Higgs-free confinement hierarchy in five colour QCD

I consider the monopole condensate of five color QCD. The naive lowest energy state is unobtainable at one-loop for five or more colors due to simple geometric considerations. The consequent adjustment of the vacuum condensate generates a hierarchy of confinement scales in a natural Higgs-free manner. The accompanying symmetry hierarchy contains hints of standard model phenomenology.Comment: 9 pages, PTP class file, discussion at bottom of page 5 correcte

Modern Approaches to Non-Perturbative QCD and other Confining Gauge Theories

This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles

Lattice gauge theories simulations in the quantum information era

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analyzing the symmetry properties of Hamiltonian and states: the most striking example are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realization of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary Physics, the final version will appear soon on the on-line version of the journal. 34 page

Torsion at different scales: from materials to the Universe

The concept of torsion in geometry, although known for a long time, has not gained considerable attention by the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of contexts of physical interest. These range from novel materials, such as graphene and graphene-like materials, to advanced theoretical ideas, such as string theory and supersymmetry/supergravity and applications thereof in understanding the dark sector of our Universe. This work reviews such applications of torsion at different physical scales.Comment: 48 pages, 9 figures incorporated. Invited review, the version matches the published version in the journal Univers

Emergence and Breakdown of Quantum Scale Symmetry: From Correlated Condensed Matter to Physics Beyond the Standard Model

