Quantum dynamics and phase transitions in low-dimensional systems
Low-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-...
- Autores:
-
Higuera Quintero, Santiago
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2023
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/68998
- Acceso en línea:
- http://hdl.handle.net/1992/68998
- Palabra clave:
- Quantum phase transitions
Low-dimensional systems
Condensed matter physics
Quantum computing
Física
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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Quantum dynamics and phase transitions in low-dimensional systems |
| dc.title.alternative.none.fl_str_mv |
Dinámicas cuánticas y transiciones de fase en sistemas de baja dimensionalidad |
| title |
Quantum dynamics and phase transitions in low-dimensional systems |
| spellingShingle |
Quantum dynamics and phase transitions in low-dimensional systems Quantum phase transitions Low-dimensional systems Condensed matter physics Quantum computing Física |
| title_short |
Quantum dynamics and phase transitions in low-dimensional systems |
| title_full |
Quantum dynamics and phase transitions in low-dimensional systems |
| title_fullStr |
Quantum dynamics and phase transitions in low-dimensional systems |
| title_full_unstemmed |
Quantum dynamics and phase transitions in low-dimensional systems |
| title_sort |
Quantum dynamics and phase transitions in low-dimensional systems |
| dc.creator.fl_str_mv |
Higuera Quintero, Santiago |
| dc.contributor.advisor.none.fl_str_mv |
Rodríguez Dueñas, Ferney Javier |
| dc.contributor.author.none.fl_str_mv |
Higuera Quintero, Santiago |
| dc.contributor.jury.none.fl_str_mv |
Quiroga Puello, Luis |
| dc.contributor.researchgroup.es_CO.fl_str_mv |
Grupo de Fisica Teorica de la Materia Condensada |
| dc.subject.keyword.none.fl_str_mv |
Quantum phase transitions Low-dimensional systems Condensed matter physics Quantum computing |
| topic |
Quantum phase transitions Low-dimensional systems Condensed matter physics Quantum computing Física |
| dc.subject.themes.es_CO.fl_str_mv |
Física |
| description |
Low-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. |
| publishDate |
2023 |
| dc.date.accessioned.none.fl_str_mv |
2023-08-01T19:03:54Z |
| dc.date.available.none.fl_str_mv |
2023-08-01T19:03:54Z |
| dc.date.issued.none.fl_str_mv |
2023-06-06 |
| dc.type.es_CO.fl_str_mv |
Trabajo de grado - Pregrado |
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info:eu-repo/semantics/bachelorThesis |
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info:eu-repo/semantics/acceptedVersion |
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http://purl.org/coar/resource_type/c_7a1f |
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Text |
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http://purl.org/redcol/resource_type/TP |
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eng |
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Clarence 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. M Morifuji and C Hamaguchi. Wannier stark effect in transport. In Mesoscopic Physics and Electronics, pages 104-108. Springer, 1998. Paul N Butcher, Norman H March, and Mario P Tosi. Physics of low-dimensional semiconductor structures. Springer Science & Business Media, 2013. Michael R Geller. Quantum phenomena in low-dimensional systems. Technical report, 2001. Simon M Sze, Yiming Li, and Kwok K Ng. Physics of semiconductor devices. John wiley & sons, 2008. Klaus 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. Klaus 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. Yuan 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. Wei Lu and Charles M Lieber. Semiconductor nanowires. Journal of Physics D: Applied Physics, 39(21):R387, 2006. Daniel Loss and David P DiVincenzo. Quantum computation with quantum dots. Physical Review A, 57(1):120, 1998. Shivaji Lal Sondhi, SM Girvin, JP Carini, and Dan Shahar. Continuous quantum phase transitions. Reviews of modern physics, 69(1):315, 1997. Subir Sachdev. Quantum phase transitions. Physics world, 12(4):33, 1999. Matthias Vojta. Quantum phase transitions. Reports on Progress in Physics, 66(12):2069, 2003. Debasis Bera, Lei Qian, Teng-Kuan Tseng, and Paul H Holloway. Quantum dots and their multimodal applications: a review. Materials, 3(4):2260-2345, 2010. Kushal 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. Oleh 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. Gang 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. D. 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. Max Born and Vladimir Fock. Beweis des adiabatensatzes. Zeitschrift f¨ur Physik, 51(3-4):165-180, 1928. Izrail Solomonovich Gradshteyn and Iosif Moiseevich Ryzhik. Table of integrals, series, and products. Academic press, 2014. Junhong Goo, Younghoon Lim, and Yong-il Shin. Defect saturation in a rapidly quenched bose gas. Physical Review Letters, 127(11):115701, 2021. Martin 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. Ming 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. Jin-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. Bogdan 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. Bogdan 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. Morten 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. IBM-Corporation. Quantum computing IBM. https://quantum-computing.ibm.com, 2022. Accessed: 2022-07-27. Santiago 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. Florian Marquardt and Annett P¨uttmann. Introduction to dissipation and decoherence in quantum systems, 2008. Thierry Giamarchi. Quantum physics in one dimension, volume 121. Clarendon press, 2003. Johannes Voit. One-dimensional fermi liquids. Reports on Progress in Physics, 58(9):977, 1995. Hidetoshi Fukuyama, Robert A Bari, and Hans C Fogedby. Tightly bound electrons in a uniform electric field. Physical Review B, 8(12):5579, 1973. Timo Hartmann, F Keck, HJ Korsch, and S Mossmann. Dynamics of bloch oscillations. New Journal of Physics, 6(1):2, 2004. Fabio Franchini et al. An introduction to integrable techniques for one-dimensional quantum systems, volume 940. Springer, 2017. Markus Heyl. Dynamical quantum phase transitions: a review. Reports on Progress in Physics, 81(5):054001, 2018. M. 