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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Fermionic shift symmetries in (anti) de Sitter space

We study extended shift symmetries that arise for fermionic fields on anti-de Sitter (AdS) space and de Sitter (dS) space for particular values of the mass relative to the curvature scale. We classify these symmetries for general mixed-symmetry fermionic fields in arbitrary dimension and describe how fields with these symmetries arise as the decoupled longitudinal modes of massive fermions as they approach partially massless points. For the particular case of AdS 4 , we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. We study from this perspective the minimal such theory, the Akulov-Volkov theory on AdS 4 , which is a non-linear theory of a spin-1/2 Goldstino field that describes the spontaneous breaking of $\mathcal{N}$ = 1 supersymmetry on AdS 4 down to the isometries of AdS 4 . We show how to write the nonlinear supersymmetry transformation for this theory using the fermionic ambient space formalism. We also study the Lie superalgebras of candidate multi-field examples and rule out the existence of a supersymmetric special galileon on AdS 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2024

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Cross-Coupling Reaction↗
DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗
DOE OSTI2025

Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons

The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.

Chern numbers↗
DOE OSTI2021

Lowest-dimensional portals to SU( N ) exotics

New matter fields charged under the strong nuclear force would have dramatic phenomenological implications. In this work, we systematically explore how these new states, which we postulate belong to some representation of SU(3) of quantum chromo-dynamics, could interact with standard model fields: We analyze all lowest-dimensional “portal” operators for any SU(3) representation, and motivated by grand unification, we extend our results to SU( N ) for N > 3. We provide a publicly available python code, “tessellation,” that automatically constructs said lowest-dimensional portal operators for any new exotic matter field charged under SU( N ) for any N .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Topological Invariant of Manifolds in Slawianowski’s Field Theory [Slides]

Witten constructed topological invariants of manifolds by introducing actions depending only on smooth structures of the manifold without using a metric. He focused on an example of Chern-Simons’ theory on 3D manifolds. Slawianowski based his field theory on frame/coframe fields without a metric. A Witten-type topological invariant can be introduced in Slawianowski’s framework, using an integral over the reper fields. Such invariant behaves differently for group manifolds than for all others. It additionally distinguishes semi-simple Lie group manifolds from other group manifolds. Further study of this new invariant is needed, including possible generalizations to other field theories.

42 ENGINEERING↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Nonperturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1) dimensions

In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group G f of the ground state splits as G f = G b × $Z^f_2$, where $Z^f_2$ is generated by fermion parity, (–1) F . In contrast, (2+1)-dimensional [(2+1)D] topological superconductors (TSC) can host unpaired MZMs at defects even when G f is not of the form G b × $Z^f_2$. In this paper we study how G f together with the chiral central charge c – strongly constrain the existence of unpaired MZMs and the quantum numbers of symmetry defects. Our results utilize a recent algebraic characterization of (2+1)D invertible fermionic topological states, which provides a non-perturbative approach based on topological quantum field theory, beyond free fermions. We study physically relevant groups such as U(1) f $\rtimes$ H, SU (2) f × H, U(2) f $\rtimes$ H, generic Abelian groups, as well as more general compact Lie groups, antiunitary symmetries and crystalline symmetries. Further, we present an algebraic formula for the fermionic crystalline equivalence principle, which gives an equivalence between states with crystalline and internal symmetries. In light of our theory, we discuss several previously proposed realizations of unpaired MZMs in TSC materials such as Sr 2 RuO 4 , transition metal dichalcogenides and iron superconductors, in which crystalline symmetries are often important; in some cases we present additional predictions for the properties of these models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2022

Entropic order parameters in weakly coupled gauge theories

The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Topological symplectic Kondo effect

Multiple conduction channels interacting with a quantum impurity—a spin in the conventional “multichannel Kondo effect” or a topological mesoscopic device (“topological Kondo effect”)—has been proposed as a platform to realize anyonic quasiparticles. However, the above implementations require either perfect channel symmetry or the use of Majorana fermions. Here, in this work, we propose a Majorana-free mesoscopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and parafermions) even in the absence of perfect channel symmetry. In addition to the detailed prescription of the implementation, we present the strong coupling solution by mapping the model to the multichannel Kondo effect associated to an internal symmetry and exploit conformal field theory to predict the nontrivial scaling of a variety of observables, including conductance, as a function of temperature. This work does not only open the door for robust Kondo-based anyon platforms, but also sheds light on the physics of strongly correlated materials with competing order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb 2

EuMnSb 2 is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. In this study we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline 151 Eu Mössbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below T N Mn = 323 (1) K with the ordered Mn magnetic moment μ Mn lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below T N Eu1 = 23 (1) K with the ordered Eu magnetic moment μ Eu canted away from the layer normal and μ Mn retaining its higher temperature order. μ Eu is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $\mathcal{Pn'm'a'}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below T N Eu2 =9 (1) K reveals a third AFM phase where μ Mn remains unchanged but μ Eu develops an additional substantial in-plane canting. This phase has MSG $\mathcal{P11}$ $\frac{2_1}{a′}$. We also find some evidence of short-range magnetic correlations associated with the Eu between 12 K≲ T≲ 30 K . Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in EuMnSb 2 and their potential for tuning topological properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Symmetric Mass Generation with Four SU(2) Doublet Fermions

