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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Treelike structure of symmetry topological field theories and multisector QFTs

The global symmetries of a D -dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( D + 1 )-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( D + 1 )-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large M averaging where the topological sectors of different large M replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Generalized symmetry constraints on deformed 4D SCFTs

We explore the consequence of generalized symmetries in four-dimensional N = 1 superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the Adler-Bell-Jackiw (ABJ) anomaly, we find that many of these theories have mixed zero-form or one-form ’t Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two D 3 ( S U ( N ) ) theories and S U ( N ) gauge theory with two adjoints. We also repeat our analysis for a host of nonsupersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs. Published by the American Physical Society 2025

Kang, Monica Jinwoo (ORCID:0000000204542064)↗
DOE OSTI2025

Hidden conformal symmetry of the discrete series scalars in dS 2

In D dimensional de Sitter space, a scalar field has an infinite tower of special tachyonic mass values at which enhanced shift symmetries appear. After modding out by these shift symmetries, these fields correspond to the unitary irreducible representations of the de Sitter group known as the discrete series. We show that in D = 2 these theories have global conformal symmetry. In all but the massless case, these theories have no stress tensor and the conformal symmetry does not act in the usual way on the scalar field. We find the conformal symmetry by explicitly computing the correlators of the shift invariant local operators and showing that they take conformally invariant forms. We also demonstrate how these fields are self-dual in D = 2 , and dual to the shift invariant massive vector fields, which are therefore also conformally invariant. Published by the American Physical Society 2025

Farnsworth, Kara (ORCID:000000020200078X)↗
DOE OSTI2020

Nature of Symmetry Breaking at the Excitonic Insulator Transition: Ta 2 NiSe 5

Ta 2 NiSe 5 is one of the most promising materials for hosting an excitonic insulator ground state. While a number of experimental observations have been interpreted in this way, the precise nature of the symmetry breaking occurring in Ta 2 NiSe 5 , the electronic order parameter, and a realistic microscopic description of the transition mechanism are, however, missing. By a symmetry analysis based on first-principles calculations, we uncover the discrete lattice symmetries which are broken at the transition. We identify a purely electronic order parameter of excitonic nature that breaks these discrete crystal symmetries and contributes to the experimentally observed lattice distortion from an orthorombic to a monoclinic phase. Our results provide a theoretical framework to understand and analyze the excitonic transition in Ta 2 NiSe 5 and settle the fundamental questions about symmetry breaking governing the spontaneous formation of excitonic insulating phases in solid-state materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. Further, by analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature T N ≈ 400 K and a charge density wave (CDW) transition at T CDW ≈ 110 K , followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around T N , the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10 − 4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to T CDW , the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

We establish a holographic duality between d -dimensional mixed-state symmetry-protected topological (mSPT) phases and ( d + 1 ) -dimensional subsystem symmetry-protected topological (SSPT) states. Specifically, we show that the reduced density matrix of the boundary layer of a ( d + 1 ) -dimensional SSPT state with subsystem symmetry S and global symmetry G corresponds to a d -dimensional mSPT phase with strong S and weak G symmetries. Conversely, we demonstrate that the wave function of an SSPT state can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT phase. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wave functions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPT phases that are unique to open quantum systems, without pure-state analogues. We show that strange correlators and twisted Rényi- N correlators can diagnose these nontrivial phases and we explore their connection to strange correlators in pure-state SSPT phases. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT phases through the duality. Published by the American Physical Society 2025

Sun, Shijun (ORCID:0000000168880030)↗
DOE OSTI2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)-dimensional topological order

A (2+1)D topologically ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It has recently been discovered that there are “higher” versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states that obstruct symmetry-preserving gapped edge states beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the “partial rotation” unitary, which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with 𝜈=1/3 and 1/5, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determine if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

2-dimensional systems↗
DOE OSTI2026

Symmetry-energy expansion with strange dense matter

The quantum chromodynamics (QCD) phase diagram at large densities and low temperatures can be probed using both neutron stars and low-energy heavy-ion collisions. Heavy-ion collisions are nearly isospin-symmetric systems, whereas neutron stars are highly isospin asymmetric since they are neutron rich. The symmetry-energy expansion is used to connect these regimes across isospin asymmetry. However, the current symmetry-energy expansion does not account for strange particles. In this work, we include finite strangeness by redefining the isospin-asymmetry parameter and the symmetry-energy expansion in a way that is consistent with QCD SU(3) flavor symmetry. Furthermore, our new symmetry energy works well beyond typical neutron star central densities and admits a skewness term in the presence of strangeness for the case of weak equilibrium.