Scale symmetry is notoriously fickle: even when (approximately) present at the classical level, quantum fluctuations often break it, sometimes rather dramatically. Indeed, contemporary physics encompasses the study of very different phenomena at very different scales, e.g., from the (nominally) meV scale of spin systems, via the eV of electronic band structures, to the GeV of elementary particles, and possibly even the 10¹⁹ GeV of quantum gravity. However, there are often – possibly surprising – analogies between systems across these seemingly disparate settings. Studying the possible emergence of quantum scale symmetry and its breakdown is one way to systematically exploit these similarities, and in fact allows one to make testable predictions within a unified technical framework (viz., the renormalization group). The aim of this thesis is to do so for a few explicit scenarios. In the first four of these, quantum scale symmetry emerges in the long-wavelength limit near a quantum phase transition, over length scales of the order of the correlation length. In the fifth example, quantum scale symmetry is restored at very high energies (i.e., at and above the Planck scale), but severely constrains the phenomenology at 'low' energies (e.g., at accelerator scales), despite scale invariance being badly broken there. We begin with the Gross–Neveu (= chiral) SO(3) transition in D = 2+1 spacetime dimensions, which notably has been proposed to describe the transition of certain spin-orbital liquids to antiferromagnets. The chiral fermions that suffer a spontaneous breakdown of their isospin symmetry in this setting are fractionalized excitations (called spinons), and are as such difficult to observe directly in experiment. However, as gapless degrees of freedom, they leave their imprint on critical exponents, which may hence serve as a diagnostic tool for such unconventional excitations. These may be computed using (comparatively) conventional field-theoretic techniques. Here, we employ three complementary methods: a three-loop expansion in D = 4 - ε spacetime dimensions, a second-next-leading order expansion in large flavour number N , and a non-perturbative calculation using the functional renormalization group in the improved local potential approximation. The results are in fair agreement with each other, and yield combined best-guess estimates that may serve as benchmarks for numerical simulations, and possibly experiments on candidate spin liquids. We next turn our attention to spontaneous symmetry breaking at zero temperature in quasi-planar (electronic) semimetals. We begin with Luttinger semimetals, i.e., semimetals where two bands touch quadratically at isolated points of the Brioullin zone; Bernal-stacked bilayer graphene (BBLG) within certain approximations is one example. Luttinger semimetals are unstable at infinitesimal 4-Fermi interaction towards an ordered state (i.e., the field theory is asymptotically free rather than safe). Nevertheless, since the interactions are marginal, there are several pathologies in the critical behaviour. We show how these pathologies may be understood as a collision between the IR-stable Gaußian fixed point and a critical fixed point distinct from the Gaußian one in d = 2 + ε spatial dimensions. Observables like the order-parameter expectation value develop essential rather than power-law singularities; their exponent, as shown herein by explicit computation for the minimal model of two-component ‘spinors’, is distinct from the mean-field one. More tellingly, although finite critical exponents often default to canonical power-counting values, the susceptibility exponent turns out to be one-loop exact, and, in said minimal model takes the value γ = 2γᵐᵉᵃⁿ⁻ᶠᶦᵉˡᵈ = 2. Such an exact yet non-mean-field prediction can serve as a useful benchmark for numerical methods. We then proceed to scenarios in D = 2 + 1 spacetime dimensions where Dirac fermions can arise from Luttinger fermions due to low rotational symmetry. In BBLG, the 'Dirac from Luttinger' mechanism can occur both due to explicit and spontaneous breaking of rotational symmetry. The explicit symmetry breaking is due to the underlying honeycomb lattice, which only has C₃ symmetry around the location of the band crossings (so-called K points). As a consequence, the quadratic band crossing points each split into four Dirac cones, which is shown explicitly by computing the two-loop self-energy in the 4-Fermi theory. Within our approximations, we can estimate the critical coupling up to which a semimetallic state survives; it is finite (unlike a quadratic band touching point with high rotational symmetry), but significantly smaller than a 'vanilla' Dirac semimetal. Based on the ordering temperature of BBLG, our rough estimate further shows that the (effective) coupling strength in BBLG may be close to the critical value, in sharp contrast to other quasi-planar Dirac semimetals (such as monolayer graphene). Rotational symmetry in BBLG may also be broken spontaneously, i.e., due to the presence of nematic order, whereby a quadratic band crossing splits into two Dirac cones. Such a scenario is also very appealing for BBLG, since the precise nature of the ordered ground state of BBLG has not been established unambiguously: whilst some experiments show an insulating ground state with a full bulk gap, others show a partial gap opening with four isolated linear band crossings. Here, we show within a simplified