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Results for “Topological Field Theories”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Axion insulator state in ferromagnetically ordered CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructures

Ferromagnetic (FM) axion insulators may greatly simplify experimental explorations of the topological magnetoelectric effect, as the FM ordering can be stable in a broad range of magnetic field. Through density functional theory calculations and four-band model studies, we find that two-dimensional van der Waals FM CrI 3 and MnBi 2 Se 4 overlayers induce opposite-sign exchange fields in the topological surface states of Bi 2 Se 3 film when they are ferromagnetically ordered. As a consequence, the CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructure is a robust FM axion insulator, according to surface-resolved Berry curvature calculations. Our work opens up opportunities for the design of materials with the topological magnetoelectric effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions

The topological structure of vacuum is the cornerstone of non-Abelian gauge theories describing strong and electroweak interactions within the standard model of particle physics. However, transitions between different topological sectors of the vacuum (believed to be at the origin of the baryon asymmetry of the Universe) have never been observed directly. Additionally, an experimental observation of such transitions in quantum chromodynamics (QCD) has become possible in heavy-ion collisions, where the chiral magnetic effect converts the chiral asymmetry (generated by topological transitions in hot QCD matter) into an electric current, under the presence of the magnetic field produced by the colliding ions. The Relativistic Heavy Ion Collider programme on heavy-ion collisions such as the zirconium-zirconium and ruthenium-ruthenium isobars thus has the potential to uncover the topological structure of vacuum in a laboratory experiment. This discovery would have far-reaching implications for the understanding of QCD, the origin of the baryon asymmetry in the present-day Universe, and other areas, including condensed matter physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets

Abstract Emergent axion electrodynamics in magneto-electric media is expected to provide novel ways to detect and control material properties with electromagnetic fields. However, despite being studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Here, we introduce a theory of axion electrodynamics at general frequencies. We define a proper optical axion magneto-electric coupling through its relation to optical surface Hall conductivity and provide ways to calculate it in lattice systems. By employing our formulas, we show that axion electrodynamics can lead to a significant Kerr effect in thin-film antiferromagnets at wavelengths that are seemingly too long to resolve the spatial modulation of magnetism. We identify the wavelength scale above which the Kerr effect is suppressed. Our theory is particularly relevant to materials like MnBi 2 Te 4 , a topological antiferromagnet whose magneto-electric response is shown here to be dominated by the axion contribution even at optical frequencies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Absence of quantization in the circular photogalvanic effect in disordered chiral Weyl semimetals

The circularly polarized photogalvanic effect (CPGE) is studied in chiral Weyl semimetals with short-range quenched disorder. Without disorder, the topological properties of chiral Weyl semimetals lead to quantization of the CPGE, which is a second-order optical response. Furthermore, using a combination of diagrammatic perturbation theory in the continuum and exact numerical calculations via the kernel polynomial method on a lattice model, we show that disorder perturbatively destabilizes the quantization of the CPGE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Fermi surfaces of the topological semimetal CaSn 3 probed through de Haas van Alphen oscillations

Abstract In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta (TRIM) in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn 3 with torque magnetometry in high magnetic fields up to 35 T. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn 3 enclose an odd number of TRIM, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn 3 .

Physics↗
DOE OSTI2023

Theoretical investigations on Kerr and Faraday rotations in topological multi-Weyl Semimetals

Motivated by the recent proposal of giant Kerr rotation in WSMs, we investigate the Kerr and Faraday rotations in time-reversal broken multi-Weyl semimetals (mWSMs) in the absence of an external magnetic field. Using the framework of Kubo response theory, we find that both the longitudinal and transverse components of the optical conductivity in mWSMs are modified by the topological charge ( n n ). Engendered by the optical Hall conductivity, we show in the thin film limit that, while the giant Kerr rotation and corresponding ellipticity are independent of n n , the Faraday rotation and its ellipticity angle scale as n n and n^2 n 2 , respectively. In contrast, the polarization rotation in semi-infinite mWSMs is dominated by the axion field showing n n dependence. In particular, the magnitude of Kerr (Faraday) angle decreases (increases) with increasing n n in Faraday geometry, whereas in Voigt geometry, it depicts different n n -dependencies in different frequency regimes. The obtained results on the behavior of polarization rotations in mWSMs could be used in experiments as a probe to distinguish single, double, and triple WSMs, as well as discriminate the surfaces of mWSMs with and without hosting Fermi arcs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

