21,423 research outputs found
Lattice study of trapped fermions at unitarity
We present a lattice study of up to N=20 unitary fermions confined to a
harmonic trap. Our preliminary results show better than 1% agreement with high
precision solutions to the many-body Schrodinger equation for up to N=6. We are
able to make predictions for larger N which were inaccessible by the
Hamiltonian approach due to computational limitations. Harmonic traps are used
experimentally to study cold atoms tuned to a Feshbach resonance. We show that
they also provide certain benefits to numerical studies of many-body
correlators on the lattice. In particular, we anticipate that the methods
described here could be used for studying nuclear physics.Comment: 7 pages, 5 figures, presented at the XXVIII International Symposium
on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 14-19 201
Lattice calculation for unitary fermions in a finite box
A fundamental constant in systems of unitary fermions is the so-called
Bertsch parameter, the ratio of the ground state energy for spin paired unitary
fermions to that for free fermions at the same density. I discuss how we
computed this parameter as well as the pairing gap using a recently developed
lattice construction for unitary fermions, by measuring correlation functions
for up to 38 fermions in a finite box. Our calculation illustrates interesting
issues facing the study of many-body states on the lattice, which may
eventually be confronted in QCD calculations as well.Comment: 7 pages, 6 figures, The XXVIII International Symposium on Lattice
Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Ital
Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path
integral formulations: at finite chemical potential one formulation has a
severe sign problem similar to that found in QCD, while the other does not. At
large N, where N is the number of flavors, one can compute the probability
distributions of fermion correlators analytically in both formulations. In the
former case one finds a broad distribution with small mean; in the latter one
finds a heavy tailed positive distribution amenable to the cumulant expansion
techniques developed in earlier work. We speculate on the implications of this
model for QCD.Comment: 16 pages, 5 figures; Published version with minor changes from the
origina
The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory
We examine the role of the Delta-Delta intermediate state in low energy NN
scattering using effective field theory. Theories both with and without pions
are discussed. They are regulated with dimensional regularization and MSbar
subtraction. We find that the leading effects of the Delta-Delta state can be
absorbed by a redefinition of the contact terms in a theory with nucleons only.
It does not remove the requirement of a higher dimension operator to reproduce
data out to moderate momentum. The explicit decoupling of the Delta-Delta state
is shown for the theory without pions.Comment: 16 pages, 3 figures, uses harvma
Lattice Monte Carlo calculations for unitary fermions in a finite box
We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a
finite box using a highly improved lattice action for nonrelativistic spin 1/2
fermions. We obtain a value of for the Bertsch
parameter, defined as the energy of the unitary Fermi gas measured in units of
the free gas energy in the thermodynamic limit. In addition, for up to four
unitary fermions, we compute the spectrum of the lattice theory by exact
diagonalization of the transfer matrix projected onto irreducible
representations of the octahedral group for small to moderate size lattices,
providing an independent check of our few-body simulation results. We compare
our exact numerical and simulation results for the spectrum to benchmark
studies of other research groups, as well as perform an extended analysis of
our lattice action improvement scheme, including an analysis of the errors
associated with higher partial waves and finite temporal discretization.Comment: Significant revisions from previous version. Included data at a
larger volume and performed an infinite volume extrapolation of the Bertsch
parameter. Published versio
Few-body physics in effective field theory
Effective Field Theory (EFT) provides a powerful framework that exploits a
separation of scales in physical systems to perform systematically improvable,
model-independent calculations. Particularly interesting are few-body systems
with short-range interactions and large two-body scattering length. Such
systems display remarkable universal features. In systems with more than two
particles, a three-body force with limit cycle behavior is required for
consistent renormalization already at leading order. We will review this EFT
and some of its applications in the physics of cold atoms and nuclear physics.
In particular, we will discuss the possibility of an infrared limit cycle in
QCD. Recent extensions of the EFT approach to the four-body system and N-boson
droplets in two spatial dimensions will also be addressed.Comment: 10 pages, 5 figures, Proceedings of the INT Workshop on "Nuclear
Forces and the Quantum Many-Body Problem", Oct. 200
Supersymmetry on a Spatial Lattice
We construct a variety of supersymmetric gauge theories on a spatial lattice,
including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice
supersymmetry greatly reduces or eliminates the need for fine tuning to arrive
at the desired continuum limit in these examples.Comment: Version 3: Text brought in line with published version (extended
discussion of orbifolding
- …