Dynamical mean-field theory studies on real materials

Numerical studies on strongly correlated fermionic systems are very complicated and still provide essential problems. The main reason is the exponential growth of the un- derlying Hilbert state space with the system size and the fermionic sign problem for Monte Carlo studies. Among the most widely employed numerical techniques for study- ing two-dimensional quantum many-body systems are cluster extensions of the dynamical mean-field theory (DMFT), e.g. dynamical cluster approximation (DCA). They map an infinitely large multi-dimensional lattice problem to a one-dimensional impurity problem. In 2015 it was shown that the density matrix renormalisation group (DMRG) used as an impurity solver for DMFT (DMFT+DMRG) on the imaginary-frequency axis allows to solve multi-site and multi-band problems extremely fast compared to other solvers. Within this thesis, we further develop this DMRG+DMFT approach to apply the method on real material settings. The step from artificial, completely degenerate multi-band mod- els with simple dispersion relations on a Bethe lattice, studied in 2015, to systems with realistic band structures and lifted degeneracies involves more challenges than originally suspected. In this thesis, we will first recapitulate relevant methods for our approach like matrix prod- uct states, the density matrix renormalisation group and several time evolution methods. In this context we will present several improvements ranging from optimised time evo- lutions to entanglement based optimisations of tensor networks. Second, we will present a very detailed description of the dynamical mean field theory. We will focus on both methodological aspects and implementation details. This chapter is intended to allow other researcher to implement their own DMFT code using DMRG as an impurity solver. Third, we will discuss three different models to show the extent of problems DMRG+ DMFT is able to solve. We will focus on multi-site DCA calculations in the case of the two-dimensional Hubbard model and show that DMRG allows to tackle systems with intermediate interaction strengths at low temperatures, which are unsolvable with other solvers. In the second case, the real material Sr2VO4, we will show the first two-site DCA results for a realistic three-band model. In contrast to assumptions, partly reintroducing the momentum dependence of the self-energy does not improve agreement between exper- imental observations and theoretical results. Finally, we will move on to another realistic three-band model, which describes Sr2RuO4, to show how to deal with the influence of spin-orbit coupling on DMFT. We will present the first low-temperature results for this material and will confirm previous results of simplified model calculations.Numerische Untersuchungen stark korrelierter fermionischer Systeme sind schwierig und beinhalten noch heute essentielle Probleme. Die Hauptgründe dafür sind das exponen- tielle Wachstum des Hilbertraumes der Quantenzustände mit der Systemgröße und das fermionische Vorzeichenproblem bei Monte-Carlo-Rechnungen. Eine der am häufigsten verwendeten Methoden zur Untersuchung zweidimensionaler Gittersysteme sind Cluster- Erweiterungen der dynamische Molekularfeld Theory (DMFT), wie zum Beispiel die dy- namische Cluster Approximation (DCA). Diese Methoden bilden mehrdimensionale Git- tersysteme auf eindimensionale Störstellen-Probleme ab. 2015 wurde gezeigt, dass DMFT auf der imaginären Frequenzachse kombiniert mit der Dichtematrix-Renormierungsgruppe (DMFT+DMRG) Mehrband- und Multisite-Systeme schneller lösen kann, als wenn an- dere Störstellen-Löser verwendet werden. In dieser Arbeit entwickeln wir diesen Ansatz weiter und wenden ihn auf Modelle realer Materialen an. Am Anfang dieser Arbeit besprechen wir relevante Methoden für DMRG+ DMFT, wie zum Beispiel Matrix-Produkt-Zustände, die Dichtematrix-Renormierungs- gruppe und mehrere Zeitentwicklungs-Methoden. In diesem Zusammenhang werden wir auch mehrere Verbesserungen besprechen, die von methodischen Anpassungen von Zeit- entwicklungen bis hin zur Neuordnung des Tensornetzwerkes basierend auf Verschrän- kungs-Eigenschaften reichen. Danach werden wir uns detailliert mit den methodologischen und programmiertechnischen Aspekten von DMFT beschäftigen. Dieses Kapitel dient als Grundlage für andere Forscher, die eigene DMRG+DMFT-Codes programmieren wollen. Abschließend werden wir drei verschiedene Modelle besprechen, um das Ausmaß der Sys- teme zu zeigen, die mit diesem Ansatz gelöst werden können. Wir werden uns im Kon- text des Hubbard-Modells detailliert mit Multisite-DCA beschäftigen und zeigen, dass DMRG+DMFT Ergebnisse für Systeme mit mittleren Wechselwirkungsstärken bei niedri- gen Temperaturen erzeugen kann. Das ist mit anderen Störstellen-Lösern bisher nicht möglich. Im zweiten Fall beschäftigen wir uns mit Strontiumvanadat Sr2VO4 und werden die ersten Zweisite-DCA-Ergebnisse für ein realistisches Dreiband-Modell präsentieren. Im Gegensatz zu bisherigen Erwartungen führt die teilweise Wiedereinführung der Im- pulsabhängigkeit der Selbstenergie nicht zu einer besseren Übereinstimmung von Theorie und Experiment. Das dritte Modell beschreibt Strontiumruthenat Sr2RuO4. In diesem Fall besprechen wir den Einfluss der Spin-Bahn-Kopplung auf DMFT und wie die damit verbundenen Probleme optimal gelöst werden können. Abschließend zeigen wir die ersten Ergebnisse für dieses Modell bei niedrigen Temperaturen