42 ENGINEERING↗
DOE OSTI2021

Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion

Highlights: • The effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling lead to the 2D topological semimetal. • The ground state phase diagram is calculated. • The topological semimetal phase is characterized by the zero energy Majorana states. In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin–orbit Rashba coupling and the Coulomb repulsion. The spin–orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. Topological phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The region of existence of the zero energy Majorana states tends to zero at the point of the Mott phase transition. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model).

36 MATERIALS SCIENCE↗
DOE OSTI2020

A topological way of finding solutions to the Yang–Mills equation

We propose a systematic way of finding solutions to the classical Yang–Mills equation with nontrivial topology. This approach is based on one of the Wightman axioms for quantum field theory, which is referred to as the form invariance condition in this paper. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general ansatz, a systematic way of solving the Yang–Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases, as well as producing new solutions not previously reported in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

AdS 2 holography and effective QFT

We discuss AdS 2 quantum gravity from an unconventional perspective that emphasizes bulk geometry. In our approach, AdS 2 has no boundary, there are no divergences that require renormalization, and the dilaton of JT-gravity can be omitted altogether. The result is the standard Schwarzian theory. However, it may be advantageous that our derivation just relies on conventional AdS/CFT correspondence and effective quantum field theory. For example, it clarifies the symmetry breaking pattern. It also puts the non-compact AdS 2 topology on the same footing as compact Riemann surfaces.

2D Gravity↗
DOE OSTI2021

Quantum algorithms for open lattice field theory

Certain aspects of some unitary quantum systems are well described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be accommodated in a corresponding unitary system + environment model via a generalization of Wigner-Weisskopf theory. This demonstrates the physical relevance of novel features such as exceptional points in quantum dynamics, and opens up avenues for studying many-body systems in the complex plane of coupling constants. In the case of lattice field theory, sparsity lends these channels the promise of efficient simulation on standardized quantum hardware. We thus consider quantum operations that correspond to Suzuki-Lie-Trotter approximation of lattice field theories undergoing nonunitary time evolution, with potential applicability to studies of spin or gauge models at finite chemical potential, with topological terms, to quantum phase transitions—a range of models with sign problems. We develop non-Hermitian quantum circuits and explore their promise on a benchmark, the quantum one-dimensional Ising model with complex longitudinal magnetic field, showing that observables can probe the Lee-Yang edge singularity. The development of attractors past critical points in the space of complex couplings indicates a potential for study on near-term noisy hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Plethora of tunable Weyl fermions in kagome magnet Fe 3 Sn 2 thin films

Interplay of magnetism and electronic band topology in unconventional magnets enables the creation and fine control of novel electronic phenomena. In this work, we use scanning tunneling microscopy and spectroscopy to study thin films of a prototypical kagome magnet Fe 3 Sn 2 . Our experiments reveal an unusually large number of densely-spaced spectroscopic features straddling the Fermi level. These are consistent with signatures of low-energy Weyl fermions and associated topological Fermi arc surface states predicted by theory. By measuring their response as a function of magnetic field, we discover a pronounced evolution in energy tied to the magnetization direction. Electron scattering and interference imaging further demonstrates the tunable nature of a subset of related electronic states. Our experiments provide a direct visualization of how in-situ spin reorientation drives changes in the electronic density of states of the Weyl fermion band structure. Combined with previous reports of massive Dirac fermions, flat bands, and electronic nematicity, our work establishes Fe 3 Sn 2 as an interesting platform that harbors an extraordinarily wide array of topological and correlated electron phenomena.

