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Tensor network simulations of open quantum systems
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dc.contributor.advisor | Keeling, Jonathan Mark James | |
dc.contributor.author | Kilda, Dainius | |
dc.coverage.spatial | xi, 211 p. | en_US |
dc.date.accessioned | 2020-03-03T10:26:50Z | |
dc.date.available | 2020-03-03T10:26:50Z | |
dc.date.issued | 2020-06-22 | |
dc.identifier.uri | https://hdl.handle.net/10023/19584 | |
dc.description.abstract | The nonequilibrium effects of dissipation and drive play a key role in an immense variety of nanoscale and mesoscale quantum systems. To understand the behaviour of open quantum systems, we need accurate methods that capture the influence of the environment on the system, while managing the exponentially large Hilbert space required to describe the system. Tensor network algorithms offer an efficient way to approach this challenge. In this thesis, we develop and apply tensor network techniques to study the dynamics and steady states of various open quantum systems. The first part of the thesis focuses on the driven dissipative many body physics in coupled cavity arrays described by Born-Markov master equations. We extend transfer matrix product operator methods to Liouvillian dynamics, and utilize them to compute dynamical correlation functions and fluorescence spectrum of an infinite coupled cavity array in 1D. We also investigate thermalization, and observe the emergence of a quasi-thermal steady state with a negative effective temperature. In another study, we use infinite projected entangled pair state (iPEPS) methods to compute steady states of coupled cavity lattices in 2D. We find that a straightforward adaptation of iPEPS to Liouvillian dynamics is unstable, contradicting a recent publication in the field. The second part investigates more general systems involving strong couplings and structured environments that induce non-Markovian dynamics. We develop a powerful time-evolving matrix product operator (TEMPO) algorithm that builds on Feynman-Vernon influence functional formalism, and uses matrix product states (MPS) to represent the temporal non-Markovian correlations efficiently. We apply TEMPO to study the localization phase transition of the spin-boson model and the dynamics of two spatially separated two-level systems coupled to a common environment. Finally, we propose the Toblerone TEMPO algorithm, which extends TEMPO to many-body systems interacting with general bosonic environments. | en_US |
dc.description.sponsorship | "This work was supported by the EPSRC CM-CDT (grant EP/L015110/1). This work was supported by the University of St. Andrews (School of Physics and Astronomy)." -- Funding | en |
dc.language.iso | en | en_US |
dc.publisher | University of St Andrews | |
dc.relation | Data underpinning Dainius Kilda's thesis. Kilda, D., University of St Andrews. DOI: https://doi.org/10.17630/2ffcdde0-57f0-48b5-bc2c-817f03cb2756 | en |
dc.relation | Kilda, D., & Keeling, J. (2019). Fluorescence spectrum and thermalization in a driven coupled cavity array. Physical Review Letters, 122(4), [043602]. https://doi.org/10.1103/PhysRevLett.122.043602 [http://hdl.handle.net/10023/16901 : Open Access version] | en |
dc.relation | Strathearn, A., Kirton, P. G., Kilda, D., Keeling, J. M. J., & Lovett, B. W. (2018). Efficient non-Markovian quantum dynamics using time-evolving matrix product operators. Nature Communications, 9, [3322]. https://doi.org/10.1038/s41467-018-05617-3 | |
dc.relation.uri | https://doi.org/10.17630/2ffcdde0-57f0-48b5-bc2c-817f03cb2756 | |
dc.relation.uri | http://hdl.handle.net/10023/16901 | |
dc.relation.uri | https://doi.org/10.1038/s41467-018-05617-3 | |
dc.rights | Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Open quantum systems | en_US |
dc.subject | Non-Markovian quantum dynamics | en_US |
dc.subject | Circuit QED | en_US |
dc.subject | Tensor networks | en_US |
dc.subject.lcc | QC174.45K5 | |
dc.subject.lcsh | Quantum systems | en |
dc.subject.lcsh | Quantum theory | en |
dc.subject.lcsh | Quantum electrodynamics | en |
dc.title | Tensor network simulations of open quantum systems | en_US |
dc.type | Thesis | en_US |
dc.contributor.sponsor | Scottish Doctoral Training Centre in Condensed Matter Physics (CM-CDT) | en_US |
dc.contributor.sponsor | University of St Andrews. School of Physics and Astronomy | en |
dc.type.qualificationlevel | Doctoral | en_US |
dc.type.qualificationname | PhD Doctor of Philosophy | en_US |
dc.publisher.institution | The University of St Andrews | en_US |
dc.rights.embargodate | 2022-02-18 | |
dc.rights.embargoreason | Embargo period has ended, thesis made available in accordance with University regulations | en |
dc.identifier.doi | https://doi.org/10.17630/10023-19584 | |
dc.identifier.grantnumber | EP/L015110/1 | en_US |
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