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. P Bosco and G Dattoli. Solution of the generalised raman-nath equation. Journal of Physics A: Mathematical and General, 16(18):4409, 1983. Bultrini, 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. |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rodríguez Dueñas, Ferney Javier7e9a57df-a656-423b-8e41-e4ebe93dcafd600Higuera Quintero, Santiagofd3a70d8-2357-4580-a88d-2506d6b012cd600Quiroga Puello, LuisGrupo de Fisica Teorica de la Materia Condensada2023-08-01T19:03:54Z2023-08-01T19:03:54Z2023-06-06http://hdl.handle.net/1992/68998instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/Low-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.Los 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.Facultad de Ciencias-UniAndes projects: INV-2021-128-2292, and INV-2019-84-1841European Commission FET-Open project AVaQus GA 899561FísicoPregrado59 páginasapplication/pdfengUniversidad de los AndesFísicaFacultad de CienciasDepartamento de FísicaQuantum dynamics and phase transitions in low-dimensional systemsDinámicas cuánticas y transiciones de fase en sistemas de baja dimensionalidadTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPQuantum phase transitionsLow-dimensional systemsCondensed matter physicsQuantum computingFísicaClarence 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.M Morifuji and C Hamaguchi. Wannier stark effect in transport. In Mesoscopic Physics and Electronics, pages 104-108. Springer, 1998.Paul N Butcher, Norman H March, and Mario P Tosi. Physics of low-dimensional semiconductor structures. Springer Science & Business Media, 2013.Michael R Geller. Quantum phenomena in low-dimensional systems. Technical report, 2001.Simon M Sze, Yiming Li, and Kwok K Ng. Physics of semiconductor devices. John wiley & sons, 2008.Klaus 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.Klaus 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.Yuan 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.Wei Lu and Charles M Lieber. Semiconductor nanowires. Journal of Physics D: Applied Physics, 39(21):R387, 2006.Daniel Loss and David P DiVincenzo. Quantum computation with quantum dots. Physical Review A, 57(1):120, 1998.Shivaji Lal Sondhi, SM Girvin, JP Carini, and Dan Shahar. Continuous quantum phase transitions. Reviews of modern physics, 69(1):315, 1997.Subir Sachdev. Quantum phase transitions. Physics world, 12(4):33, 1999.Matthias Vojta. Quantum phase transitions. Reports on Progress in Physics, 66(12):2069, 2003.Debasis Bera, Lei Qian, Teng-Kuan Tseng, and Paul H Holloway. Quantum dots and their multimodal applications: a review. Materials, 3(4):2260-2345, 2010.Kushal 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.Oleh 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.Gang 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.D. 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.Max Born and Vladimir Fock. Beweis des adiabatensatzes. Zeitschrift f¨ur Physik, 51(3-4):165-180, 1928.Izrail Solomonovich Gradshteyn and Iosif Moiseevich Ryzhik. Table of integrals, series, and products. Academic press, 2014.Junhong Goo, Younghoon Lim, and Yong-il Shin. Defect saturation in a rapidly quenched bose gas. Physical Review Letters, 127(11):115701, 2021.Martin 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.Ming 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.Jin-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.Bogdan 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.Bogdan 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.Morten 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.IBM-Corporation. Quantum computing IBM. https://quantum-computing.ibm.com, 2022. Accessed: 2022-07-27.Santiago 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.Florian Marquardt and Annett P¨uttmann. Introduction to dissipation and decoherence in quantum systems, 2008.Thierry Giamarchi. Quantum physics in one dimension, volume 121. Clarendon press, 2003.Johannes Voit. One-dimensional fermi liquids. Reports on Progress in Physics, 58(9):977, 1995.Hidetoshi Fukuyama, Robert A Bari, and Hans C Fogedby. Tightly bound electrons in a uniform electric field. Physical Review B, 8(12):5579, 1973.Timo Hartmann, F Keck, HJ Korsch, and S Mossmann. Dynamics of bloch oscillations. New Journal of Physics, 6(1):2, 2004.Fabio Franchini et al. An introduction to integrable techniques for one-dimensional quantum systems, volume 940. Springer, 2017.Markus Heyl. Dynamical quantum phase transitions: a review. Reports on Progress in Physics, 81(5):054001, 2018.M. 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.P Bosco and G Dattoli. Solution of the generalised raman-nath equation. Journal of Physics A: Mathematical and General, 16(18):4409, 1983.Bultrini, D. , Gordon, M. , L´opez, E. and Sierra, G. Simple mitigation strategy for a systematic gate error in ibmq. 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