phenomenological model using mean-field theory that there exists an extended region of parameter space with coexisting nematic and layer-polarized antiferromagnetic order, with a gapless nematic phase on one side and a gapped antiferromagnetic phase on the other. We then show that the nematic-to-coexistence quantum phase transition has emergent Lorentz invariance to one-loop in D = 2 + ε as well as D = 4 - ϵ dimensions, and thus falls into the celebrated Gross-Neveu-Heisenberg universality class. Combining previous higher-order field-theoretic results, we derive best-guess estimates for the critical exponents of this transition, with the theoretical uncertainty coming out somewhat smaller than in the monolayer counterpart due to the enlarged number of fermion components. Overall, BBLG may hence be a promising candidate for experimentally accessible Gross–Neveu quantum criticality in D = 2 + 1 spacetime dimensions. Finally, we turn our attention to the 'low-energy' consequences of transplanckian quantum scale symmetry. Extensions to the Standard Model that tend to lower the Higgs mass have many phenomenologically attractive properties (e.g., it would allow one to accommodate a more stable electroweak vacuum). Dark matter is one well-motivated candidate for such an extension. However, even in the most conservative settings, one usually has to contend with a significantly enlarged number of free parameters, and a concomitant reduction of predictivity. Here, we investigate how asymptotic safety (i.e., imposing quantum scale symmetry at the Planck scale and above) may constrain the Higgs mass in Standard Model (plus quantum gravity) when coupled to Yukawa dark matter via a Higgs portal. Working in a toy version of the Standard Model consisting of the top quark and the radial mode of the Higgs, we show within certain approximations that the Higgs mass may be lowered by the necessary amount if the dark scalar undergoes spontaneous symmetry breaking, as a function of the dark scalar mass, which is the only free parameter left in the theory.:1 Introduction 1.1 Scale invariance – why and where 1.1.1 Fundamental quantum field theories 1.1.2 Universality 1.1.3 Novel phases of matter 1.2 Outline of this thesis 2 Renormalization Group: A Brief Review 2.1 Quantum fluctuations and generating functionals 2.2 Renormalization group flow 2.3 Basic notions 2.4 Scale transformations, scale symmetry and RG fixed points 2.5 Characterization and interpretation of RG fixed points 2.5.1 Formal aspects 2.5.2 Scaling at (quantum) phase transitions 2.5.3 Predictivity in fundamental physics 2.5.4 Effective asymptotic safety in particle physics and condensed matter 3 Gross–Neveu SO(3) Quantum Criticality in 2 + 1 Dimensions 3.1 Effective field theory 3.2 Renormalization and critical exponents 3.2.1 4 - ϵ expansion 3.2.1.1 Method 3.2.1.2 Flow equations 3.2.1.3 Critical exponents 3.2.2 Large-N expansion 3.2.2.1 Method 3.2.2.2 Critical exponents 3.2.3 Non-perturbative FRG 3.2.3.1 Flow equations 3.2.3.2 Representation of the effective potential 3.2.3.3 Choice of regulator 3.2.3.4 Limiting behaviour 3.3 Discussion 3.3.1 General behaviour and qualitative aspects 3.3.2 Quantitative estimates for D = 3 3.4 Summary and outlook 4 Luttinger Fermions in Two Spatial Dimensions 4.1 Introduction 4.2 Action from top-down construction 4.3 Renormalization 4.3.1 4-Fermi formulation 4.3.2 Yukawa formulation 4.4 Fixed-point analysis 4.5 Non-mean-field behaviour 4.5.1 Order-parameter expectation value 4.5.2 Susceptibility exponent 4.6 Bottom-up construction: Spinless fermions on kagome lattice 4.6.1 Tight-binding dispersion 4.6.2 From Hubbard to Fermi 4.6.3 Fate of particle-hole asymmetry 4.7 Discussion 5 Dirac from Luttinger I: Explicit Symmetry Breaking 5.1 From lattice to continuum 5.1.1 Fermions on Bernal-stacked honeycomb bilayer 5.1.2 Continuum limit 5.1.3 Interactions 5.2 Mean-field theory 5.3 Renormalization-group analysis 5.3.1 Flow equations 5.3.2 Basic flow properties 5.3.3 Phase diagrams 5.4 Discussion 5.5 Summary and outlook 6 Dirac from Luttinger II: Spontaneous Symmetry Breaking 6.1 Model 6.2 Phase diagram and transitions 6.3 Emergent Lorentz symmetry 6.3.1 Loop expansion near lower critical dimension 6.3.1.1 Minimal 4-Fermi model 6.3.1.2 Gross–Neveu–Heisenberg fixed point 6.3.1.3 Fate of rotational symmetry breaking 6.3.2 Loop expansion near upper critical dimension 6.3.2.1 Gross–Neveu–Yukawa–Heisenberg model 6.3.2.2 Gross–Neveu–Yukawa–Heisenberg fixed point 6.3.2.3 Fate of rotational symmetry breaking 6.4 Critical exponents 6.5 Discussion 7 Higgs Mass in Asymptotically Safe Gravity with a Dark Portal 7.1 Review: The asymptotic safety scenario for quantum gravity and matter 7.2 Review: Higgs mass, and RG flow in the SM and beyond 7.2.1 Higgs mass in the SM 7.2.2 Higgs mass bounds in bosonic portal models 7.2.3 Higgs mass in asymptotic safety 7.2.4 Higgs Portal and Asymptotic Safety 7.3 Higgs mass in an asymptotically safe dark portal model 7.3.1 The UV regime 7.3.2 Flow towards the IR 7.3.3 Infrared masses 7.3.4 From the UV to the IR – Contrasting effective field theory and asymptotic safety 7.4 Discussion 8 Conclusions Appendices A Position-space propagator for C₃-symmetric QBT B Two-sided Padé approximants for C₃-symmetric QBTs C Corrections to the mean-field nematic order-parameter effective potential due to explicit symmetry breaking D Self-energy in anisotropic Yukawa theory E Master integrals for anisotropic Yukawa theory Bibliograph

