82 research outputs found
Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
The low-energy theory of graphene exhibits spontaneous chiral symmetry
breaking due to pairing of quasiparticles and holes, corresponding to a
semimetal-insulator transition at strong Coulomb coupling. We report a Lattice
Monte Carlo study of the critical exponents of this transition as a function of
the number of Dirac flavors , finding for
, for and for , with throughout. We compare our
results with recent analytical work for graphene and closely related systems,
and discuss scenarios for the fate of the chiral transition at finite
temperature and carrier density, an issue of relevance for upcoming experiments
with suspended graphene samples.Comment: 5 pages, 5 figures. Published versio
Lattice methods for strongly interacting many-body systems
Lattice field theory methods, usually associated with non-perturbative
studies of quantum chromodynamics, are becoming increasingly common in the
calculation of ground-state and thermal properties of strongly interacting
non-relativistic few- and many-body systems, blurring the interfaces between
condensed matter, atomic and low-energy nuclear physics. While some of these
techniques have been in use in the area of condensed matter physics for a long
time, others, such as hybrid Monte Carlo and improved effective actions, have
only recently found their way across areas. With this topical review, we aim to
provide a modest overview and a status update on a few notable recent
developments. For the sake of brevity we focus on zero-temperature,
non-relativistic problems. After a short introduction, we lay out some general
considerations and proceed to discuss sampling algorithms, observables, and
systematic effects. We show selected results on ground- and excited-state
properties of fermions in the limit of unitarity. The appendix contains details
on group theory on the lattice.Comment: 64 pages, 32 figures; topical review for J. Phys. G; replaced with
published versio
Entanglement, noise, and the cumulant expansion
We put forward a simpler and improved variation of a recently proposed method
to overcome the signal-to-noise problem found in Monte Carlo calculations of
the entanglement entropy of interacting fermions. The present method takes
advantage of the approximate lognormal distributions that characterize the
signal-to-noise properties of other approaches. In addition, we show that a
simple rewriting of the formalism allows circumvention of the inversion of the
restricted one-body density matrix in the calculation of the -th R\'enyi
entanglement entropy for . We test our technique by implementing it in
combination with the hybrid Monte Carlo algorithm and calculating the R\'enyi entropies of the 1D attractive Hubbard model. We use that
data to extrapolate to the von Neumann () and cases.Comment: Significantly expanded manuscript; improved presentation, new data
and figures, new approach to the calculation of R\'enyi entropies. 8
pages, 8 figure
Zero-temperature equation of state of mass-imbalanced resonant Fermi gases
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.Comment: 5 pages, 2 figures, 2 table
Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases
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.Comment: 5 pages, 3 figure
Phase structure of mass- and spin-imbalanced unitary Fermi gases
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.Comment: 17 pages, 7 figure
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