Dynamical mean-field theory studies on real materials

Numerical studies on strongly correlated fermionic systems are very complicated and still provide essential problems. The main reason is the exponential growth of the un- derlying Hilbert state space with the system size and the fermionic sign problem for Monte Carlo studies. Among the most widely employed numerical techniques for study- ing two-dimensional quantum many-body systems are cluster extensions of the dynamical mean-field theory (DMFT), e.g. dynamical cluster approximation (DCA). They map an infinitely large multi-dimensional lattice problem to a one-dimensional impurity problem. In 2015 it was shown that the density matrix renormalisation group (DMRG) used as an impurity solver for DMFT (DMFT+DMRG) on the imaginary-frequency axis allows to solve multi-site and multi-band problems extremely fast compared to other solvers. Within this thesis, we further develop this DMRG+DMFT approach to apply the method on real material settings. The step from artificial, completely degenerate multi-band mod- els with simple dispersion relations on a Bethe lattice, studied in 2015, to systems with realistic band structures and lifted degeneracies involves more challenges than originally suspected. In this thesis, we will first recapitulate relevant methods for our approach like matrix prod- uct states, the density matrix renormalisation group and several time evolution methods. In this context we will present several improvements ranging from optimised time evo- lutions to entanglement based optimisations of tensor networks. Second, we will present a very detailed description of the dynamical mean field theory. We will focus on both methodological aspects and implementation details. This chapter is intended to allow other researcher to implement their own DMFT code using DMRG as an impurity solver. Third, we will discuss three different models to show the extent of problems DMRG+ DMFT is able to solve. We will focus on multi-site DCA calculations in the case of the two-dimensional Hubbard model and show that DMRG allows to tackle systems with intermediate interaction strengths at low temperatures, which are unsolvable with other solvers. In the second case, the real material Sr2VO4, we will show the first two-site DCA results for a realistic three-band model. In contrast to assumptions, partly reintroducing the momentum dependence of the self-energy does not improve agreement between exper- imental observations and theoretical results. Finally, we will move on to another realistic three-band model, which describes Sr2RuO4, to show how to deal with the influence of spin-orbit coupling on DMFT. We will present the first low-temperature results for this material and will confirm previous results of simplified model calculations.Numerische Untersuchungen stark korrelierter fermionischer Systeme sind schwierig und beinhalten noch heute essentielle Probleme. Die Hauptgründe dafür sind das exponen- tielle Wachstum des Hilbertraumes der Quantenzustände mit der Systemgröße und das fermionische Vorzeichenproblem bei Monte-Carlo-Rechnungen. Eine der am häufigsten verwendeten Methoden zur Untersuchung zweidimensionaler Gittersysteme sind Cluster- Erweiterungen der dynamische Molekularfeld Theory (DMFT), wie zum Beispiel die dy- namische Cluster Approximation (DCA). Diese Methoden bilden mehrdimensionale Git- tersysteme auf eindimensionale Störstellen-Probleme ab. 2015 wurde gezeigt, dass DMFT auf der imaginären Frequenzachse kombiniert mit der Dichtematrix-Renormierungsgruppe (DMFT+DMRG) Mehrband- und Multisite-Systeme schneller lösen kann, als wenn an- dere Störstellen-Löser verwendet werden. In dieser Arbeit entwickeln wir diesen Ansatz weiter und wenden ihn auf Modelle realer Materialen an. Am Anfang dieser Arbeit besprechen wir relevante Methoden für DMRG+ DMFT, wie zum Beispiel Matrix-Produkt-Zustände, die Dichtematrix-Renormierungs- gruppe und mehrere Zeitentwicklungs-Methoden. In diesem Zusammenhang werden wir auch mehrere Verbesserungen besprechen, die von methodischen Anpassungen von Zeit- entwicklungen bis hin zur Neuordnung des Tensornetzwerkes basierend auf Verschrän- kungs-Eigenschaften reichen. Danach werden wir uns detailliert mit den methodologischen und programmiertechnischen Aspekten von DMFT beschäftigen. Dieses Kapitel dient als Grundlage für andere Forscher, die eigene DMRG+DMFT-Codes programmieren wollen. Abschließend werden wir drei verschiedene Modelle besprechen, um das Ausmaß der Sys- teme zu zeigen, die mit diesem Ansatz gelöst werden können. Wir werden uns im Kon- text des Hubbard-Modells detailliert mit Multisite-DCA beschäftigen und zeigen, dass DMRG+DMFT Ergebnisse für Systeme mit mittleren Wechselwirkungsstärken bei niedri- gen Temperaturen erzeugen kann. Das ist mit anderen Störstellen-Lösern bisher nicht möglich. Im zweiten Fall beschäftigen wir uns mit Strontiumvanadat Sr2VO4 und werden die ersten Zweisite-DCA-Ergebnisse für ein realistisches Dreiband-Modell präsentieren. Im Gegensatz zu bisherigen Erwartungen führt die teilweise Wiedereinführung der Im- pulsabhängigkeit der Selbstenergie nicht zu einer besseren Übereinstimmung von Theorie und Experiment. Das dritte Modell beschreibt Strontiumruthenat Sr2RuO4. In diesem Fall besprechen wir den Einfluss der Spin-Bahn-Kopplung auf DMFT und wie die damit verbundenen Probleme optimal gelöst werden können. Abschließend zeigen wir die ersten Ergebnisse für dieses Modell bei niedrigen Temperaturen

