de baja dimensionalidad han atraído un interés central en la física actual de la materia condensada debido a novedosos fenómenos cuánticos que surgen de su confinamiento característico. En este trabajo revisaremos la dinámica cuántica de dos sistemas de dimensionalidad reducida: un punto cuántico de dimensión cero bajo un Hamiltoniano de Landau-Zener (LZ) y el modelo de Wannier-Stark (WS) de una cadena unidimensional. El propósito de este trabajo será sondear las transiciones de fase cuánticas en equilibrio a través de procesos dinámicos de no equilibrio. Para el primer sistema, se presenta la conexión entre la dinámica de LZ y el mecanismo de Kibble-Zurek (KZM) para transiciones de fase continuas. Además, se muestran simulaciones cuánticas experimentales en computadoras cuánticas digitales que validan su relación. Luego, se caracterizan las fases cuánticas de equilibrio del modelo WS y se presenta un estudio del eco de Loschmidt a través de simulaciones numéricas de quenches repentinos.
dc.languageeng
dc.publisherUniversidad de los Andes
dc.publisherFísica
dc.publisherFacultad de Ciencias
dc.publisherDepartamento de Física
dc.relationClarence Zener and Ralph Howard Fowler. Non-adiabatic crossing of energy levels. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 137(833):696-702, 1932.
dc.relationM Morifuji and C Hamaguchi. Wannier stark effect in transport. In Mesoscopic Physics and Electronics, pages 104-108. Springer, 1998.
dc.relationPaul N Butcher, Norman H March, and Mario P Tosi. Physics of low-dimensional semiconductor structures. Springer Science & Business Media, 2013.
dc.relationMichael R Geller. Quantum phenomena in low-dimensional systems. Technical report, 2001.
dc.relationSimon M Sze, Yiming Li, and Kwok K Ng. Physics of semiconductor devices. John wiley & sons, 2008.
dc.relationKlaus von Klitzing, Tapash Chakraborty, Philip Kim, Vidya Madhavan, Xi Dai, James McIver, Yoshinori Tokura, Lucile Savary, Daria Smirnova, Ana Maria Rey, et al. 40 years of the quantum hall effect. Nature Reviews Physics, 2(8):397-401, 2020.
dc.relationKlaus von Klitzing, Gerhard Dorda, and Michael Pepper. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Physical review letters, 45(6):494, 1980.
dc.relationYuan Cao, Valla Fatemi, Shiang Fang, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, and Pablo Jarillo-Herrero. Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556(7699):43-50, 2018.
dc.relationWei Lu and Charles M Lieber. Semiconductor nanowires. Journal of Physics D: Applied Physics, 39(21):R387, 2006.
dc.relationDaniel Loss and David P DiVincenzo. Quantum computation with quantum dots. Physical Review A, 57(1):120, 1998.
dc.relationShivaji Lal Sondhi, SM Girvin, JP Carini, and Dan Shahar. Continuous quantum phase transitions. Reviews of modern physics, 69(1):315, 1997.
dc.relationSubir Sachdev. Quantum phase transitions. Physics world, 12(4):33, 1999.
dc.relationMatthias Vojta. Quantum phase transitions. Reports on Progress in Physics, 66(12):2069, 2003.
dc.relationDebasis Bera, Lei Qian, Teng-Kuan Tseng, and Paul H Holloway. Quantum dots and their multimodal applications: a review. Materials, 3(4):2260-2345, 2010.
dc.relationKushal Yadav, Prashant Kumar, Dharmasanam Ravi Teja, Sudipto Chakraborty, Monojit Chakraborty, Soumya Sanjeeb Mohapatra, Abanti Sahoo, Mitch MC Chou, Chi-Te Liang, and Da-Ren Hang. A review on low-dimensional nanomaterials: Nanofabrication, characterization and applications. Nanomaterials, 13(1):160, 2022.
dc.relationOleh V. Ivakhnenko, Sergey N. Shevchenko, and Franco Nori. Nonadiabatic landau zenerst¨uckelberg majorana transitions, dynamics, and interference. Physics Reports, 995:1-89, 2023. Nonadiabatic Landau-Zener-St¨uckelberg-Majorana transitions, dynamics, and interference.
dc.relationGang Cao, Hai-Ou Li, Tao Tu, Li Wang, Cheng Zhou, Ming Xiao, Guang-Can Guo, Hong-Wen Jiang, and Guo-Ping Guo. Ultrafast universal quantum control of a quantum-dot charge qubit using landauzenerst¨uckelberg interference. Nature Communications, 4(1):1401, 2013.
