non-Abelian Symmetry Research Articles

Theory of quantum circuits with Abelian symmetries

Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed-matter theory and quantum thermodynamics. However, despite their widespread use, fundamental properties of such circuits are not well understood. Recently, it was found that generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry. This observation raises important open questions: What unitary transformations can be realized with k-local gates that respect a global symmetry? In other words, in the presence of a global symmetry, how does the locality of interactions constrain the possible time evolution of a composite system? In this work, we address these questions for the case of Abelian (commutative) symmetries and develop constructive methods for synthesizing circuits with such symmetries. Remarkably, as a corollary, we find that, while the locality of interactions still imposes additional constraints on realizable unitaries, certain restrictions observed in the case of non-Abelian symmetries do not apply to circuits with Abelian symmetries. For instance, in circuits with a general non-Abelian symmetry such as SU(d), the unitary realized in a subspace with one irreducible representation (charge) of the symmetry dictates the realized unitaries in multiple other sectors with inequivalent representations of the symmetry. Furthermore, in certain sectors, rather than all unitaries respecting the symmetry, the realizable unitaries are the symplectic or orthogonal subgroups of this group. We prove that none of these restrictions appears in the case of Abelian symmetries. This result suggests that global non-Abelian symmetries may affect the thermalization of quantum systems in ways not possible under Abelian symmetries. Published by the American Physical Society 2024

Unraveling T duality: Magnetic quivers in rank-zero little string theories

An intriguing class of 6D supersymmetric theories are known as little strings theories, which exhibit a rich network of T-dualities. A robust feature of these theories are their Higgs branches. Focusing on the little string theories that are realized on a single curve of zero self-intersection, we utilize brane systems to derive the magnetic quivers. Using a variety of techniques (including branching rules, brane dynamics, F-theory geometry, quiver subtraction, and the decay and fission algorithm), we detail the Higgs branch Hasse diagram and determine the transverse slices for every elementary Higgs branch RG-flow. Building on these insights, we pursue two directions: first, we infer potential T-dual models by linking changes in 2-group structure constants along Higgs branch RG-flows to the RG-flow transition types encoded in the Hasse diagram. Second, we conjecture an algorithm for the non-Abelian flavor symmetry of the compactified little string theory by inspecting the magnetic quivers of all T-dual frames. Published by the American Physical Society 2024

Symmetry-Enforced Entanglement in Maximally Mixed States

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is “strongly symmetric,” i.e., it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., SU(2)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qudits N. Published by the American Physical Society 2024

QSpace - An open-source tensor library for Abelian and non-Abelian symmetries

QSpace - An open-source tensor library for Abelian and non-Abelian symmetries

T-dualities in gauged linear sigma models

In this paper, we describe non-Abelian T-dualities for a two-dimensional (2D) gauged linear sigma model (GLSM) with [Formula: see text] supersymmetry (SUSY). We start with the case of left and right SUSY [Formula: see text], [Formula: see text] gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group [Formula: see text], whose original model is the resolved conifold. We analyze the dual model and compute the periods on the dual geometry, matching the effective potential for the [Formula: see text] gauge field, and discussing the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with [Formula: see text] SUSY, analyzing the case of global symmetry [Formula: see text]. In this case, the full non-Abelian duality can be solved. The dual geometries with and without nonperturbative corrections to the superpotential coincide. The structure of the dual nonperturbative corrections is determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories.

Non-Abelian symmetry-resolved entanglement entropy

We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-Abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-Abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-Abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the Abelian case, new phenomena arise from the interplay of locality and non-Abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2)SU(2) symmetry.

Tensor Network State Algorithms on AI Accelerators.

We introduce novel algorithmic solutions for hybrid CPU-multiGPU tensor network state algorithms utilizing non-Abelian symmetries building on AI-motivated state-of-the-art hardware and software technologies. The presented numerical simulations on the FeMo cofactor, which plays a crucial role in converting atmospheric nitrogen to ammonia, are far beyond the scope of traditional approaches. Our large-scale SU(2) spin adapted density matrix renormalization group calculations up to bond dimension D = 216 on complete active space (CAS) size of 18 electrons in 18 orbitals [CAS(18, 18)] demonstrate that the current limit of exact solution, i.e. full-CI limit, can be achieved in fraction of time. Furthermore, benchmarks up to CAS(113, 76) demonstrate the utilization of NVIDIA's highly specialized AI accelerators via NVIDIA Tensor Cores, leading to performance around 115 TFLOPS on a single node supplied with eight NVIDIA A100 devices. As a consequence of reaching 71% of the full capacity of the hardware, the cubic scaling of computational time with bond dimension can be reduced to a linear form for a broad range of D values; thus, breaking the current computational limits of small CAS spaces in ab initio quantum chemistry and material science is becoming a reality. In comparison to strict U(1) implementations with matching accuracy, our solution has an estimated effective performance of 300-500 TFLOPS, which emphasizes the mutual need for both algorithmic and technological developments to push current frontiers on classical computation.

