arXiv subjects

Jens Braun

Publications and source records attributed to Jens Braun.

At least 73 records · Page 4Linked to original sources

arXiv2013

Improved Polyakov-loop potential for effective models from functional calculations

We investigate the quark backreaction on the Polyakov loop and its impact on the thermodynamics of quantum chromodynamics. The dynamics of the gluons generating the Polyakov-loop potential is altered by the presence of dynamical quarks. However, this backreaction of the quarks has not yet been taken into account in Polyakov-loop extended model studies. In the present work, we show within a 2+1 flavour Polyakov-quark-meson model that a quark-improved Polyakov-loop potential leads to a smoother transition between the low-temperature hadronic phase and the high-temperature quark-gluon plasma phase. In particular, we discuss the dependence of our results on the remaining uncertainties that are the critical temperature and the parametrisation of the Polyakov-loop potential as well as the mass of the sigma-meson.

hep-ph↗

arXiv2013

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

cond-mat.stat-mech↗

arXiv2013

QCD thermodynamics of effective models with an improved Polyakov-loop potential

We analyse the role of the quark backreaction on the gauge-field dynamics and its impact on the Polyakov-loop potential. Based on our analysis we construct an improved Polyakov-loop potential that can be used in future model studies. In the present work, we employe this improved potential in a study of a 2+1 flavour Polyakov-quark-meson model and show that the temperature dependence of the order parameters and thermodynamics is closer to full QCD. We discuss the results for QCD thermodynamics and outline briefly the dependence of our results on the critical temperature and the parametrisation of the Polyakov-loop potential as well as the mass of the sigma-meson.

hep-ph↗

arXiv2012

Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature

We study the phase diagram of the Gross-Neveu model in d=2+1 space-time dimensions in the plane spanned by temperature and the number of massless fermion flavors. We use a functional renormalization group approach based on a nonperturbative derivative expansion that accounts for fermionic as well as composite bosonic fluctuations. We map out the phase boundary separating the ordered massive low-temperature phase from the disordered high-temperature phase. The phases are separated by a second-order phase transition in the 2d Ising universality class. We determine the size of the Ginzburg region and show that it scales to zero for large $\Nf$ following a powerlaw, in agreement with large-$\Nf$ and lattice studies. We also study the regimes of local order above as well as the classical regime below the critical temperature.

hep-ph↗

arXiv2012

On the Phase Structure of QCD in a Finite Volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.

hep-ph↗

arXiv2012

On the Relation of the Deconfinement and the Chiral Phase Transition in Gauge Theories with Fundamental and Adjoint Matter

We study the relation of confinement and chiral symmetry breaking in gauge theories with non-trivial center, such as SU(N) gauge theories. To this end, we deform these gauge theories by introducing an additional control parameter into the theory and by varying the representation of the quark fields. We then consider a large-d(R) expansion of the effective action, where d(R) denotes the dimension of the representation R of the quark fields. We show how our large-d(R) expansion can be extended in a systematic fashion and discuss the effects of 1/d(R)-corrections on the dynamics close to the finite-temperature phase boundary. Our analysis of the fixed-point structure of the theory suggests that the order, in which the chiral and the deconfinement phase transition occur, is dictated by the representation of the quark fields and by the underlying gauge group. In particular, we find that the phase diagram in the plane spanned by the temperature and our additional control parameter exhibits an intriguing phase structure for quarks in the fundamental representation. For SU(N) gauge theories with adjoint quarks, on the other hand, the structure of this phase diagram appears to be less rich, at least in leading order in the 1/d(R)-expansion.

hep-ph↗

arXiv2012

Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations

We present the Mathematica application DoFun which allows to derive Dyson-Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross-Neveu model.

hep-th↗

arXiv2011

Scaling behavior in two-flavor QCD, finite quark masses and finite volume effects

The question of the exact nature of the phase transition in two-flavor QCD is still under discussion. Recent results for small quark masses in simulations with 2+1 flavors show scaling behavior consistent with the O(4) or O(2) universality class. For a precise determination, an assessment of deviations from the ideal scaling behavior due to finite quark masses and finite simulation volumes is necessary. We study the scaling behavior at the chiral phase transition with an effective quark-meson model. In our Renormalization Group approach, the quark masses in the model can be varied from the chiral limit over a wide range of values, which allows us to estimate scaling deviations due to large quark masses and the extent of the scaling region. We conclude that scaling deviations are already large at pion masses of 75 MeV, but that the effect is difficult to see in the absence of results for even smaller masses. Comparing results only in a narrow window of pion masses leads to the observation of apparent scaling behavior. While the scaling deviations are not necessarily universal, we expect that this may affect current lattice simulation results. By placing the system in a finite box, we investigate the transition between infinite-volume scaling behavior and finite-size scaling. We estimate that finite-size scaling behavior can be tested in regions where pion mass times box size is approximately 2 - 3, which is smaller than in most current lattice simulations. We expect that finite-volume effects are small for pion masses of 75 MeV and lattice aspect ratios with TL > 8, but that they will become significant when pion masses in lattice simulations become smaller.

hep-ph↗

arXiv2011

Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity

We investigate an ultracold Fermi gas at unitarity confined in a periodic box $V=L^3$ using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value in the thermodynamic limit as a function of increasing box size. On the other hand, we observe that the fermion gap shows a significantly stronger dependence on the box size, in particular for small values of the pairing source. Our results may contribute to a better understanding of finite-size and particle-number effects present in Monte-Carlo simulations of ultracold Fermi gases.