Anatomy of quantum critical wave functions in dissipative impurity problems

Quantum phase transitions reflect singular changes taking place in a many-body ground state, however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. New physical insights into the sub-Ohmic spin-boson model are provided by the coherent state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking, while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix product states (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.Comment: 11 pages, 8 figures. The paper was expanded in V

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

Peer reviewe

Measurement of the W gamma Production Cross Section in Proton-Proton Collisions at root s=13 TeV and Constraints on Effective Field Theory Coefficients

A fiducial cross section for W gamma production in proton-proton collisions is measured at a center-of-mass energy of 13 TeV in 137 fb(-1) of data collected using the CMS detector at the LHC. The W -> e nu and mu nu decay modes are used in a maximum-likelihood fit to the lepton-photon invariant mass distribution to extract the combined cross section. The measured cross section is compared with theoretical expectations at next-to-leading order in quantum chromodynamics. In addition, 95% confidence level intervals are reported for anomalous triple-gauge couplings within the framework of effective field theory.Peer reviewe

Performance of the CMS muon trigger system in proton-proton collisions at √s = 13 TeV

The muon trigger system of the CMS experiment uses a combination of hardware and software to identify events containing a muon. During Run 2 (covering 2015-2018) the LHC achieved instantaneous luminosities as high as 2 × 10 cm s while delivering proton-proton collisions at √s = 13 TeV. The challenge for the trigger system of the CMS experiment is to reduce the registered event rate from about 40 MHz to about 1 kHz. Significant improvements important for the success of the CMS physics program have been made to the muon trigger system via improved muon reconstruction and identification algorithms since the end of Run 1 and throughout the Run 2 data-taking period. The new algorithms maintain the acceptance of the muon triggers at the same or even lower rate throughout the data-taking period despite the increasing number of additional proton-proton interactions in each LHC bunch crossing. In this paper, the algorithms used in 2015 and 2016 and their improvements throughout 2017 and 2018 are described. Measurements of the CMS muon trigger performance for this data-taking period are presented, including efficiencies, transverse momentum resolution, trigger rates, and the purity of the selected muon sample. This paper focuses on the single- and double-muon triggers with the lowest sustainable transverse momentum thresholds used by CMS. The efficiency is measured in a transverse momentum range from 8 to several hundred GeV

Search for long-lived particles decaying to jets with displaced vertices in proton-proton collisions at root s=13 Te V

A search is presented for long-lived particles produced in pairs in proton-proton collisions at the LHC operating at a center-of-mass energy of 13 TeV. The data were collected with the CMS detector during the period from 2015 through 2018, and correspond to a total integrated luminosity of 140 fb(-1). This search targets pairs of long-lived particles with mean proper decay lengths between 0.1 and 100 mm, each of which decays into at least two quarks that hadronize to jets, resulting in a final state with two displaced vertices. No significant excess of events with two displaced vertices is observed. In the context of R-parity violating supersymmetry models, the pair production of long-lived neutralinos, gluinos, and top squarks is excluded at 95% confidence level for cross sections larger than 0.08 fb, masses between 800 and 3000 GeV, and mean proper decay lengths between 1 and 25 mm.Peer reviewe