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Results for “Z_2 symmetry”

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 OSTI2025

Entanglement maximization and mirror symmetry in two-Higgs-doublet models

We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets Φ a , a = 1, 2, can be viewed as a qubit: Φ 1 = |0⟩ and Φ 2 = |1⟩. More specifically, we compute the scattering amplitudes for Φ a Φ b → Φ c Φ d and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of {|00⟩, |01⟩, |10⟩, |11⟩}. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an U(2) × U(2) global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact U(2) × U(2) symmetry, which is spontaneously broken to U(1) × U(1). As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The U(2) × U(2) symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete Z 2 symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the Z 2 symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

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↗
DOE OSTI2024

Impact of new experimental data on the C2HDM: the strong interdependence between LHC Higgs data and the electron EDM

The complex two-Higgs doublet model (C2HDM) is one of the simplest extensions of the Standard Model with a source of CP-violation in the scalar sector. It has a $\mathbb{Z}$ 2 symmetry, softly broken by a complex coefficient. There are four ways to implement this symmetry in the fermion sector, leading to models known as Type-I, Type-II, Lepton Specific and Flipped. In the latter three models, there is a priori the surprising possibility that the 125 GeV Higgs boson couples mostly as a scalar to top quarks, while it couples mostly as a pseudoscalar to bottom quarks. This “maximal” scenario was still possible with the data available in 2017. Since then, there have been more data on the 125 GeV Higgs boson, direct searches for CP-violation in angular correlations of $τ$-leptons produced in Higgs boson decays, new results on the electron electric dipole moment, new constraints from LHC searches for additional Higgs bosons and new results on $b$ → $sγ$ transitions. Highlighting the crucial importance of the physics results of LHC’s Run 2, we combine all these experiments and show that the “maximal” scenario is now excluded in all models. Still, one can have a pseudoscalar component in $hτ\overline{τ}$ couplings in the Lepton-Specific case as large as 87% of the scalar component for all mass orderings of the neutral scalar bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Is the HEFT matching unique?

Physics beyond the Standard Model (BSM) can be described in a consistent and general way through the Higgs effective field theory (HEFT). Measurements of model-independent HEFT coefficients allow one to constrain the parameter space of BSM models via a matching procedure. In this work, we show that this procedure is not unique and depends on the scalings of the parameters of the Lagrangian. As examples, we consider three BSM models: the real singlet extension of the SM with a Z 2 symmetry, the complex singlet extension of the SM and the two Higgs doublet model. We discuss several physical observables, and show that different scalings of the model parameters with the UV scale in the matching to the HEFT can yield quite different results. This complicates the interpretation of HEFT measurements in terms of parameters of BSM models. Additionally, as a byproduct, we report the first matching of the complex singlet extension to the HEFT. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Ratio-preserving approach to cosmological concordance

Cosmological observables are particularly sensitive to key ratios of energy densities and rates, both today and at earlier epochs of the Universe. Well-known examples include the photon-to-baryon and the matter-to-radiation ratios. Equally important, though less publicized, are the ratios of pressure-supported to pressureless matter and the Thomson scattering rate to the Hubble rate around recombination, both of which observations tightly constrain. Preserving these key ratios in theories beyond the Λ Cold-Dark-Matter ( Λ CDM ) model ensures broad concordance with a large swath of datasets when addressing cosmological tensions. We demonstrate that a mirror dark sector, reflecting a partial Z 2 symmetry with the Standard Model, in conjunction with percentage level changes to the visible fine-structure constant and electron mass which represent a phenomenological change to the Thomson scattering rate, maintains essential cosmological ratios. Incorporating this ratio-preserving approach into a cosmological framework significantly improves agreement to observational data ( Δ χ 2 = - 35.72 ) and completely eliminates the Hubble tension with a cosmologically inferred H 0 = 73.80 ± 1.02 km / s / Mpc when including the S H 0 ES calibration in our analysis. While our approach is certainly nonminimal, it emphasizes the importance of keeping key ratios constant when exploring models beyond Λ CDM .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of nonequilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. Here, these properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of the Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging Z 2 symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

