Jens Braun

Technical University Darmstadt, Darmstadt, Hesse, Germany

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Publications (42)134.44 Total impact

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    ABSTRACT: We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
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    ABSTRACT: We present an analysis of the dynamics of two-flavour QCD in the vacuum. Special attention is payed to the transition from the high energy quark-gluon regime to the low energy regime governed by hadron dynamics. This is done within a functional renormalisation group approach to QCD amended by dynamical hadronisation techniques. The latter allow us to describe conveniently the transition from the perturbative high-energy regime to the nonperturbative low-energy limit without suffering from a fine-tuning of model parameters. In the present work, we apply these techniques to two-flavour QCD with physical quark masses and show how the dynamics of the dominant low-energy degrees of freedom emerge from the underlying quark-gluon dynamics.
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    ABSTRACT: We revisit the Gross-Neveu model with N fermion flavors in 1+1 dimensions and compute its phase diagram at finite temperature and chemical potential in the large-N limit. To this end, we double the number of fermion degrees of freedom in a specific way which allows us to detect inhomogeneous phases in an efficient manner. We show analytically that this "fermion doubling trick" predicts correctly the position of the boundary between the chirally symmetric phase and the phase with broken chiral symmetry. Most importantly, we find that the emergence of an inhomogeneous ground state is predicted correctly. We critically analyze our approach based on this trick and discuss its applicability to other theories, such as fermionic models in higher dimensions, where it may be used to guide the search for inhomogeneous phases.
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    ABSTRACT: We calculate the zero-temperature equation of state of mass-imbalanced resonant Fermi gases in an ab initio fashion, by implementing the recent proposal of imaginary-valued mass difference to bypass the sign problem in lattice Monte Carlo calculations. The fully non-perturbative results thus obtained are analytically continued to real mass imbalance to yield the physical equation of state, providing predictions for upcoming experiments with mass-imbalanced atomic Fermi gases. In addition, we present an exact relation for the rate of change of the equation of state at small mass imbalances, showing that it is fully determined by the energy of the mass-balanced system.
    Physical Review Letters 07/2014; 114(5). DOI:10.1103/PhysRevLett.114.050404 · 7.73 Impact Factor
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    ABSTRACT: We analyze the many-flavor phase diagram of quantum electrodynamics (QED) in 2+1 (Euclidean) space-time dimensions. We compute the critical flavor number above which the theory is in the quasi-conformal massless phase. For this, we study the renormalization group fixed-point structure in the space of gauge interactions and pointlike fermionic self-interactions, the latter of which are induced dynamically by fermion-photon interactions. We find that a reliable estimate of the critical flavor number crucially relies on a careful treatment of the Fierz ambiguity in the fermionic sector. Using a Fierz-complete basis, our results indicate that the phase transition towards a chirally-broken phase occurring at small flavor numbers could be separated from the quasi-conformal phase at larger flavor numbers, allowing for an intermediate phase which is dominated by fluctuations in a vector channel. If these interactions approach criticality, the intermediate phase could be characterized by a Lorentz-breaking vector condensate.
    Physical Review D 04/2014; 90(3). DOI:10.1103/PhysRevD.90.036002 · 4.86 Impact Factor
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    ABSTRACT: We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ Density Functional Theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely: a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and finally a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage, and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.
    Physical Review A 02/2014; 89(5). DOI:10.1103/PhysRevA.89.053613 · 2.99 Impact Factor
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    ABSTRACT: We compute the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem.
    Physical Review A 11/2013; 89(6). DOI:10.1103/PhysRevA.89.063609 · 2.99 Impact Factor
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    ABSTRACT: We investigate the effect of a finite volume on the critical behavior of the theory of the strong interaction (QCD) by means of a quark-meson model for two quark flavors. In particular, we analyze the effect of a finite volume on the location of the critical point in the phase diagram existing in our model. In our analysis, we take into account the effect of long-range fluctuations with the aid of renormalization group techniques. We find that these quantum and thermal fluctuations, absent in mean-field studies, play an import role for the dynamics in a finite volume. We show that the critical point is shifted towards smaller temperatures and larger values of the quark chemical potential if the volume size is decreased. This behavior persists for antiperiodic as well as periodic boundary conditions for the quark fields as used in many lattice QCD simulations.
    Physical Review D 08/2013; 90(5). DOI:10.1103/PhysRevD.90.054012 · 4.86 Impact Factor
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    Sandra Kemler, Jens Braun
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    ABSTRACT: We discuss a two-point particle irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. In particular, the general structure and properties of this RG flow equation are analyzed in detail. Moreover, we discuss how our 2PPI RG approach relates to Density Functional Theory and argue that it can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. For illustration purposes, we use our formalism to compute the ground-state properties of two toy models.
    Journal of Physics G Nuclear and Particle Physics 07/2013; 40(8):085105. DOI:10.1088/0954-3899/40/8/085105 · 2.84 Impact Factor
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    ABSTRACT: Fermi gases in strongly coupled regimes, such as the unitary limit, are inherently challenging for many-body methods. Although much progress has been made with purely analytic methods, quantitative results require ab initio numerical approaches, such as Monte Carlo (MC) calculations. However, mass-imbalanced and spin-imbalanced gases are not accessible to MC calculations due to the infamous sign problem. It was recently pointed out that the sign problem, for finite spin imbalance, can be circumvented by resorting to imaginary polarizations and analytic continuation. Large parts of the phase diagram spanned by temperature and polarization then become accessible to MC calculations. We propose to apply a similar strategy to the mass-imbalanced case, which opens up the possibility to study the associated phase diagram with MC calculations. In particular, our analysis suggests that a detection of a (tri-)critical point in this phase diagram is possible. We also discuss calculations in the zero-temperature limit with our approach.
    Journal of Physics G Nuclear and Particle Physics 06/2013; 41(5). DOI:10.1088/0954-3899/41/5/055110 · 2.84 Impact Factor
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    ABSTRACT: 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.
    Physical Review Letters 03/2013; 110(13):130404. DOI:10.1103/PhysRevLett.110.130404 · 7.73 Impact Factor
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    ABSTRACT: 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.
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    ABSTRACT: 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.
    Physical review D: Particles and fields 02/2013; 87(7). DOI:10.1103/PhysRevD.87.076004 · 4.86 Impact Factor
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    ABSTRACT: 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.
    Journal of Physics A Mathematical and Theoretical 12/2012; 46(28). DOI:10.1088/1751-8113/46/28/285002 · 1.69 Impact Factor
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    ABSTRACT: 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. 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 non-relativistic systems? Are the interesting features of the phase diagram accessible in this manner? Introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the non-relativistic 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.
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    Jens Braun, Tina K. Herbst
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    ABSTRACT: 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.
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    ABSTRACT: 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.
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    ABSTRACT: 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.
    Physics Letters B 10/2011; 713(3). DOI:10.1016/j.physletb.2012.05.053 · 6.02 Impact Factor
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    Jens Braun
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    ABSTRACT: 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.
    Journal of Physics G Nuclear and Particle Physics 08/2011; DOI:10.1088/0954-3899/39/3/033001 · 2.84 Impact Factor
  • Jens Braun
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    ABSTRACT: Strongly interacting theories of fermions are of great interest both experimentally and theoretically. While heavy-ion collision experiments provide us with information on hot and dense QCD, experiments with ultracold trapped atoms provide an accessible and controllable system where quantum many-body phenomena can be studied experimentally in great detail. Our theoretical understanding of these theories has improved in recent years. However, finite-size effects in these systems are not yet fully understood. We review some aspects related to finite-size effects and the role that these effects are playing in strongly-interacting fermionic theories.
    Few-Body Systems 07/2011; 53(1-2). DOI:10.1007/s00601-011-0285-y · 1.51 Impact Factor