Equations of state of nuclear matter↗
DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗
DOE OSTI2020

SMART U(1)$$_X$$: standard model with axion, right handed neutrinos, two Higgs doublets and U(1)$$_X$$ gauge symmetry

Abstract To address five fundamental shortcomings of the Standard Model (SM) of particle physics and cosmology, we propose a phenomenologically viable framework based on a $$U(1)_X \times U(1)_{PQ}$$ U ( 1 ) X × U ( 1 ) PQ extension of the SM, that we call “SMART U(1) $$_X$$ X ”. The $$U(1)_X$$ U ( 1 ) X gauge symmetry is a well-known generalization of the $$U(1)_{B-L}$$ U ( 1 ) B - L symmetry and $$U(1)_{PQ}$$ U ( 1 ) PQ is the global Peccei–Quinn (PQ) symmetry. Three right handed neutrinos are added to cancel $$U(1)_X$$ U ( 1 ) X related anomalies, and they play a crucial role in understanding the observed neutrino oscillations and explaining the observed baryon asymmetry in the universe via leptogenesis. Implementation of PQ symmetry helps resolve the strong CP problem and also provides axion as a compelling dark matter (DM) candidate. The $$U(1)_X$$ U ( 1 ) X gauge symmetry enables us to implement the inflection-point inflation scenario with $$H_{inf} \lesssim 2 \times 10^{7}$$ H inf ≲ 2 × 10 7 GeV, where $$H_{inf}$$ H inf is the value of Hubble parameter during inflation. This is crucial to overcome a potential axion domain wall problem as well as the axion isocurvature problem. The SMART U(1) $$_X$$ X framework can be successfully implemented in the presence of SU (5) grand unification, as we briefly show.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Spectral anomalies and broken symmetries in maximally chaotic quantum maps

Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify “ergodicity,” including the presence of underlying macroscopic symmetries, in generic quantum systems ranging from quantized chaotic maps to interacting many-body systems. By studying various quantizations of maximally chaotic maps that break a discrete classical symmetry upon quantization, we demonstrate that this approach can be misleading and fail to detect macroscopic symmetries. Notably, the same classical map can exhibit signatures of different random matrix symmetry classes in short-range spectral statistics depending on the quantization. While the long-range spectral statistics encoded in the early time ramp of the SFF are more robust and correctly identify macroscopic symmetries in several common quantizations, we also demonstrate analytically and numerically that the presence of Berry-like phases in the quantization leads to spectral anomalies, which break this correspondence. Finally, we provide numerical evidence that long-range spectral rigidity remains directly correlated with ergodicity in the quantum dynamical sense of visiting a complete orthonormal basis.

Shou, Laura [Univ. of Maryland, College Park, MD (↗
DOE OSTI2020

Lorentz symmetry fractionalization and dualities in (2+1)d

We discuss symmetry fractionalization of the Lorentz group in (2+1) d d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous \mathbb{Z}_2 ℤ 2 one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Field theories with a vector global symmetry

Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Emergent symmetries in atomic nuclei: Probing nuclear dynamics and physics beyond the standard model

Dominant shapes naturally emerge in atomic nuclei from first principles, thereby establishing the shape-preserving symplectic Sp(3, \mathbb{R} ℝ ) symmetry as remarkably ubiquitous and almost perfect symmetry in nuclei. We discuss the critical role of this emergent symmetry in enabling machine-learning descriptions of heavy nuclei, ab initio modeling of \alpha α clustering and collectivity, as well as tests of beyond-the-standard-model physics. In addition, the Sp(3, \mathbb{R} ℝ ) and SU(3) symmetries provide relevant degrees of freedom that underpin the ab initio symmetry-adapted no-core shell model with the remarkable capability of reaching nuclei and reaction fragments beyond the lightest and close-to-spherical species.

Launey, Kristina D.↗
DOE OSTI2021

SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]

Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗
NASA NTRS1986

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Golubitsky, Martin↗