cond-mat.quant-gas↗

arXiv2011

Fermion Interactions and Universal Behavior in Strongly Interacting Theories

The theory of the strong interaction, Quantum Chromodynamics (QCD), describes the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. As a complement, experiments with ultracold fermionic atoms provide a clean environment to benchmark our understanding of dynamical formation of condensates and the generation of bound states in strongly interacting many-body systems. Renormalization group (RG) techniques offer great potential for theoretical advances in both hot and dense QCD as well as many-body physics, but their connections have not yet been investigated in great detail. We aim to take a further step to bridge this gap. A cross-fertilization is indeed promising since it may eventually provide us with an ab-initio description of hadronization, condensation, and bound-state formation in strongly interacting theories. After giving a thorough introduction to the derivation and analysis of fermionic RG flows, we give an introductory review of our present understanding of universal long-range behavior in various different theories, ranging from non-relativistic many-body problems to relativistic gauge theories, with an emphasis on scaling behavior of physical observables close to quantum phase transitions (i. e. phase transitions at zero temperature) as well as thermal phase transitions.

hep-ph↗

arXiv2011

Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD

We study the fixed-point structure of four-fermion interactions in two-flavor QCD with Nc colors close to the finite-temperature phase boundary. In particular, we analyze how the fixed-point structure of four-fermion interactions is related to the confining dynamics in the gauge sector. We show that there exists indeed a mechanism which dynamically locks the chiral phase transition to the deconfinement phase transition. This mechanism allows us to determine a window for the values of physical observables in which the two phase transitions lie close to each other.

hep-ph↗

arXiv2010

On the QCD phase diagram at finite chemical potential

We present results for the phase diagram of QCD with two massless quark flavours as obtained from a first-principles functional renormalisation group approach. In particular we compute order parameters for chiral symmetry breaking and quark confinement at vanishing and non-zero imaginary chemical potential. Our analytical and numerical results suggest a close relation between the chiral and the deconfinement phase transition. We discuss the properties of dual order parameters at imaginary and real chemical potential.

hep-ph↗

arXiv2010

Beyond Miransky Scaling

We study the scaling behavior of physical observables in strongly-flavored asymptotically free gauge theories, such as many-flavor QCD. Such theories approach a quantum critical point when the number of fermion flavors is increased. It is well-known that physical observables at this quantum critical point exhibit an exponential scaling behavior (Miransky scaling), provided the gauge coupling is considered as a constant external parameter. This scaling behavior is modified when the scale dependence of the gauge coupling is taken into account. Provided that the gauge coupling approaches an IR fixed point, we derive the resulting universal power-law corrections to the exponential scaling behavior and show that they are uniquely determined by the IR critical exponent of the gauge coupling. To illustrate our findings, we compute the universal corrections in many-flavor QCD with the aid of nonperturbative functional renormalization group methods. In this case, we expect the power-law scaling to be quantitatively more relevant if the theories are probed, for instance, at integer Nf as done in lattice simulations.

hep-ph↗

arXiv2010

Curvature of the QCD phase transition line in a finite volume

The curvature which characterizes the QCD phase transition at finite temperature and small values of the chemical potential is accessible to lattice simulations. The results for this quantity which have been obtained by several different lattice simulation methods differ due to different numbers of flavors, different pion masses and different sizes of the simulation volume. In order to reconcile these results, it is important to investigate finite-volume effects on the curvature. We investigate the curvature of the chiral phase transition line at finite temperature and chemical potential in a finite volume. We use a phenomenological model for chiral symmetry breaking and apply non-perturbative functional renormalization group methods which account for critical long-range fluctuations at the phase transition. We find an intermediate volume region in which the curvature of the phase transition line is actually reduced relative to its infinite-volume value, provided periodic spatial boundary conditions are chosen for the quark fields. Size and location of this region depend on the value of the pion mass. Such an effect could account for differences in the curvature between lattice simulations in differently sized volumes and from functional methods in the infinite volume limit. We discuss implications of our results for the QCD phase diagram.

hep-ph↗

arXiv2010

Asymptotic safety: a simple example

We use the Gross-Neveu model in 2<d<4 as a simple fermionic example for Weinberg's asymptotic safety scenario: despite being perturbatively nonrenormalizable, the model defines an interacting quantum field theory being valid to arbitrarily high momentum scales owing to the existence of a non-Gaussian fixed point. Using the functional renormalization group, we study the UV behavior of the model in both the purely fermionic as well as a partially bosonized language. We show that asymptotic safety is realized at non-Gaussian fixed points in both formulations, the universal critical exponents of which we determine quantitatively. The partially bosonized formulation allows to make contact to the large-Nf expansion where the model is known to be renormalizable to all-orders. In this limit, the fixed-point action as well as all universal critical exponents can be computed analytically. As asymptotic safety has become an important scenario for quantizing gravity, our description of a well-understood model is meant to provide for an easily accessible and controllable example of modern nonperturbative quantum field theory.

hep-th↗

arXiv2010

Scaling laws near the conformal window of many-flavor QCD

We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral limit. We argue on general grounds that the associated critical exponents are all interrelated and can be determined from the critical exponent of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point. We illustrate our findings with the aid of nonperturbative functional Renormalization Group (RG) calculations and low-energy QCD models.

hep-ph↗

arXiv2010

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark-meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes.In particular, we find large scaling deviations for physical pion masses and significant finite volume effects for pion masses that are used in current lattice simulations.

hep-ph↗

arXiv2010

On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.

hep-ph↗