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Results for “Symmetry protected topological phases”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Obstructions to gapped phases from noninvertible symmetries

Quantum systems in 3+1 dimensions that are invariant under gauging a one-form symmetry enjoy novel noninvertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such noninvertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dual theory with $\mathbb{Z}^{(1)}_N$ one-form symmetry is gapless or spontaneously breaks the self-duality symmetry unless N = k 2 ⁢ℓ where –1 is a quadratic residue modulo . We also extend these results to noninvertible symmetries arising from invariance under more general gauging operations including, e.g., triality symmetries. Along the way, we discover how duality defects in symmetry-protected topological phases have a hidden time-reversal symmetry that organizes their basic properties. These noninvertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Controlling topology through targeted composite symmetry manipulation in magnetic systems

The possibility of selecting magnetic space groups by orienting the magnetization direction or tuning magnetic orders offers a vast playground for engineering symmetry-protected topological phases in magnetic materials. In this work, we study how selective tuning of symmetry and magnetism can influence and control the resulting topology in a two-dimensional magnetic system, and we illustrate such a procedure in the ferromagnetic monolayer MnPSe 3 . Density functional theory calculations reveal a symmetry-protected accidental semimetallic (SM) phase for out-of-plane magnetization, which becomes an insulator when the magnetization is tilted in-plane, reaching band-gap values close to 100 meV. We identify an order-2 composite antiunitary symmetry and threefold rotational symmetry that induce the band crossing, and we classify the possible topological phases using symmetry analysis, which we support with tight-binding and k · p models. Breaking of inversion symmetry opens a gap in the SM phase, giving rise to a Chern insulator. We demonstrate this explicitly in the isostructural Janus compound Mn 2 ⁢P 2 ⁢S 3 ⁢Se 3 , which naturally exhibits Rashba spin-orbit coupling that breaks inversion symmetry. Our results map out the phase space of topological properties of ferromagnetic transition-metal phosphorus trichalcogenides, and they demonstrate the potential of the magnetization-dependent metal-to-insulator transition as a spin switch in integrated two-dimensional electronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Emergent Ergodicity at the Transition between Many-Body Localized Phases

Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. In this work, we conjecture that no direct transition between distinct MBL orders can occur in one dimension; rather, an ergodic phase always intervenes. Motivated by recent advances in Rydberg-atom-based quantum simulation, we propose an experimental protocol where the intervening ergodic phase can be diagnosed via the dynamics of local observables.

1-dimensional spin chains↗
DOE OSTI2021

Comments on foliated gauge theories and dualities in 3+1d

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models. We show that these two classes of foliated field theories enjoy a duality. We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Topological prethermal strong zero modes on superconducting processors

Abstract Symmetry-protected topological phases 1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model 5 . They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations 1–4,6–8 . In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay 9–11 . Here we report the observation of a distinct type of topological edge mode 12–14 , which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach 15–18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.

Science & Technology - Other Topics↗
DOE OSTI2022

Classification of (2 + 1) D invertible fermionic topological phases with symmetry

Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups G f and general values of the chiral central charge c - . Here G f is a central extension of a bosonic symmetry group G b by fermion parity, (-1) F , specified by a second cohomology class [ω 2 ]∈ $\mathscr{H}^2$(Gb,$\mathbb{Z}_2$). Our approach proceeds by gauging fermion parity and classifying the resulting G b symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c - ) 1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c - = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c - and G f . Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with G f symmetry.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Visualizing quasiparticles from quantum entanglement for general one-dimensional phases

In this work, we present a quantum information framework for the entanglement behavior of the low-energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence between the correlation matrix and the QP entanglement Hamiltonian for free fermions and find an extended in-gap state in the QP entanglement Hamiltonian as a consequence of the position uncertainty of the QP. A more general understanding of such an in-gap state can be extended to a Kramers theorem for the QP entanglement Hamiltonian, which also applies to strongly interacting systems. Further, we present a set of ubiquitous entanglement spectrum features, dubbed entanglement fragmentation, conditional mutual information, and measurement-induced nonlocal entanglement for QPs in 1D symmetry protected topological phases. Our result thus provides another framework to identify different phases of matter in terms of their QP entanglement.