Fluctuation theorems↗
DOE OSTI2024

Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code

We consider the Z 2 toric code, surface code, and Floquet code defined on a nonorientable surface, which can be considered as families of codes extending Shor’s nine-qubit code. We investigate the fault-tolerant logical gates of the Z 2 toric code in this setup, which corresponds to e ↔ m exchanging symmetry of the underlying Z 2 gauge theory. We find that nonorientable geometry provides a new way for the emergent symmetry to act on the code space, and discover the new realization of the fault-tolerant Hadamard gate of the two-dimensional surface code with a single cross cap connecting the vertices nonlocally along a slit, dubbed a nonorientable surface code. This Hadamard gate can be realized by a constant-depth local unitary circuit modulo nonlocality caused by a cross cap. Via folding, the nonorientable surface code can be turned into a bilayer local quantum code, where the folded cross cap is equivalent to a bilayer twist terminated on a gapped boundary and the logical Hadamard only contains local gates with intralayer couplings when being away from the cross cap, as opposed to the interlayer couplings on each site needed in the case of the folded surface code. We further obtain the complete logical Clifford gate set for a stack of nonorientable surface codes and similarly for codes defined on Klein-bottle geometries. We then construct the honeycomb Floquet code in the presence of a single cross cap, and find that the period of the sequential Pauli measurements acts as a H Z logical gate on the single logical qubit, where the cross cap enriches the dynamics compared with the orientable case. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the Z 2 gauge theory, and illustrate the exotic dynamics of our code in terms of a condensation operator supported at a nonorientable surface. Published by the American Physical Society 2024

Physics↗
DOE OSTI2024

Quantum teleportation implies symmetry-protected topological order

We constrain a broad class of teleportation protocols using insights from locality. In the ``standard'' teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a ``resource state'' exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry G k = ( Z 2 × Z 2 ) k . The k logical states are teleported between the edges of the chain by measuring the corresponding 2 k string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of k qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.

Hong, Yifan↗
DOE OSTI2025

Non-invertible symmetries in finite-group gauge theory

We investigate the invertible and non-invertible symmetries of topological finite-group gauge theories in general spacetime dimensions, where the gauge group can be abelian or non-abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d \mathbb{Z}_2 ℤ 2 gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-abelian finite-group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.

Córdova, Clay↗
DOE OSTI2024

Gauging staggered fermion shift symmetries

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an S U ( 4 ) flavor symmetry which plays a crucial role in showing that staggered fermions lead to a theory of four degenerate Dirac fermions in the continuum limit. They are associated with the appearance of certain Z 2 valued global parameters. We propose a strategy to try to partially gauge these translation symmetries by allowing these parameters to vary locally in the lattice. To maintain invariance of the action requires the addition of Z 2 valued higher form lattice gauge fields. An analogous procedure can be carried out for reduced staggered fermions where the shifts correspond to a discrete subgroup of an S O ( 4 ) flavor symmetry. Published by the American Physical Society 2024

Catterall, Simon (ORCID:0000000327352682)↗
DOE OSTI2025

Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders

Superdiffusive transport with dynamical exponent z=3/2 has been firmly established at finite temperature for a class of integrable systems with a non-Abelian global symmetry G. On the inclusion of integrability-breaking perturbations, diffusive transport with z=2 is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower time scale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength λ, the characteristic timescale for diffusion goes as t*∼λ−α for some α. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the S=1/2 quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the SU(2) symmetry, leading to scaling exponents consistent with those observed in one classical study [McCarthy , Phys. Rev. B 110, L180301 (2024)2469-995010.1103/PhysRevB.110.L180301]: α=2 for symmetry-breaking terms and α=6 for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with G=SU(4) and find consistent results. Finally, we consider a generalization to an SU(3) ladder and find that the α=6 scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-Abelian symmetry G.

Wang, Kevin↗
DOE OSTI2024

Renormalization of beta decay at three loops and beyond

The anomalous dimension for heavy-heavy-light effective theory operators describing nuclear beta decay is computed through three-loop order in the static limit. The result at order Z 2 α 3 corrects a previous result in the literature. An all-orders symmetry is shown to relate the anomalous dimensions at leading and subleading powers of Z at a given order of α . The first unknown coefficient for the anomalous dimension now appears at O ( Z 2 α 4 ) . Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic States

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-König bound for $n$-dimensional topological stabilizer codes. In this work, we extend topological Pauli stabilizer codes to a broad class of $n$-dimensional Clifford hierarchy stabilizer codes. These codes correspond to the $(n+1)$D Dijkgraaf-Witten gauge theories with non-Abelian topological order. We construct transversal non-Clifford gates through automorphism symmetries represented by cup products. In 2D, we obtain the first transversal non-Clifford logical gates including T and CS for Clifford stabilizer codes, using the automorphism of the twisted $\mathbb{Z}_2^3$ gauge theory (equivalent to $\mathbb{D}_4$ topological order). We also combine it with the just-in-time decoder to fault-tolerantly prepare the logical T magic state in $O(d)$ rounds via code switching. In 3D, we construct a transversal logical $\sqrt{\text{T}}$ gate in a non-Clifford stabilizer code at the third level of the Clifford hierarchy, located on a tetrahedron corresponding to a twisted $\mathbb{Z}_2^4$ gauge theory. Furthermore, our constructions surpass the Bravyi-König bound by achieving the logical gates in the $(n+1)$-th level of Clifford hierarchy in $n$ spatial dimension.