36 MATERIALS SCIENCE↗
DOE OSTI2025

String membrane nets from higher-form gauging: An alternate route to 𝑝-string condensation

We present a new perspective on the $p$-string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in 3+1D that is generated by Abelian anyons in isotropic stacks of 2+1D topological orders naturally results in a 3+1D $p$-string condensed phase, providing a controlled non-perturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and one-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: in field theory, we derive the foliated field theory description of the $\mathbb{Z}_N$ X-Cube model by gauging a higher-form symmetry in stacks of 2+1D $\mathbb{Z}_N$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$-graded string-net models leads to string-membrane-nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d \geq 2$ and provides a step towards building an algebraic theory of $p$-string condensation.

Anyons↗
DOE OSTI2024

AdS 3 Einstein gravity and boundary description: pedagogical review

We review the various aspects of the 3D Einstein gravity theory with a negative cosmological constant and its boundary description. We also explore its connections to conformal field theories (CFTs), modular symmetry, and holography. It is worth noting that this particular theory is topological in nature, which means that all the physical degrees of freedom are located on the boundary. Additionally, we can derive the boundary description on a torus, which takes the form of a 2D Schwarzian theory. This observation suggests that the relevant degrees of freedom for the theory can be described using this 2D theory. Because of the renormalizability of the 3D gravity theory, one can probe the quantum regime. This suggests that it is possible to investigate quantum phenomena. Unlike the conventional CFTs, when considering the AdS 3 background, the boundary theory loses modular symmetry. This represents a departure from the usual behavior of CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs, and we indicate that applying this transformation to the 2D Schwarzian theory leads to similar results. Summing over all geometries with the asymptotic AdS 3 boundary condition is equivalent to summing over a modular group. The partition function is one-loop exact and therefore an analytical expression from the summation. This theory holds potential applications in Quantum Information and is a recurring theme in the study of holography, where gravitational theories are connected with CFTs.

2D Schwarzian theory↗
DOE OSTI2022

Thermalization of Gauge Theories from their Entanglement Spectrum

Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the entanglement structure of Z 2 lattice gauge theory in (2 + 1) spacetime dimensions. Here we demonstrate Li and Haldane’s conjecture, and show consistency of the entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying nonequilibrium dynamics after a quench, we provide an extensive description of thermalization in Z 2 gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients α = 0.8 ± 0.2 and β = 0.0 ± 0.1 at intermediate times, and finally thermal saturation of the von Neumann entropy.

2-dimensional systems↗
DOE OSTI2023

Quantum Computation of Dynamical Quantum Phase Transitions and Entanglement Tomography in a Lattice Gauge Theory

Strongly coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute nonequal-time correlation functions and perform entanglement tomography of nonequilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently predicted dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent nonequilibrium dynamics in three ways: (i) overlap echos signaling dynamical transitions, (ii) nonequal-time correlation functions with an underlying topological nature, and (iii) the entanglement structure of nonequilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Extracting the Quantum Hall Conductance from a Single Bulk Wave Function

In this work, we propose a new formula that extracts the quantum Hall conductance from a single (2+1)⁢ D gapped wave function. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow, i.e., unitary dynamics generated from the entanglement structure of the wave function. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a noninteracting Chern band where excellent agreement is obtained.

2-dimensional systems↗
DOE OSTI2021

Meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets

The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet Co 8 Zn 9 Mn 3 confirms that the skyrmion crystals discovered in 2009 are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current challenge is to find the combinations of these ingredients that produce specific topological spin textures. In this work, we report a simple mechanism for the stabilization of meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. In particular, the meron/skyrmion crystals can form even in absence of magnetic field. The application of magnetic field leads to a rich variety of topological spin textures that survive in the long wavelength limit of the theory. When conduction electrons are coupled to the spins, these topological spin textures twist the electronic wave functions to induce Chern insulators and Weyl semimetals for specific band filling fractions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