26 research outputs found
Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin
We calculate the pressure and density of polarized non-relativistic systems
of two-component fermions coupled via a contact interaction at finite
temperature. For the unpolarized one-dimensional system with an attractive
interaction, we perform a third-order lattice perturbation theory calculation
and assess its convergence by comparing with hybrid Monte Carlo. In that
regime, we also demonstrate agreement with real Langevin. For the repulsive
unpolarized one-dimensional system, where there is a so-called complex phase
problem, we present lattice perturbation theory as well as complex Langevin
calculations. For our studies, we employ a Hubbard-Stratonovich transformation
to decouple the interaction and automate the application of Wick's theorem for
perturbative calculations, which generates the diagrammatic expansion at any
order. We find excellent agreement between the results from our perturbative
calculations and stochastic studies in the weakly interacting regime. In
addition, we show predictions for the strong coupling regime as well as for the
polarized one-dimensional system. Finally, we show a first estimate for the
equation of state in three dimensions where we focus on the polarized unitary
Fermi gas.Comment: 8 pages, 6 figures, proceedings of Lattice2017, Granada, Spai
Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
We present a nonperturbative computation of the equation of state of
polarized, attractively interacting, nonrelativistic fermions in one spatial
dimension at finite temperature. We show results for the density, spin
magnetization, magnetic susceptibility, and Tan's contact. We compare with the
second-order virial expansion, a next-to-leading-order lattice perturbation
theory calculation, and interpret our results in terms of pairing correlations.
Our lattice Monte Carlo calculations implement an imaginary chemical potential
difference to avoid the sign problem. The thermodynamic results on the
imaginary side are analytically continued to obtain results on the real axis.
We focus on an intermediate- to strong-coupling regime, and cover a wide range
of temperatures and spin imbalances.Comment: 14 pages, 19 figures; published versio
Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
Using the lattice Monte Carlo method, we compute the energy and Tan's contact
in the ground state as well as the first excited state of few- to many-fermion
systems in a one-dimensional periodic box. We focus on unpolarized systems of
N=4,6,...,12 particles, with a zero-range interaction, and a wide range of
attractive couplings. In addition, we provide extrapolations to the
infinite-volume and thermodynamic limits.Comment: 8 pages, 12 figures; published versio
Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension
We analyze the pressure and density equations of state of unpolarized
non-relativistic fermions at finite temperature in one spatial dimension. For
attractively interacting regimes, we perform a third-order lattice perturbation
theory calculation, assess its convergence properties by comparing with hybrid
Monte Carlo results (there is no sign problem in this regime), and demonstrate
agreement with real Langevin calculations. For repulsive interactions, we
present lattice perturbation theory results as well as complex Langevin
calculations, with a modified action to prevent uncontrolled excursions in the
complex plane. Although perturbation theory is a common tool, our
implementation of it is unconventional; we use a Hubbard-Stratonovich
transformation to decouple the system and automate the application of Wick's
theorem, thus generating the diagrammatic expansion, including symmetry
factors, at any desired order. We also present an efficient technique to tackle
nested Matsubara frequency sums without relying on contour integration, which
is independent of dimension and applies to both relativistic and
non-relativistic systems, as well as all energy-independent interactions. We
find exceptional agreement between perturbative and non-perturbative results at
weak couplings, and furnish predictions based on complex Langevin at strong
couplings. We additionally present perturbative calculations of up to the
fifth-order virial coefficient for repulsive and attractive couplings. Both the
lattice perturbation theory and complex Langevin formalisms can easily be
extended to a variety of situations including polarized systems, bosons, and
higher dimension.Comment: 17 pages, 8 figure
Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension
Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
We present finite-temperature, lattice Monte Carlo calculations of the
particle number density, compressibility, pressure, and Tan's contact of an
unpolarized system of short-range, attractively interacting spin-1/2 fermions
in one spatial dimension, i.e., the Gaudin-Yang model. In addition, we compute
the second-order virial coefficients for the pressure and the contact, both of
which are in excellent agreement with the lattice results in the low-fugacity
regime. Our calculations yield universal predictions for ultracold atomic
systems with broad resonances in highly constrained traps. We cover a wide
range of couplings and temperatures and find results that support the existence
of a strong-coupling regime in which the thermodynamics of the system is
markedly different from the noninteracting case. We compare and contrast our
results with identical systems in higher dimensions.Comment: 6 pages, 7 figures; improved, published versio
Complex Langevin and other approaches to the sign problem in quantum many-body physics
We review the theory and applications of complex stochastic quantization to
the quantum many-body problem. Along the way, we present a brief overview of a
number of ideas that either ameliorate or in some cases altogether solve the
sign problem, including the classic reweighting method, alternative
Hubbard-Stratonovich transformations, dual variables (for bosons and fermions),
Majorana fermions, density-of-states methods, imaginary asymmetry approaches,
and Lefschetz thimbles. We discuss some aspects of the mathematical
underpinnings of conventional stochastic quantization, provide a few
pedagogical examples, and summarize open challenges and practical solutions for
the complex case. Finally, we review the recent applications of complex
Langevin to quantum field theory in relativistic and nonrelativistic quantum
matter, with an emphasis on the nonrelativistic case.Comment: 51 pages, 19 figures, review articl
Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances
Mise en place d'une expérience avec le grand public: entre recherche, vulgarisation et pédagogie
Methodological considerations on implementing a participative experimentWe present the implementation of an economic experiment conducted simultaneously in 11 French cities, with over 2700 participants, during four uninterrupted hours, during a popular-science event held in September 2015. Our goal is both to provide a roadmap for a possible replication and to discuss how the discipline can be used in new fields (science popularization, popular education, public communication)