Crystal gravity

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".Comment: 64 pages, 22 figures. The introduction has been revised compared to the first versio

Exact diagonalization studies of quantum simulators

Understand and tame complex quantum mechanical systems to build quantum technologies is one of the most important scientific endeavour nowadays. In this effort, Atomic, molecular and Optical systems have clearly played a major role in producing proofs of concept of several important applications. Notable examples are Quantum Simulators for difficult problems in other branches of physics i.e. spin systems, disordered systems, etc., and small sized Quantum Computers. In particular, ultracold atomic gases and trapped ion experiments are nowadays at the forefront in the field. This fantastic experimental effort needs to be accompanied by a matching theoretical and numerical one. The main two reasons are: 1) theoretical work is needed to identify suitable regimes where the AMO systems can be used as efficient quantum simulators of important problems in physics and mathematics, 2) thorough numerical work is needed to benchmark the results of the experiments in parameter regions where a solution to the problem can be found with classical devices. In this dissertation, we present several important examples of systems, which can be numerically solved. The technique used, which is common to all the work presented in the dissertation, is exact diagonalization. This technique works solely for systems of a small number of particles and/or a small number of available quantum states. Despite this limitation, one can study a large variety of quantum systems in relevant parameter regimes. A notable advantage is that it allows one to compute not only the ground state of the system but also most of the spectrum and, in some cases, to study dynamics. The dissertation is organized in the following way. First, we provide an introduction, outlining the importance of this technique for quantum simulation and quantum validation and certification. In Chapter 2, we detail the exact diagonalization technique and present an example of use for the phases of the 1D Bose-Hubbard chain. Then in Chapters 3 to 6, we present a number of important uses of exact diagonalization. In Chapter 3, we study the quantum Hall phases, which are found in two-component bosons subjected to artificial gauge fields. In Chapter 4, we turn into dynamical gauge fields, presenting the topological phases which appear in a bosonic system trapped in a small lattice. In Chapter 5, a very different problem is tackled, that of using an ultracold atomic gases to simulate a spin model. Quantum simulation is again the goal of Chapter 6, where we propose a way in which the number-partitioning problem can be solved by means of a quantum simulator made with trapped ions. Finally, in Chapter 7, we collect the main conclusions of the dissertation and provide a brief outlook.Entendre i controlar sistemes complexos regits per la mecànica quàntica per a construir tecnologies quàntiques es un dels reptes mes rellevants de la ciència en l’actualitat. Els sistemes atòmics, moleculars i òptics han jugat clarament un rol capital en aquest esforç, produint proves de concepte per a diverses aplicacions de consideració. Exemples notables en son els simuladors quàntics dissenyats per a resoldre problemes complicats d’altres branques de la física, com ara sistemes d’espins, sistemes desordenats, etc.... i ordinadors quàntics de dimensions reduïdes. En particular, els experiments amb gasos d’àtoms ultrafreds i amb trampes iòniques son la punta de llança del camp en l’actualitat. El fantàstic afany experimental ha d’anar associat amb d’altres teòric i numèric que el corresponguin. Les raons principals son: 1) els estudis teòrics son necessaris per tal d’identificar règims adients en que els sistemes AMO puguin esser emprats com a simuladors quàntics eficients de problemes rellevants de la Física i les Matemàtiques, 2) els treballs numèrics exhaustius son necessaris per a contrastar els resultats dels experiments en regions de paràmetres en que els dispositius clàssics son capaços de trobar solucions. En aquesta tesi, presentem diversos exemples de sistemes rellevants que poden esser resolts numèricament. La tècnica emprada -que es comuna per a tot el treball- es la diagonalització exacta. L’ús d’aquesta tècnica es limitat a sistemes amb nombres baixos partícules i/o pocs estats quàntics accessibles. Malgrat aquesta limitació, es poden estudiar una gran varietat de sistemes quàntics en els règims rellevants dels paràmetres de control. Un avantatge notable es el fet que permet calcular no nomes l’estat de mínima energia del sistema, sinó que també la majoria de l’espectre i, en alguns casos, àdhuc estudiar-ne la dinàmica. La tesi s’organitza tal i com prossegueix. En primer lloc, proveïm una introducció, subratllant la importància d’aquesta tècnica per a la simulació