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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking

Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

Shah, Jeet [University of Maryland, College Park, ↗
DOE OSTI2024

Nonlocal Finite-Depth Circuits for Constructing Symmetry-Protected Topological States and Quantum Cellular Automata

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are . Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with k - gates, i.e., gates that act on no more than k degrees of freedom but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric k -local gates that create symmetry-protected topological (SPT) states from an initial product state. Our construction applies to SPT states protected by global symmetries or subsystem symmetries but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of k -local gates. These results imply that the topological classifications of SPT phases and quantum cellular automata both collapse to a single trivial phase in the presence of k -local interactions. We furthermore argue that SPT phases are fragile to k -local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Carbon-Based Quantum Information Science with Symmetry Protected Topological States (Final Report, DOE-BES award DE-SC0023105)

This research program established the scientific foundation for the rational, bottom-up design, synthesis, isolation, and investigation of symmetry-protected topological (SPT) electron spin qubits embedded in graphene nanoribbons (GNRs). The work focused on integrating atomically precise low-dimensional carbon nanostructures with emerging quantum logic architectures, providing a pathway toward scalable quantum materials for next-generation computing and sensing technologies. A central component of the program was the elucidation of fundamental relationships between real-space molecular architecture, local spin density distributions, electronic band dispersion, and energy level alignment in atomically precise GNR systems. These correlations define key operational parameters of SPT qubits and were systematically investigated to establish quantitative benchmarks against established molecular and solid-state spin qubit platforms. Attention was given to properties critical for quantum device performance, e.g. decoherence times, spectral sharpness of energy transitions, and tunable exchange interactions between spin states. The research demonstrated that these parameters can be engineered with atomic precision through scalable bottom-up synthetic strategies. Theory-guided design played a central role in identifying candidate structures hosting topologically protected spin states. Experimental validation was performed using both ensemble measurements and single-molecule characterization. In addition to advances in quantum materials synthesis, the program developed and applied spin-sensitive scanning probe microscopy techniques capable of directly probing quantum states and dynamic processes with atomic-scale spatial resolution. These capabilities enabled direct observation and characterization of quantum structures at the single-atom level. While the research activities were primarily hypothesis-driven fundamental investigations, the program adopted a comprehensive materials-by-design framework aimed at translating scientific discoveries into technological concepts compatible with scalable and intelligent manufacturing approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

We establish a holographic duality between d -dimensional mixed-state symmetry-protected topological (mSPT) phases and ( d + 1 ) -dimensional subsystem symmetry-protected topological (SSPT) states. Specifically, we show that the reduced density matrix of the boundary layer of a ( d + 1 ) -dimensional SSPT state with subsystem symmetry S and global symmetry G corresponds to a d -dimensional mSPT phase with strong S and weak G symmetries. Conversely, we demonstrate that the wave function of an SSPT state can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT phase. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wave functions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPT phases that are unique to open quantum systems, without pure-state analogues. We show that strange correlators and twisted Rényi- N correlators can diagnose these nontrivial phases and we explore their connection to strange correlators in pure-state SSPT phases. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT phases through the duality. Published by the American Physical Society 2025

Sun, Shijun (ORCID:0000000168880030)↗
DOE OSTI2023

Winding θ and destructive interference of instantons

While the θ dependence of field theories is 2π periodic, the ground-state wavefunctions at θ and θ + 2π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d CP N-1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the CP N-1 quantum mechanics with the Berry phase.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd 3 As 2

Here, we show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd 3 As 2 is a promising platform for BCL Floquet engineering. Without strain, BCL irradiation induces a transition to a noncentrosymmetric magnetic Weyl semimetal phase with tunable energy separation between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topological crystalline insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2') and can be controlled by light.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Study of gapped phases of 4d gauge theories using temporal gauging of the ℤN 1-form symmetry

To study gapped phases of 4d gauge theories, we introduce the temporal gauging of Z N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $\tilde{Z}_N$ × Z N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $\tilde{Z}_N$ × Z N symmetry must be spontaneously broken to an order-N subgroup H, and we can classify the 4d gapped phases by specifying H. This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Gapless Floquet topology

Symmetry-protected topological (SPT) phases in insulators and superconductors are known for their robust edge modes, linked to bulk invariants through the bulk-boundary correspondence. While this principle traditionally applies to gapped phases, recent advances have extended it to gapless systems, where topological edge-states persist even in the absence of a bulk gap. We extend this framework to periodically driven chains with chiral symmetry, revealing the existence of topological edge zero and π modes despite the lack of bulk gaps in the quasienergy spectrum. By examining the half-period decomposition of chiral evolutions, we construct topological invariants that circumvent the need to define the Floquet Hamiltonian, making them more suitable for generalization to the gapless regime. We provide explicit examples, including generalizations of the Kitaev chain and related spin models, where localized π modes emerge even when the bulk is gapless at the same quasienergy as the edge modes. Here, we numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's golden rule.