dc.relationD. V. Khomitsky and S. A. Studenikin. Single-spin landau-zener-st¨uckelberg-majorana interferometry of zeeman-split states with strong spin-orbit interaction in a double quantum dot. Phys. Rev. B, 106:195414, Nov 2022.
dc.relationMax Born and Vladimir Fock. Beweis des adiabatensatzes. Zeitschrift f¨ur Physik, 51(3-4):165-180, 1928.
dc.relationIzrail Solomonovich Gradshteyn and Iosif Moiseevich Ryzhik. Table of integrals, series, and products. Academic press, 2014.
dc.relationJunhong Goo, Younghoon Lim, and Yong-il Shin. Defect saturation in a rapidly quenched bose gas. Physical Review Letters, 127(11):115701, 2021.
dc.relationMartin Anquez, BA Robbins, HM Bharath, M Boguslawski, TM Hoang, and MS Chapman. Quantum kibble-zurek mechanism in a spin-1 bose-einstein condensate. Physical review letters, 116(15):155301, 2016.
dc.relationMing Gong, Xueda Wen, Guozhu Sun, Dan-Wei Zhang, Dong Lan, Yu Zhou, Yunyi Fan, Yuhao Liu, Xinsheng Tan, Haifeng Yu, Yang Yu, Shi-Liang Zhu, Siyuan Han, and Peiheng Wu. Simulating the Kibble-Zurek mechanism of the ising model with a superconducting qubit system. Scientific Reports, 6:22667, 2016.
dc.relationJin-Ming Cui, Yun-Feng Huang, Zhao Wang, Dong-Yang Cao, Jian Wang, Wei-Min Lv, Le Luo, Adolfo del Campo, Yong-Jian Han, Chuan-Feng Li, and Guang-Can Guo. Experimental trapped-ion quantum simulation of the Kibble-Zurek dynamics in momentum space. Scientific Reports, 6(1), sep 2016.
dc.relationBogdan Damski. The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective. Phys. Rev. Lett., 95:035701, Jul 2005.
dc.relationBogdan Damski and Wojciech H. Zurek. Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again. Phys. Rev. A, 73:063405, Jun 2006.
dc.relationMorten Kjaergaard, Mollie E Schwartz, Jochen Braum¨uller, Philip Krantz, Joel I-J Wang, Simon Gustavsson, and William D Oliver. Superconducting qubits: Current state of play. Annual Review of Condensed Matter Physics, 11:369-395, 2020.
dc.relationIBM-Corporation. Quantum computing IBM. https://quantum-computing.ibm.com, 2022. Accessed: 2022-07-27.
dc.relationSantiago Higuera-Quintero, Ferney J. Rodríguez, Luis Quiroga, and Fernando J. Gómez-Ruiz. Experimental validation of the kibble-zurek mechanism on a digital quantum computer. Frontiers in Quantum Science and Technology, 1, 2022.
dc.relationFlorian Marquardt and Annett P¨uttmann. Introduction to dissipation and decoherence in quantum systems, 2008.
dc.relationThierry Giamarchi. Quantum physics in one dimension, volume 121. Clarendon press, 2003.
dc.relationJohannes Voit. One-dimensional fermi liquids. Reports on Progress in Physics, 58(9):977, 1995.
dc.relationHidetoshi Fukuyama, Robert A Bari, and Hans C Fogedby. Tightly bound electrons in a uniform electric field. Physical Review B, 8(12):5579, 1973.
dc.relationTimo Hartmann, F Keck, HJ Korsch, and S Mossmann. Dynamics of bloch oscillations. New Journal of Physics, 6(1):2, 2004.
dc.relationFabio Franchini et al. An introduction to integrable techniques for one-dimensional quantum systems, volume 940. Springer, 2017.
dc.relationMarkus Heyl. Dynamical quantum phase transitions: a review. Reports on Progress in Physics, 81(5):054001, 2018.
dc.relationM. Faridfar, A. Ahmadi Fouladi, and J. Vahedi. Dynamical quantum phase transitions in stark quantum spin chains. Physica A: Statistical Mechanics and its Applications, 619:128732, 2023.
dc.relationP Bosco and G Dattoli. Solution of the generalised raman-nath equation. Journal of Physics A: Mathematical and General, 16(18):4409, 1983.
dc.relationBultrini, D. , Gordon, M. , L´opez, E. and Sierra, G. Simple mitigation strategy for a systematic gate error in ibmq. Journal of Applied Mathematics and Physics, 9, 2021.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightshttp://purl.org/coar/access_right/c_abf2
dc.titleQuantum dynamics and phase transitions in low-dimensional systems
dc.typeTrabajo de grado - Pregrado


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