The breaking of μ − τ reflection symmetry in a B − L extended 3HDM with (Z2 × Z4)⋊Z2 (II) symmetry

We propose a new neutrino mass matrix texture satisfying the μ−τ reflection symmetry in a B−L model with three Higgs doublets based on non-Abelian discrete symmetry (Z2×Z4)⋊Z2(II). The Dirac and Majorana mass matrices, which is motivated in the framework of the Type I seesaw mechanism in association with (Z2×Z4)⋊Z2(II) symmetry, hint for a realistic lepton mixing pattern where the co-bimaximal mixing pattern is broken by the charged-lepton contribution. The hierarchy of lepton masses is naturally achieved and the constraints on the effective neutrino mass are consistent with the recent experimental limits.

The eclectic flavor symmetries of T2/ℤK orbifolds

Only four T2/ℤK orbifold building blocks are admissible in heterotic string compactifications. We investigate the flavor properties of all of these building blocks. In each case, we identify the traditional and modular flavor symmetries, and determine the corresponding representations and (fractional) modular weights of the available massless matter states. The resulting finite flavor symmetries include Abelian and non-Abelian traditional symmetries, discrete R symmetries, as well as the double-covered finite modular groups (S3 × S3) ⋊ ℤ4, T′, 2D3 and S3 × T′. Our findings provide restrictions for bottom-up model building with consistent ultraviolet embeddings.

Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set.

Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene (D6h) in correlation-consistent polarized basis sets of both double- and triple-ζ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.

Neutrino Masses from Generalized Symmetry Breaking

We explore generalized global symmetries in theories of physics beyond the standard model. Theories of Z′ bosons generically contain “noninvertible” chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well motivated U(1)Lμ−Lτ, there is a noninvertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g., U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas, e.g., yν∼yτexp(−Sinst). These theories require no bevy of new fields nor additional global symmetries but are instead simple, natural, and predictive: The discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry. Published by the American Physical Society 2024

Phenomenology of the flavor symmetric scoto-seesaw model with dark matter and TM1 mixing

We propose a hybrid scoto-seesaw model based on the A4×Z4×Z3×Z2 non-Abelian discrete flavor symmetry. Light neutrino masses come from the tree-level type-I seesaw mechanism, and from the one-loop scotogenic contribution accommodating viable dark matter candidates responsible for the observed relic abundance of dark matter (DM). These contributions restore the atmospheric and solar neutrino mass scales, respectively. With only one right-handed neutrino, the model features specific predictions with the normal ordering of light neutrino masses, the lightest neutrino being massless, and only one relevant CP Majorana phase. Further, an experimentally favorable TM1 mixing scheme is realized with concrete correlations and constraints on the mixing angles and associated CP phases. The model predicts the atmospheric mixing angle to be in the upper octant with specific ranges 0.531(0.580)≤sin2θ23≤0.544(0.595), and the Dirac CP phase is restricted within the range ±(1.44–1.12) rad. The Majorana phase is also tightly constrained, with the ranges 0.82–0.95 and 1.58–1.67 rad, which are otherwise unconstrained from neutrino oscillations. Strict predictions on the Majorana phases also yield an accurate prediction for the effective mass parameter for neutrinoless double beta within the range of 1.61–3.85 meV. The model offers a rich phenomenology regarding DM relic density and direct-search constraints, and the fermionic DM scenario has been discussed in detail, estimating its possible connection with the neutrino sector. As an example of the model studies at colliders, the SM Higgs in the diphoton decay channel is examined. The model predicts strictly vanishing τ→eγ, τ→3e decays and testable signals by MEG-II and SINDRUM/Mu3e experiments for the μ→eγ and μ→3e decays, respectively. Published by the American Physical Society 2024

