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

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

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

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 $0.366^{+0.016}_{-0.011}$ 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

Data-Driven Prediction and Design of bZIP Coiled-Coil Interactions

Selective dimerization of the basic-region leucine-zipper (bZIP) transcription factors presents a vivid example of how a high degree of interaction specificity can be achieved within a family of structurally similar proteins. The coiled-coil motif that mediates homo- or hetero-dimerization of the bZIP proteins has been intensively studied, and a variety of methods have been proposed to predict these interactions from sequence data. In this work, we used a large quantitative set of 4,549 bZIP coiled-coil interactions to develop a predictive model that exploits knowledge of structurally conserved residue-residue interactions in the coiled-coil motif. Our model, which expresses interaction energies as a sum of interpretable residue-pair and triplet terms, achieves a correlation with experimental binding free energies of R = 0.68 and significantly out-performs other scoring functions. To use our model in protein design applications, we devised a strategy in which synthetic peptides are built by assembling 7-residue native-protein heptad modules into new combinations. An integer linear program was used to find the optimal combination of heptads to bind selectively to a target human bZIP coiled coil, but not to target paralogs. Using this approach, we designed peptides to interact with the bZIP domains from human JUN, XBP1, ATF4 and ATF5. Testing more than 132 candidate protein complexes using a fluorescence resonance energy transfer assay confirmed the formation of tight and selective heterodimers between the designed peptides and their targets. This approach can be used to make inhibitors of native proteins, or to develop novel peptides for applications in synthetic biology or nanotechnology.National Institutes of Health (U.S.) (Award GM067681

Public and Community Perceptions of Safe Injection Sites

Background The opioid epidemic began in 1999 and the number of deaths from overdoses has since quadrupled by 2019 50,000 deaths in the US in 2019 from opioid overdoses and the numbers increase each year Research Question: What are the public’s and communities\u27 perceptions of safe injection sites

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

We present a new 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. Our lattice action is highly improved, with sources of discretization and finite volume errors systematically removed; we are able to demonstrate the expected volume scaling of energy levels of two and three untrapped fermions, and to reproduce the high precision calculations published previously for the ground state energies for N = 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3, . . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty). We 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 64^3 x 72; our approach avoids the use of importance sampling or calculation of a fermion determinant and employs a novel statistical method for estimating observables, allowing us to generate ensembles as large as 10^8 while requiring only relatively modest computational resources.Comment: 48 pages, 19 figures, published version, some text revised, typos corrected, title changed in journal; previously "Unitary fermions on the lattice I: in a harmonic trap

Extended study for unitary fermions on a lattice using the cumulant expansion technique

A recently developed lattice method for large numbers of strongly interacting nonrelativistic fermions exhibits a heavy tail in the distributions of correlators for large Euclidean time {\tau} and large number of fermions N, which only allows the measurement of ground state energies for a limited number of fermions using standard techniques. In such cases, it is suggested that measuring the log of the correlator is more efficient, and a cumulant expansion of this quantity can be exactly related to the correlation function. The cumulant expansion technique allows us to determine the ground state energies of up to 66 unpolarized unitary fermions on lattices as large as 72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic potential on lattices as large as 72$\times$64^3. We have also improved our lattice action with a Galilean invariant form for the four-fermion interaction, which results in predictive volume scaling of the lowest energy of three fermions in a periodic box and in good agreement of our results for N \leq 6 trapped unitary fermions with those from other benchmark calculations.Comment: 7 pages, 6 figures, Presented at 29th International Symposium on Lattice Field Theory (Lattice2011), Squaw Valley, Lake Tahoe, CA, USA, 10-16 July 201