Rammelmüller, Lukas (2020)
Exploring imbalanced Fermi gases with stochastic quantization.
Technische Universität Darmstadt
doi: 10.25534/tuprints-00011308
Dissertation, Erstveröffentlichung
Kurzbeschreibung (Abstract)
Strongly coupled quantum matter displays a rich phenomenology including phase transitions and often unexpected collective behavior. Remarkable advances in experiments with ultracold Fermi gases allow us to gain deep insight into these intriguing systems. Their theoretical description, however, is often challenging as exact analytic solutions are available only in a few special cases, and approximate techniques such as mean-field or perturbation theory are of limited use. Numerical treatment with Monte Carlo (MC) methods has led to profound success in this regard. Unfortunately, for many systems - and especially for asymmetric quantum gases - the infamous sign problem slows progress due to an exponentially scaling of the computational effort with inceasing system size. In this thesis, we set out to explore the rich physics of two-component Fermi gases in the presence of finite spin polarization and/or mass imbalance. To surmount an arising sign problem, we learn from methodological advances made in the field of quantum chromodynamics and further develop these lattice approaches in the context of nonrelativistic Fermi gases. An extensive overview of the numerical methods is presented, including several toy problems to detail the capabilities and shortcomings of the developed approaches. With these tools in hand, we perform extensive benchmarks of the hybrid Monte Carlo method with imaginary asymmetries (iHMC) and the complex Langevin (CL) method, which is based on a complex version of stochastic quantization. Both approaches are shown to yield excellent results for the ground-state energy equation of state of mass-imbalanced Fermi gases in one spatial dimension. Due to its great versatility, the CL method is subsequently employed to study pairing in one-dimensional Fermi gases, for which suitable two-body correlations are computed, revealing unexpected pairing patterns for spin- and mass-imbalanced systems. Another major system of interest in this thesis is the paradigmatic unitary Fermi gas which is investigated at finite temperature and spin polarization. A precise determination of the density equation of state in the normal phase enables us to explore a broad range of thermodynamic properties. We infer valuable information on the finite-temperature phase diagram, such as a flat phase boundary of the normal-to-superfluid transition near the balanced limit and indications for the absence of an extensive pseudogap phase above this transition. The presented results provide experimentally testable ab initio predictions for a range of previously inaccessible thermodynamic quantities.
Typ des Eintrags: | Dissertation | ||||
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Erschienen: | 2020 | ||||
Autor(en): | Rammelmüller, Lukas | ||||
Art des Eintrags: | Erstveröffentlichung | ||||
Titel: | Exploring imbalanced Fermi gases with stochastic quantization | ||||
Sprache: | Englisch | ||||
Referenten: | Braun, Prof. Dr. Jens ; Hammer, Prof. Dr. Hans-Werner | ||||
Publikationsjahr: | 2020 | ||||
Ort: | Darmstadt | ||||
Datum der mündlichen Prüfung: | 16 Dezember 2019 | ||||
DOI: | 10.25534/tuprints-00011308 | ||||
URL / URN: | https://tuprints.ulb.tu-darmstadt.de/11308 | ||||
Kurzbeschreibung (Abstract): | Strongly coupled quantum matter displays a rich phenomenology including phase transitions and often unexpected collective behavior. Remarkable advances in experiments with ultracold Fermi gases allow us to gain deep insight into these intriguing systems. Their theoretical description, however, is often challenging as exact analytic solutions are available only in a few special cases, and approximate techniques such as mean-field or perturbation theory are of limited use. Numerical treatment with Monte Carlo (MC) methods has led to profound success in this regard. Unfortunately, for many systems - and especially for asymmetric quantum gases - the infamous sign problem slows progress due to an exponentially scaling of the computational effort with inceasing system size. In this thesis, we set out to explore the rich physics of two-component Fermi gases in the presence of finite spin polarization and/or mass imbalance. To surmount an arising sign problem, we learn from methodological advances made in the field of quantum chromodynamics and further develop these lattice approaches in the context of nonrelativistic Fermi gases. An extensive overview of the numerical methods is presented, including several toy problems to detail the capabilities and shortcomings of the developed approaches. With these tools in hand, we perform extensive benchmarks of the hybrid Monte Carlo method with imaginary asymmetries (iHMC) and the complex Langevin (CL) method, which is based on a complex version of stochastic quantization. Both approaches are shown to yield excellent results for the ground-state energy equation of state of mass-imbalanced Fermi gases in one spatial dimension. Due to its great versatility, the CL method is subsequently employed to study pairing in one-dimensional Fermi gases, for which suitable two-body correlations are computed, revealing unexpected pairing patterns for spin- and mass-imbalanced systems. Another major system of interest in this thesis is the paradigmatic unitary Fermi gas which is investigated at finite temperature and spin polarization. A precise determination of the density equation of state in the normal phase enables us to explore a broad range of thermodynamic properties. We infer valuable information on the finite-temperature phase diagram, such as a flat phase boundary of the normal-to-superfluid transition near the balanced limit and indications for the absence of an extensive pseudogap phase above this transition. The presented results provide experimentally testable ab initio predictions for a range of previously inaccessible thermodynamic quantities. |
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URN: | urn:nbn:de:tuda-tuprints-113088 | ||||
Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik | ||||
Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Kernphysik 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik > Stark gekoppelte fermionische Systeme |
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Hinterlegungsdatum: | 02 Feb 2020 20:55 | ||||
Letzte Änderung: | 02 Feb 2020 20:55 | ||||
PPN: | |||||
Referenten: | Braun, Prof. Dr. Jens ; Hammer, Prof. Dr. Hans-Werner | ||||
Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 16 Dezember 2019 | ||||
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