We study a single exactly massless staggered fermion in the fundamental representation of an SU(2) gauge group. We utilize an nHYP-smeared fermion action supplemented with additional heavy Pauli-Villars fields that serve to decrease lattice artifacts. The phase diagram exhibits a clear two-phase structure with a conformal phase at weak coupling and a novel new phase, the symmetric mass generation (SMG) phase, appearing at strong coupling. The SMG phase is confining with all states gapped and chiral symmetry unbroken. Our finite size scaling analysis provides strong evidence that the phase transition between these two phases is continuous, which would allow for the existence of a continuum SMG phase. Furthermore, the renormalization group flows are consistent with a 𝛽 function that vanishes quadratically at the new fixed point, suggesting that the 𝑁 𝑓 = 4 flavor SU(2) gauge theory lies at the opening of the conformal window.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Less Common Topological Phenomena in Bulk Materials

"Prediction and subsequent discovery of topological insulators is considered to be one of the main results in condensed matter physics in the last decades. Not surprisingly, it has received major attention of both researchers and funding agencies. This attention is well-deserved; yet, one cannot but note that nearly all this research revolves about essentially the same concept: electronic excitations with linear dispersion, covering, of course, such diverse and intriguing phenomena as topological insulator, bulk Dirac states (or Weyl, if not spin degenerate), Mayorana fermions. In this project, we will address, mainly, other topological phenomena, such as topologically nontrivial magnetic patterns (as, for instance, topological Hall and related phenomena). Specifically, we propose three interrelated trusts: (1) Time-reversal symmetry breaking nonrelativistic antiferromagnets, called altermagnets. These are materials that break Kramers degeneracy of electronic bands, despite having zero net magnetization by symmetry and being fully collinear, and not necessarily non-centrosymmetric. The corresponding band structure is very similar to the band structure in non-centrosymmetric spin-orbital materials, but materials that we propose to study are distinctly different, first and foremost in the sense that despite sharing many aspects of their electronic properties with the latter, they break the time-reversal symmetry without either spin-orbit coupling or lack of inversion symmetry. (2) Topologically nontrivial magnetic spirals. The PI has been engaged with the experimental group of Dr. Ghimire at GMU investigating Dirac materials with helical magnetism, based on stacked magnetic Kagome layers, with a generic formula of RMn6Sn6. In particular, Y Mn6Sn6 demonstrates a component of the Hall effect that is naturally interpreted in terms of a topological spin texture, as well as linear magnetoresistance. Our calculation identify Dirac states that are robust with respect to the spiral formation, and let us derive an advance mean-field model explaining the observed phase diagram. This model predicted four distinct phases, with very distinct properties, which have now been seen in neutron experiments. The same compound is known to demonstrate topological Hall effect in a particular magnetic phase, and only at elevated temperature. Based on our understanding of the phase diagram, we have worked out a phenomenological theory of a chiral (skyrmionic) response to an external magnetic field, similar to the nematic response to external strain in Fe-based superconductors, which is possible in a centrosymmetric lattice and without interplanar Dzyaloshinskii-Moriya interaction. This phenomenological theory agrees quantitatively with the experiment. It is in our plans to research other similar materials for this effect. (3) Search for 3D analogues of Fe-based superconductors. We want to investigate materials that can be viewed as 3D analogues of FeSe. Specifically, we want materials that are good metals and host antiferromagnetism, which can be suppressed by pressure and generate an s-wave superconductivity, as in Fe-based superconductors. We have in mind some candidates already. This work will proceed in close collaboration with the experimental group of Prof. Nirmal Ghimire in the same department, whose expertise lies in sample making, magnetometry and transport measurements of materials with complex magnetic structures."

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Microscopic study of the coupled-wire construction and plausible realization in spin-dependent optical lattices

Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong-coupling limits, which impose severe constraints on the physical systems where they could be realized. In this work, we investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong interwire tunneling. Contrary to previous studies relying on renormalization group arguments, our microscopic approach exposes the connection between coupled-wire constructions and model wave functions in continuum Landau levels. Then, we use exact-diagonalization methods to investigate the appearance of these fractional quantum Hall states in more realistic settings. We examine the parameter regimes where these strongly correlated phases arise, and provide a way to detect their appearance in cold-atom experiments through standard time-of-flight measurements. Motivated by this experimental probe, we finally propose a realization of our model with cold atoms in spin-dependent optical lattices. Our estimates show that the previous fractional quantum Hall phases lie within experimentally accessible parameter regimes, giving a viable route toward their experimental study.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