arXiv subjects

Dean Lee

Publications and source records attributed to Dean Lee.

At least 145 records · Page 8Linked to original sources

arXiv2010

Causality and the effective range expansion

We derive the generalization of Wigner's causality bounds and Bethe's integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.

nucl-th↗

arXiv2010

Lattice effective field theory calculations for A = 3,4,6,12 nuclei

We present lattice results for the ground state energies of tritium, helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our analysis includes isospin-breaking, Coulomb effects, and interactions up to next-to-next-to-leading order in chiral effective field theory.

nucl-th↗

arXiv2010

Causality and universality in low-energy quantum scattering

We generalize Wigner's causality bounds and Bethe's integral formula for the effective range to arbitrary dimension and arbitrary angular momentum. Moreover, we discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy quantum scattering.

nucl-th↗

arXiv2009

Ground state energy of dilute neutron matter at next-to-leading order in lattice chiral effective field theory

We present lattice calculations for the ground state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.

nucl-th↗

arXiv2009

Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order

We consider low-energy nucleons at next-to-next-to-leading order in lattice chiral effective field theory. Three-body interactions first appear at this order, and we discuss several methods for determining three-body interaction coefficients on the lattice. We compute the energy of the triton and low-energy neutron-deuteron scattering phase shifts in the spin-doublet and spin-quartet channels using Luescher's finite volume method. In the four-nucleon system we calculate the energy of the alpha particle using auxiliary fields and projection Monte Carlo.

nucl-th↗

arXiv2008

Nuclear Lattice Simulations with Chiral Effective Field Theory

We present recent results on lattice simulations using chiral effective field theory. In particular we discuss lattice simulations for dilute neutron matter at next-to-leading order and three-body forces in light nuclei at next-to-next-to-leading order.

nucl-th↗

arXiv2008

Lattice simulations for few- and many-body systems

We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory is discussed for cold atoms as well as low-energy nucleons with and without pions. A number of different lattice formulations and computational algorithms are considered, and an effort is made to show common themes in studies of cold atoms and low-energy nuclear physics as well as common themes in work by different collaborations.

nucl-th↗

arXiv2008

Nuclear effective field theory on the lattice

In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.

hep-lat↗

arXiv2008

The ground state energy at unitarity

We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection, we compute the ground state energy using four computationally different but physically identical auxiliary-field methods. The best performance is obtained using a bounded continuous auxiliary field and a non-local updating algorithm called hybrid Monte Carlo. With this method we calculate results for 10 and 14 fermions at lattice volumes 4^3, 5^3, 6^3, 7^3, 8^3 and extrapolate to the continuum limit. For 10 fermions in a periodic cube, the ground state energy is 0.292(12) times the ground state energy for non-interacting fermions. For 14 fermions the ratio is 0.329(5).

nucl-th↗

arXiv2008

Chiral effective field theory on the lattice at next-to-leading order

We study nucleon-nucleon scattering on the lattice at next-to-leading order in chiral effective field theory. We determine phase shifts and mixing angles from the properties of two-nucleon standing waves induced by a hard spherical wall in the center-of-mass frame. At fixed lattice spacing we test model independence of the low-energy effective theory by computing next-to-leading-order corrections for two different leading-order lattice actions. The first leading-order action includes instantaneous one-pion exchange and same-site contact interactions. The second leading-order action includes instantaneous one-pion exchange and Gaussian-smeared interactions. We find that in each case the results at next-to-leading order are accurate up to corrections expected at higher order.

nucl-th↗

arXiv2008

Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory

We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground state energy as an expansion about the unitarity limit with corrections due to finite scattering length, effective range, and P-wave interactions.

nucl-th↗

arXiv2008

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N-body density correlations. While the original Hamiltonian has an exact Z_2 symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z_2 symmetry is recovered by enforcing Z_2 symmetry as a constraint on N-body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.

cond-mat.supr-con↗

arXiv2007

Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly-spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.

nucl-th↗

arXiv2007

Spectral convexity for attractive SU(2N) fermions

We prove a general theorem on spectral convexity with respect to particle number for 2N degenerate components of fermions. The number of spatial dimensions is arbitrary, and the system may be uniform or constrained by an external potential. We assume only that the interactions are governed by an SU(2N)-invariant two-body potential whose Fourier transform is negative definite. The convexity result implies that the ground state is in a 2N-particle clustering phase. We discuss implications for light nuclei as well as asymmetric nuclear matter in neutron stars.

nucl-th↗

arXiv2007

Temperature-dependent errors in nuclear lattice simulations

We study the temperature dependence of discretization errors in nuclear lattice simulations. We find that for systems with strong attractive interactions the predominant error arises from the breaking of Galilean invariance. We propose a local "well-tempered" lattice action which eliminates much of this error. The well-tempered action can be readily implemented in lattice simulations for nuclear systems as well as cold atomic Fermi systems.

nucl-th↗

arXiv2006

Superfluidity and excitations at unitarity

We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a periodic cube. Using Euclidean time projection, we analyze ground state properties and transient behavior due to low-energy excitations. At asymptotically large values of t we see long-range order consistent with spontaneously broken U(1) fermion-number symmetry and a superfluid ground state. At intermediate times we see exponential decay in the t-dependent signal due to an unknown low-energy excitation. We probe this low-energy excitation further by calculating two-particle correlation functions. We find that the excitation has the properties of a chain of particles extending across the periodic lattice.

cond-mat.stat-mech↗

arXiv2006

Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order

We discuss lattice simulations of light nuclei at leading order in chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.

nucl-th↗

arXiv2006

Large-N droplets in two dimensions

Using lattice effective field theory, we study the ground state binding energy of N distinct particles in two dimensions with equal mass interacting weakly via an attractive SU(N)-symmetric short range potential. We find that in the limit of zero range and large N, the ratio of binding energies B_{N}/B_{N-1} approaches the value 8.3(6).

physics.atm-clus↗