Amy N. Nicholson

Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD

We present a determination of nucleon-nucleon scattering phase shifts for l≥0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For l>0, this is the first lattice QCD calculation using the Luscher finite-volume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to mπ=mK≈800MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V≈(3.5fm)3 and V≈(4.6fm)3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Luscher formalism for two-nucleon systems.

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 technical details on group theory on the lattice.

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

Noise, sign problems, and statistics.

0.366^{+0.016}_{-0.011}

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

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.

Sign problems, noise, and chiral symmetry breaking in a QCD-like theory

We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions.

N -Body Efimov States from Two-Particle Noise

We present a lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For N=3 unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our 0.3% uncertainty; as additional benchmarks we reproduce precision calculations of N=3,...,6 unitary fermions in a harmonic trap to within our {approx}1% uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64{sup 3}x72. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of N considered.

Low energy scattering phase shifts for meson-baryon systems

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.

Listening to Noise

The ground state energies of universal N-body clusters tied to Efimov trimers, for N even, are shown to be encapsulated in the statistical distribution of two particles interacting with a background auxiliary field at large Euclidean time when the interaction is tuned to the unitary point. Numerical evidence that this distribution is log normal is presented, allowing one to predict the ground state energies of the N-body system.

Low lying modes of triplet-condensed neutron matter and their effective theory

In this work, we calculate meson-baryon scattering phase shifts in four channels using lattice QCD methods. From a set of calculations at four volumes, corresponding to spatial sizes of 2, 2.5, 3, and 4 fm, and a pion mass of m_pi ~ 390 MeV, we determine the scattering lengths and effective ranges for these systems at the corresponding quark masses. We also perform the calculation at a lighter quark mass, m_pi ~ 230 MeV, on the largest volume. Using these determinations, along with those in previous work, we perform a chiral extrapolation of the scattering lengths to the physical point after correcting for the effective range contributions using the multi-volume calculations performed at m_pi ~ 390 MeV.