Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Lattice Field Theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Ligand Hole Driven Metal–Insulator Transition Exemplified in a Layered Transition Metal Oxide

The interplay of cooperative Jahn–Teller (JT) distortions and charge-disproportionation (CD) with a strong electronic correlation in transition metal oxides leads to structural symmetry breaking. Both JT and CD often manifest in the form of significant modifications in electronic and structural properties such as band splitting, metal–insulator transitions (MIT), and enhanced electron lattice interactions. Notably, the charge-disproportionation is a key electronic feature that drives the MIT. Here, we demonstrate and quantify it using first-principles calculations combining density-functional theory, dynamical mean-field theory, and spin–lattice Monte Carlo simulations. Taking Ca 2 FeMnO 6 as a prototypical example of a correlated oxide, our ab initio study shows that MIT in Ca 2 FeMnO 6 arises from the partial localization of oxygen ligand holes at alternate Fe sites that control both charge and magnetic ordering. Interestingly, the band gap was found to be fundamentally controlled by the strength of the charge-transfer energy and not by the Mott–Hubbard interactions. The novel physics and insights presented in this work reveal promising routes for tuning the electronic functionality in transition-metal oxides.

36 MATERIALS SCIENCE↗

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Squaring the fermion: The threefold way and the fate of zero modes

In this work, we investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension, we establish three fundamental no-go theorems that prove the absence of parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting noninteracting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of noninteracting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Learning the generating functional for variance reduction in lattice QCD

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Abbott, Ryan [Columbia U.] (ORCID:0000000258778005↗

Large-momentum effective theory

Since the parton model was introduced by Feynman more than 50 years ago, much has been learned about the partonic structure of the proton through a large body of high-energy experimental data and dedicated global fits. However, limited progress has been made in calculating partonic observables such as the parton distribution function (PDFs) from the fundamental theory of strong interactions, quantum chromodynamics (QCD). Recently some advocated for a formalism, large-momentum effective theory (LaMET), through which one can extract parton physics from the properties of the proton traveling at a moderate boost factor such as γ ~ 2 – 5 . The key observation behind this approach is that Lorentz symmetry allows the standard formalism of partons in terms of light-front operators to be replaced by an equivalent one with large-momentum states and time-independent operators of a universality class. With LaMET, the PDFs, generalized PDFs or generalized parton distributions, transverse-momentum-dependent PDFs, and light-front wave functions can all be extracted in principle from lattice simulations of QCD (or other nonperturbative methods) through standard effective field theory matching and running. Future lattice QCD calculations with exascale computational facilities could help one to understand the experimental data related to the hadronic structure, including those from the upcoming electron-ion colliders dedicated to exploring the partonic landscape of the proton. In this work, the progress made in the past few years in the development of the LaMET formalism and its applications is reviewed, with an emphasis on a demonstration of its effectiveness from initial lattice QCD simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Matching Curved Lattices to Anisotropic Tangent Planes

Radial quantization would be the ideal formalism for studying strongly-coupled near-conformal quantum field theories but it requires the ability to perform lattice calculations on static, curved manifolds, specifically a very long cylinder whose cross section is a sphere. Smoothly discretizing the surface of a sphere requires a graph with unequal edge lengths. The geometry of such graphs is well understood since 1961 using Regge Calculus. But, lattice quantum field theories are defined in terms of couplings which appear in the action rather than edge lengths and so the relationship between couplings and lengths must be determined dynamically. A simple example is computing the ratio of spatial to temporal lattice spacings in anisotropic lattice QCD. I will discuss our conjecture that computing anisotropic lattice spacing ratios on affine transformations of regular flat lattices is sufficient to determine coupling assignments on curved lattices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Anomalies of coset non-invertible symmetries

Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can be realized in symmetry-protected topological (SPT) phases. Coset symmetry can be present in many physical systems including quantum spin liquids, and the coset symmetry can be a non-invertible symmetry. We introduce twists in coset symmetries, which modify the fusion rules and the generalized Frobenius-Schur indicators. We call such coset symmetries twisted coset symmetries, and they are labeled by the quadruple (G, K, ω D+1 , α D ) in D spacetime dimensions where G is a group and K ⊂ G is a discrete subgroup, ω D+1 is a (D + 1)-cocycle for group G, and α D is a D-cochain for group K. We present several examples with twisted coset symmetries using lattice models and field theory, including both gapped and gapless systems (such as gapless symmetry-protected topological phases). We investigate the anomalies of general twisted coset symmetry, which presents obstructions to realizing the coset symmetry in (gapped) symmetry-protected topological phases. We show that finite coset symmetry G/K becomes anomalous when G cannot be expressed as the bicrossed product G = H ⋈ K , and such anomalous coset symmetry leads to symmetry-enforced gaplessness in generic spacetime dimensions. We illustrate examples of anomalous coset symmetries with A 5 / \Z 2 symmetry, with realizations in lattice models.

Hsin, Po-Shen [King’s College London (United Kingd↗

Toward scalable quantum computations of atomic nuclei

We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and 3 He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for 2 H and 3 He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Furthermore, based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

PT symmetry, pattern formation, and finite-density QCD

A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized ${\mathscr{PT}}$ symmetry. We review some new approaches to ${\mathscr{PT}}$-symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that ${\mathscr{PT}}$-symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a ${\mathscr{PT}}$-symmetric extension of a φ 4 model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theory of spin waves in a hexagonal antiferromagnet

We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar 120° magnetic order. The three Goldstone modes can be separated by point-group symmetry into a singlet α 0 and a doublet β. The α 0 singlet is described by the standard theory of a free relativistic scalar field. The field theory of the β doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse “speeds of sound.” The well-known Heisenberg models on the triangular and kagome lattices with nearest-neighbor exchange turn out to be special cases with accidental degeneracy of the spin-wave velocities. The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn 3 X family with stacked kagome layers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma

We perform a lattice calculation of the correlators of two chromoelectric fields in the adjoint representation connected by adjoint Wilson lines at nonzero temperature. These correlators arise in the study of quarkonium dynamics and of adjoint heavy quark diffusion in deconfined matter. We work in SU(3) gauge theory using either gradient flow or multilevel algorithms for noise reduction, and discuss the renormalization of the correlators on the lattice. We find that a Casimir factor rescaling relates the adjoint correlators corresponding to the diffusion of an adjoint heavy quark and the octet-octet quarkonium transitions to the chromoelectric correlator in the fundamental representation describing the diffusion of a heavy quark.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

The (2+1)-dimensional continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground-state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground-state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. Here, these are two different U(1) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton and lineon-elasticity dualities for the Lifshitz theory, and scalar and vector charge gauge theories.

2-dimensional systems↗

Implementing the three-particle quantization condition for π + π + K + and related systems

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Why Do Nuclei Stick Together?

Although quantum chromodynamics (QCD) has long been accepted as the underlying theory of the strong nuclear force, connecting the structure and interactions of nuclei to the fundamental parameters of QCD remains challenging. In this talk, I will present new results from lattice QCD and effective field theory that explore how nuclear interactions look in a world where the quarks are much heavier than they are in nature, and discuss lessons that can be learned for nuclear physics as well as searches for physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Diagrammatic state sums for 2D pin-minus TQFTs

The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita invariance of the construction are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