1-dimensional spin chains↗
DOE OSTI2022

Dynamical topological phase realized in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase, in a quasiperiodically driven array of ten 171 Yb + hyperfine qubits in Quantinuum’s System Model H1 trapped-ion quantum processor. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. Here, this property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient manipulation of quantum information.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Provably efficient machine learning for quantum many-body problems

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Science & Technology - Other Topics↗
DOE OSTI2020

Symmetry-enriched quantum spin liquids in (3 + 1)d

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Spin splitting of dopant edge state in magnetic zigzag graphene nanoribbons

Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena that have sparked renewed interest in carbon-based spintronics. Zigzag graphene nanoribbons (ZGNRs)-quasi one-dimensional semiconducting strips of graphene bounded by parallel zigzag edges-host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width. Despite recent advances in the bottom-up synthesis of GNRs featuring symmetry protected topological phases and even metallic zero mode bands, the unique magnetic edge structure of ZGNRs has long been obscured from direct observation by a strong hybridization of the zigzag edge states with the surface states of the underlying support. Here, we present a general technique to thermodynamically stabilize and electronically decouple the highly reactive spin-polarized edge states by introducing a superlattice of substitutional N-atom dopants along the edges of a ZGNR. First-principles GW calculations and scanning tunnelling spectroscopy reveal a giant spin splitting of low-lying nitrogen lone-pair flat bands by an exchange field (~850 tesla) induced by the ferromagnetically ordered edge states of ZGNRs. Finally, our findings directly corroborate the nature of the predicted emergent magnetic order in ZGNRs and provide a robust platform for their exploration and functional integration into nanoscale sensing and logic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics

Majorana bosons, that is, tight bosonic analogs of the Majorana fermionic quasiparticles of condensed-matter physics, are forbidden for gapped free bosonic matter within a standard Hamiltonian scenario. We show how the interplay between dynamical metastability and nontrivial bulk topology makes their emergence possible in noninteracting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability, whereby a conserved Majorana boson localized on one edge is paired, in general, with a symmetry generator localized on the opposite edge. We argue that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. Our results suggest that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which persist over practical timescales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice

The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.

Singh, Hersh [Fermilab] (ORCID:0000000220026959)↗
DOE OSTI2026

Gauging nexus between topological and fracton phases

Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases, the X-Cube model in 3+1D can be realized via such a construction by starting with a stack of 2+1D Toric Codes and turning on a coupling which condenses a composite "particle-string" object. In a recent work [Phys. Rev. B 112, 125124 (2025)], we have demonstrated that in fact, the particle-string can be viewed as a symmetry defect of a topological 1-form symmetry. In this paper, we study the result of gauging this symmetry in depth. We unveil a rich gauging web relating the X-Cube model to symmetry protected topological (SPT) phases protected by a mix of subsystem and higher-form symmetries, subsystem symmetry fractionalization in the 3+1D Toric Code, and non-trivial extensions of topological symmetries by subsystem symmetries. Here, our work emphasizes the importance of topological symmetries in non-topological, geometric phases of matter.

Anyons↗
DOE OSTI2023

Rotational symmetry protected edge and corner states in Abelian topological phases

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Discrete theta angles, symmetries and anomalies

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d 4 d QCD with SU(N),SU(N)/\mathbb{Z}_k S U ( N ) , S U ( N ) / ℤ k or SO(N) S O ( N ) gauge groups as well as various 3d 3 d and 2d 2 d gauge theories.

Hsin, Po-Shen↗
DOE OSTI2025

Many-Body Quantum Catalysts for Transforming Between Phases of Matter

A catalyst is a substance that enables otherwise impossible transformations between states of a system, without being consumed in the process. In this work, we apply the notion of catalysts to many-body quantum physics. In particular, we construct catalysts that enable transformations between different symmetry-protected topological (SPT) phases of matter using symmetric finite-depth quantum circuits. We discover a wide variety of catalysts, including GHZ-like states that spontaneously break the symmetry, gapless states with critical correlations, topological orders with symmetry fractionalization, and spin-glass states. These catalysts are all united under a single framework that has close connections to the theory of quantum anomalies, and we use this connection to put strong constraints on possible pure- and mixed-state catalysts. We also show how the catalyst approach leads to new insights into the structure of certain phases of matter, and to new methods to efficiently prepare SPT phases with long-range interactions or projective measurements.

quantum many-body systems↗
DOE OSTI2022

Chiral-Symmetric Higher-Order Topological Phases of Matter

Herein, we introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by “multipole chiral numbers,” bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order topological phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