quàntica i la validació quàntica i certificació. En el capítol 2, detallem la tècnica de la diagonalització exacta i presentem un exemple del seu us per a les fases per a una cadena de Bose-Hubbard unidimensional. En els capítols del 3 al 6, presentem alguns usos rellevants de la diagonalització exacta. En el capítol 3, estudiem les fases degudes a l’efecte Hall quàntic en un sistema de dues components de bosons sotmesos a camps de gauge artificials. En el capítol 4, canviem a camps de gauge dinàmics, presentant les fases topològiques que apareixen en un sistema de bosons atrapats en una petita xarxa reticular. En el capítol 5, s’hi tracta un problema ben diferent, el d’emprar gasos d’àtoms ultrafreds per a per a simular un model d’espín. La simulació quàntica es de nou l’objectiu del capítol 6, en que proposem una forma en que el problema de la partició de nombres pot esser resolt per mitja d’un simulador quàntic construït amb trampes iòniques. Finalment, en el capítol 7, recollim les conclusions principals del treball i donem una breu opinió del futur d’aquesta investigació.Entender y controlar sistemas complejos regidos por la mecánica cuántica para construir tecnologías cuánticas es una de los retos científicos más relevantes en la actualidad. Los sistemas atómicos, moleculares y ópticos han jugado claramente un rol capital en este esfuerzo, produciendo pruebas de concepto para diversas aplicaciones de consideración. Notables ejemplos son los simuladores cuánticos diseñados para resolver problemas complicados de otras ramas de la física, como lo son los sistemas de espines, sistemas desordenados, etc.. . . i los ordenadores cuánticos de dimensiones reducidas. En particular, los experimentos con gases de átomos ultrafríos y con trampas iónicas son la punta de lanza del campo en la actualidad. El fantástico empeño experimental tiene que ir asociado a otros teórico y numérico que le correspondan. Las principales razones son: 1) los estudios teóricos son necesarios para identificar regímenes adecuados en que los sistemas AMO puedan ser usados cómo simuladores cuánticos eficientes para problemas relevantes de la Física y las Matemáticas, 2) los trabajos numéricos exhaustivos son necesarios para contrastar los resultados de los experimentos en regiones de parámetros en que los dispositivos clásicos sean capaces de encontrar soluciones. En esta tesis, presentamos diferentes ejemplos de sistemas relevantes que pueden ser resueltos numéricamente. La técnica usada –que es común en todo el trabajo– es la diagonalización exacta. El uso de ésta técnica está restringido a sistemas con números bajos de partículas i/o estados cuánticos accesibles. A pesar de esta limitación, se puede estudiar gran variedad de sistemas cuánticos en los regímenes relevantes de los parámetros de control. Una ventaja notable es que permite calcular no sólo el estado de mínima energía del sistema, sino que también la mayoría del espectro e, en algunos casos, incluso estudiar la dinámica. La tesis se organiza como sigue. En primer lugar, ofrecemos una introducción, subrayando la importancia de esta técnica para la simulación cuántica y la validación cuántica y certificación. En el capítulo 2, detallamos la técnica de la diagonalización exacta y presentamos un ejemplo de su uso para una cadena de Bose-Hubbard unidimensional. En los capítulos del 3 al 6, presentamos algunos usos relevantes de la diagonalización exacta. En el capítulo 3, estudiamos las fases debidas al efecto Hall cuántico en un sistema de dos componentes de bosones sometidos a campos de gauge artificiales. En el capítulo 4, cambiamos hacia campos gauge dinámicos, presentando las fases topológicas que aparecen en un sistema de bosones atrapados en una pequeña malla reticular. En el capítulo 5, se trata un problema bien diferente, el de usar gases de átomos ultrafríos para simular un modelo de espín. La simulación cuántica es de nuevo el objetivo del capítulo 6, en que proponemos una forma en que el problema de la partición de números puede ser resuelta mediante un simulador cuántico construido con trampas iónicas. Finalmente, en el capítulo 7, recogemos las conclusiones principales de los trabajos y damos una breve opinión del futuro de ésta investigaciónPostprint (published version

Report / Institute für Physik

The 2017 Report of the Physics Institutes of the Universität Leipzig provides an overview of the structure and research activities of the three institutes. We are happy to announce that Prof. Dr. Caudia Schnohr from Universität Jena will join the Felix Bloch Institute for Solid State Physics beginning 2019 filling the vacant position in the department for Solid State Optics. Dr. Johannes Deiglmayr from ETH Zurich will establish an independent department for Quantum Optics at the same institute

Report / Institute für Physik

The 2015 Report of the Physics Institutes of the Universität Leipzig presents an interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide