[Show abstract][Hide abstract] 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.
Physical Review A 01/2015; 91(5). DOI:10.1103/PhysRevA.91.053611 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
Physical Review D 10/2014; 91(11). DOI:10.1103/PhysRevD.91.116006 · 4.64 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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 · 4.64 Impact Factor
[Show abstract][Hide abstract] 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 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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 · 4.64 Impact Factor
[Show abstract][Hide abstract] 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 · 2.78 Impact Factor
[Show abstract][Hide abstract] 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 · 2.78 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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 · 1.58 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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 · 6.13 Impact Factor
[Show abstract][Hide abstract] 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; 39(3). DOI:10.1088/0954-3899/39/3/033001 · 2.78 Impact Factor
[Show abstract][Hide abstract] 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 · 0.77 Impact Factor