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Results for “functional renormalization group”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene

We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. Furthermore, the degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is d-wave-like and spin-singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Structure functions from renormalization group improved small x evolution

Abstract We perform the fit to the structure function $$F_2$$ F 2 data from HERA including terms due to the resummation at small x . The equation for the unintegrated gluon density is solved, previously established within the renormalization group improved small x framework. We find very good description of the structure function $$F_2$$ F 2 and its charm component $$F_2^c$$ F 2 c . The resulting unintegrated gluon density is found to be consistent with the calculations based on similar approaches available in the literature, with only slightly higher intercept value.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O ( N ) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. Further, we work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Sublattice modulated superconductivity in the kagome Hubbard model

Here we identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to onsite Hubbard U and nearest neighbor V interactions. Within our functional renormalization group analysis, this state appears with a concomitant d-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and d-wave SC is influenced by the absolute interaction strength and coupling ratio V/U. Parametrically adjacent to this domain at weak coupling, we find an intra-unit cell modulated vestigial charge density wave and an s-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Magnetism in the two-dimensional dipolar XY model

Here, motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U⁡(1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N≈0.5, close to the one at the critical temperature, S c /N=0.585⁢(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Universal location of Yang–Lee edge singularity for a one-component field theory in 1 ≤ d ≤ 4

Herein we determine the universal location of the Yang–Lee edge singularity in the entire relevant domain of spatial dimensions 1 ≤ d ≤ 4 for the Ising universality class. To that end, we present analytical results for d = 1,2,4 and near four dimensions. For d = 3 and a set of fractional dimensions, we perform numerical calculations using a systematic Functional Renormalization Group approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Pomeranchuk instability from electronic correlations in CsTi 3 Bi 5 kagome metal

Electronic nematicity, the spontaneous breaking of rotational symmetry, has emerged as a key instability in correlated quantum systems. CsTi 3 Bi 5 , a kagome metal of the AV 3 Sb 5 (A = K, Rb, Cs) family, hosts rich unconventional electronic phases, yet the origin of its nematicity remains unsettled. Here, we combine polarization-dependent angle-resolved photoemission spectroscopy with functional renormalization group calculations on a fully interacting ab initio model. We reveal an orbital-selective nematic deformation in the low-energy band structure and identify a finite angular momentum (d-wave) Pomeranchuk instability driven by electronic correlations in specific orbital channels and detuning from Van Hove singularities. Our results establish a direct link between orbital selectivity and symmetry-breaking instabilities in CsTi 3 Bi 5 , providing a microscopic framework for nematic order in kagome systems.

Bigi, Chiara [Synchrotron SOLEIL, Saint-Aubin (Fra↗
DOE OSTI2022

Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite

Abstract We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings J ⬡ , J , and $$J^{\prime}$$ J ′ , and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear $$\overrightarrow{Q}=0$$ Q → = 0 magnetic phase, two unusual non-collinear coplanar $$\overrightarrow{Q}=(1/3,1/3)$$ Q → = ( 1 / 3 , 1 / 3 ) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-disordered kagome antiferromagnet. We further show with density functional theory calculations that the recently synthesized Y-kapellasite Y 3 Cu 9 (OH) 19 Cl 8 is a realization of this model and predict its ground state to lie in the region of $$\overrightarrow{Q}=(1/3,1/3)$$ Q → = ( 1 / 3 , 1 / 3 ) order, which remains stable even after the inclusion of quantum fluctuation effects within variational Monte Carlo and pseudofermion functional renormalization group. The presented model opens a new direction in the study of kagome antiferromagnets.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Measurement of fifth- and sixth-order fluctuations of (net-)proton number in Au + Au collisions from phase II of the beam energy scan program at RHIC

We report high-statistics measurements of fifth- and sixth-order factorial cumulants and cumulant ratios of (net-)proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7–27GeV, using data from the STAR experiment collected during the Beam Energy Scan Phase II at RHIC. Protons and antiprotons are identified at midrapidity (|𝑦| < 0.5) with transverse momentum 0.4 < 𝑝 𝑇 < 2.0GeV/𝑐. The proton factorial cumulants 𝜅 4 , 𝜅 5 , and 𝜅 6 increase with order but exhibit no sign alternation within current uncertainties, offering no evidence for a two-component structure in the proton multiplicity distribution, as might be expected near a first-order phase transition. The cumulant ratios 𝐶 5 /𝐶 1 and 𝐶 6 /𝐶 2 fluctuate around zero in collisions at 0–40% centrality. The results are consistent with both the negative predictions from lattice QCD and the positive trends obtained from the ultrarelativistic quantum molecular dynamics (UrQMD) model. At $\sqrt{s_{NN}}$ ≳ 27GeV, the 𝐶 4 /𝐶 2 and 𝐶 5 /𝐶 1 results are compatible with predictions from lattice QCD, functional renormalization group (FRG), and hadron resonance gas (HRG) models, while UrQMD describes the data better at lower energies. Here, these measurements place constraints on baryon number fluctuations and offer valuable insights into the QCD phase structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

What is the Quark-Gluon Plasma made of?

This article surveys our present understanding of the internal structure of the fully developed quark-gluon plasma at temperatures outside the crossover region. The theoretical part of the review covers perturbative and nonperturbative approaches to quark-gluon plasma structure, in particular, hard-thermal loop effective theory, lattice QCD and the functional renormalization group. The phenomenological part of the review scrutinizes the information that has been derived from bulk observables and hard probes in relativistic heavy ion collisions in terms of how it informs our knowledge about the structure of the quark-gluon plasma. The final section lists possible avenues for future progress.

FOS: Physical sciences↗
DOE OSTI2022

Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

$c$-functions in flows across dimensions

We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d N =4 SYM and compactifications of 6d N = (2, 0) theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

Herein we demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z 2 -symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C– / A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z 2 -symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C– / A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash (ORCID:000000020587962X)↗
DOE OSTI2026

Towards determination of the strong coupling $α_s(m_Z)$ from four-flavor lattice QCD using the continuous $β$-function method

The precise value of the strong coupling $α_s(m_{Z})$ at the $Z$-boson mass $m_{Z}$ is essential for high-energy phenomenology and precision tests of quantum chromodynamics (QCD). We present the status of a program targeting a $\sim 0.3\%$ determination of $α_s(m_{Z})$ using the renormalization group $β$-function in the infinite volume gradient flow scheme based on lattice QCD simulations of degenerate four-flavor highly improved staggered quark (HISQ) ensembles. In particular, we analyze both tree-level cutoff effects and finite-mass effects. We also outline the next steps of the analysis, including the infinite-volume and continuum extrapolations required for a precise determination of $α_s(m_Z)$.

Mandlecha, Yash [Michigan State U.; Michigan State↗
DOE OSTI2024

The 1 → 3 massive splitting functions from QCD factorization and SCET

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