Dynamical origin of neutrino masses and dark matter from a new confining sector

A dynamical mechanism, based on a confining non-Abelian dark symmetry, which generates Majorana masses for hyperchargeless fermions, is proposed. We apply it to the inverse seesaw scenario, which allows us to generate light neutrino masses from the interplay of TeV-scale pseudo-Dirac mass terms and a small explicit breaking of lepton number. A single generation of vectorlike dark quarks, transforming under a SU(3)D gauge symmetry, is coupled to a real singlet scalar, which serves as a portal between the dark quark condensate and three generations of heavy sterile neutrinos. Such a dark sector and the Standard Model (SM) are kept in thermal equilibrium with each other via sizable Yukawa couplings to the heavy neutrinos. In this framework, the lightest dark baryon, which has spin 3/2 and is stabilized at the renormalizable level by an accidental dark baryon number symmetry, can account for the observed relic density via thermal freeze-out from annihilations into the lightest dark mesons. These mesons, in turn, decay to heavy neutrinos, which produce SM final states upon decay. This model may be probed by next generation neutrino telescopes via neutrino lines produced from dark matter annihilations. Published by the American Physical Society 2024

Extended doubled structures of algebroids for gauged double field theory

We study an analogue of the Drinfel’d double for algebroids associated with the O(D, D + n) gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a “tripled”, which we call the extended double, rather than the “doubled” structure appearing in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a (2D + n)-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.

Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} × \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} dependence of leptogenesis in minimal Left-Right Symmetric Model with different strengths of Type-II seesaw mass

Left Right Symmetric Model (LRSM) being an extension of the Standard model of particle physics incorporates within itself Type-I and Type-II seesaw mass terms naturally. Both the mass terms can have significant amount of contribution to the resulting light neutrino mass within the model and hence on the different phenomenology associated within. In this paper, we have thoroughly analyzed and discussed the implications of specifying different weightages to both the mass terms and also the study has been carried out for different values of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} which is mass of the right-handed gauge boson. This paper also gives a deeper insight into the new physics contributions of Neutrinoless Double Beta Decay (0νββ) and their variations with the net baryon asymmetry arising out of the model. Therefore, the main objective of the present paper rests on investigating the implications of imposing different weightage to the type-I and type-II seesaw terms and different values of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{{W}_{R}}$$\\end{document} on the new physics contributions of 0νββ and net baryon asymmetry arising out as a result of resonant leptogenesis. LRSM in this work has been realized using modular group of level 3, Γ(3) which is isomorphic to non-abelian discrete symmetry group A4, the advantage being the non-requirement of flavons within the model and hence maintaining the minimality of the model.

Mirror map for Landau-Ginzburg models with nonabelian groups

BHK mirror symmetry as introduced by Berglund–Hübsch and Marc Krawitz between Landau–Ginzburg (LG) models has been the topic of much study in recent years. An LG model is determined by a potential function and a group of symmetries. BHK mirror symmetry is only valid when the group of symmetries is comprised of the so-called diagonal symmetries. Recently, an extension to BHK mirror symmetry to include nonabelian symmetry groups has been conjectured. In this article, we provide a mirror map at the level of state spaces between the LG A-model state space and the LG B-model state space for the mirror model predicted by the BHK mirror symmetry extension for nonabelian LG models. We introduce two technical conditions, the Diagonal Scaling Condition, and the Equivariant Φ condition, under which a bi-degree preserving isomorphism of state spaces (the mirror map) is guaranteed to exist, and we prove that the condition is always satisfied if the permutation part of the group is cyclic of prime order.

Modular flavor models with positive modular weights: a new lepton model building

We propose an interesting assignment of positive modular weights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries which possess good testability in current experiments. At first, we discuss possibilities for positive modular weights from a theoretical point of view. Then we show concrete examples of inverse seesaw and linear seesaw scenarios applying modular A4 symmetry as examples and demonstrate some predictions as well as consistency with experimental results such as neutrino masses and mixings.

Invariants of magnetic lines for Yang-Mills solutions

We construct a new Yang-Mills 3D-solution on the space of negative scalar curvature. We discuss a problem of non-abelian gauge symmetry is broken with the assumption that a scalar curvature of the domain is a negative small parameter. In this case we use the following fact: a geometrical scale related with Vassiliev's discriminant of magnetic lines coincides with a phisical Kolmogorov scale. This gives an estimation of α-effect by the dispersion of the asymptotic ergodic Hopf invariant in the asymptotic limit with a negative scalar curvature parameter.

General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.