Kobayashi, Ryohei [Institute for Advanced Study, P↗
DOE OSTI2024

Asymmetric reheating via inverse symmetry breaking

Asymmetric reheating is a generic requirement for models of dark sectors with light species, but its implementation is usually in tension with unique phenomenologies otherwise possible in compelling theories containing dark copies of the Standard Model. We present a simple module to implement asymmetric reheating during a Z 2 -breaking phase above some critical temperature. This reinvigorates the possibility of an exactly degenerate mirror sector and the striking phenomenology of composite particles oscillating into their mirror counterparts. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Magnetic Blocking in Fluoflavine Radical-Bridged Dilanthanide Complexes

Magnetic exchange coupling is difficult to foster in polynuclear lanthanide (Ln) complexes and poorly understood. While coupling Ln ions through closed-shell ligands is inherently weak due to the contracted 4f orbitals, placing open-shell ligands instead has proven to promote orders of magnitude stronger coupling, giving rise to single-molecule magnets (SMMs) innate to real magnetic memory effect in the case of the anisotropic Ln ions. Notably, the impact of radical bridges with differing oxidation states on magnetic blocking remains unexplored due to lack of Ln SMMs with radicals in two distinct charge states. Herein, the first dilanthanide complexes (Ln = Gd, Dy) containing fluoflavine (flv) bridges, [(Cp* 2 Ln) 2 (μ-flv z )]X, (where X = [Al(OC{CF 3 } 3 ) 4 ] − (z = 1−•), 1-Ln; X = 0 (z = 2−), 2-Ln; X =[K(crypt-222)] + (z = 3−•), 3-Ln) are reported. 1-Ln and 3-Ln, comprising the flv 1−• and flv 3−• radical bridges, were investigated via single-crystal X-ray diffraction (SCXRD), ultraviolet−visible (UV−vis) spectroscopy, Superconducting Quantum Interference Device (SQUID) magnetometry, high-field electron paramagnetic resonance (HF-EPR) spectroscopy and broken-symmetry density functional theory (BS-DFT) calculations. 1-Dy and 3-Dy constitute the first SMMs innate to radicals in two differing oxidation states. 1-Dy exhibits a spin-reversal barrier U eff of 28.36 cm −1 and open magnetic hysteresis loops below 3 K. By contrast, 3-Dy displays a much higher U eff of 143(2) cm −1 and open hysteresis loops until 9.5 K, representing a record for dilanthanide SMMs containing an organic radical bridge. The boost in SMM properties in 3-Dy is attributed to spin-phonon coupling and improved frontier orbital structure. This study paves the way for advanced design strategies of polynuclear Ln SMMs.

Benner, Florian [Michigan State Univ., East Lansin↗
DOE OSTI2024

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Abstract Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even$${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the (2 + 1)D cubic * universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O(3) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

Physics↗
DOE OSTI2024

An orbital strategy for regulating the Jahn–Teller effect

ABSTRACT The Jahn–Teller effect (JTE) arising from lattice–electron coupling is a fascinating phenomenon that profoundly affects important physical properties in a number of transition-metal compounds. Controlling JT distortions and their corresponding electronic structures is highly desirable to tailor the functionalities of materials. Here, we propose a local coordinate strategy to regulate the JTE through quantifying occupancy in the ${{d}_{{{z}^2}}}$ and ${{d}_{{{x}^2} - {{y}^2}}}$ orbitals of Mn and scrutinizing the symmetries of the ligand oxygen atoms in MnO6 octahedra in LiMn2O4 and Li0.5Mn2O4. The effectiveness of such a strategy has been demonstrated by constructing P2-type NaLixMn1–xO2 oxides with different Li/Mn ordering schemes. In addition, this strategy is also tenable for most 3d transition-metal compounds in spinel and perovskite frameworks, indicating the universality of local coordinate strategy and the tunability of the lattice–orbital coupling in transition-metal oxides. This work demonstrates a useful strategy to regulate JT distortion and provides useful guidelines for future design of functional materials with specific physical properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