1-dimensional systems↗
DOE OSTI2024

Multimodal Approach Reveals the Symmetry-Breaking Pathway to the Broken Helix in EuIn 2 ⁢As 2

Understanding and manipulating emergent phases, which are themes at the forefront of quantum-materials research, rely on identifying their underlying symmetries. This general principle has been particularly prominent in materials with coupled electronic and magnetic degrees of freedom, in which magnetic order influences the electronic band structure and can lead to exotic topological effects. However, identifying symmetry of a magnetically ordered phase can pose a challenge, particularly in the presence of small domains. Here we introduce a multimodal approach for determining magnetic structures, which combines symmetry-sensitive optical probes, scattering, and group-theoretical analysis. We apply it to EuIn 2 ⁢As 2 , a material that has received attention as a candidate axion insulator. While first-principles calculations predict this state on the assumption of a simple collinear antiferromagnetic structure, subsequent neutron-scattering measurements reveal a much more intricate magnetic ground state characterized by two coexisting magnetic wave vectors reached by successive thermal phase transitions. The proposed high- and low-temperature phases are a spin helix and a state with interpenetrating helical and Néel antiferromagnetic order termed a “broken helix,” respectively. Employing a multimodal approach, we identify the magnetic structure associated with these two phases of EuIn 2 ⁢As 2 . We find that the higher-temperature phase is characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower-temperature structure is similar to the broken helix, with one important difference: Because of local strain, the relative orientation of the magnetic structure and the lattice is not fixed. Consequently, the symmetry required to protect the axion phase is not generically protected in EuIn 2 ⁢As 2 , but we show that it can be restored if the magnetic structure is tuned with uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions that account for the complex magnetic order in EuIn 2 ⁢As 2 . Our work highlights the importance of a multimodal approach in determining the symmetry of complex order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Custodial Chiral Symmetry in a Su-Schrieffer-Heeger Electrical Circuit with Memory

Custodial symmetries are common in the standard model of particle physics. They arise when quantum corrections to a parameter are proportional to the parameter itself. Here, we show that a custodial symmetry of the chiral type is also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with memory. In the absence of memory, the SSH circuit supports a symmetry-protected topological edge state. Memory induces nonlinearities that break chiral symmetry explicitly and spread the state across the circuit. However, the resulting state is still protected against perturbations by the ensuing custodial chiral symmetry. Furthermore, these predictions can be verified experimentally and demonstrate the interplay between symmetry and memory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2025

Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

Here, we present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. Motivated by recent experimental progress on "erasure conversion" techniques that allow one to identify ($\textit{herald}$) decoherence processes, we consider open systems with biased erasure noise, which leads to strongly symmetric heralded errors. We utilize this heralding to construct a local correction protocol that effectively confines errors into short-ranged pairs in the steady-state. Using a combination of numerical simulations and mean-field analysis, we show that our protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. We further find that while introducing unheralded errors destroys SPT order in the limit of long length- and time-scales, the correction protocol is sufficient for ensuring that local SPT order persists, with a correlation length that diverges as $\xi \sim (1-f_e)^{-1/2}$, where $f_e$ is the fraction of errors that are heralded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Anomaly inflow, dualities, and quantum simulation of Abelian lattice gauge theories induced by measurements

Previous work [] has demonstrated that quantum simulation of Abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their noninvertibility are also presented. Published by the American Physical Society 2024

Okuda, Takuya↗
DOE OSTI2022

Topological edge modes without symmetry in quasiperiodically driven spin chains

Here we construct an example of a 1d quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. In a sharp departure from topological phases in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this emergent dynamical symmetry-protected topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long timescales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a type of boundary critical with no known static or Floquet analogue, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Towards string order melting of spin-1 particle chains in superconducting transmons using optimal control

Utilizing optimal control to simulate a model Hamiltonian is an emerging strategy that leverages the intrinsic physics of a device with digital quantum simulation methods. Here we evaluate optimal control for probing the nonequilibrium properties of symmetry-protected topological (SPT) states simulated with superconducting hardware. Assuming a tunable transmon architecture, we cast the evolution of these SPT states as a series of one- and two-site pulse optimization problems that are solved in the presence of leakage constraints. From the generated pulses, we classically simulate the time-dependent melting of the perturbed SPT string order across a six-site model with an average state infidelity of 10 -3 . The feasibility of these pulses as well as their efficient application indicate that high-fidelity simulations of string order melting are within reach of current quantum computing systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗
DOE OSTI2024

Monoatomic orbital-based one-dimensional topological crystalline insulator

The bulk-boundary correspondence in topological crystalline insulators (TCIs) links the topological properties of the bulk to robust observables on the edges, e.g., the existence of robust edge modes or fractional charge. In one dimension, TCIs protected by reflection symmetry have been realized in a variety of systems in which each unit cell has spatially distributed degrees of freedom (SDOF). However, these realizations exhibit sensitivity of the resulting edge modes to variations in edge termination and to the local breaking of the protective spatial symmetries by inhomogeneity. Here we demonstrate topologically protected edge states in a monoatomic, orbital-based TCI that mitigates both of these issues. By collapsing all SDOF within the unit cell to a singular point in space, we eliminate the ambiguity in unit-cell definition and hence remove a prominent source of boundary termination variability. The topological observables are also more tolerant to disorder in the orbital energies. To validate this concept, we experimentally realize a lattice of mechanical resonators where each resonator acts as an “atom” that harbors two key orbital degrees of freedom having opposite reflection parity. Finally, our measurements of this system provide direct visualization of the sp-hybridization between orbital modes that leads to a nontrivial band inversion in the bulk.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

(SPT-)LSM theorems from projective non-invertible symmetries

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized 1+1 1 + 1 D quantum XY model based on group-valued qudits. This model is specified by a finite group G G and enjoys a projective \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on G G for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging \mathsf{Rep}(G) 𝖱 𝖾 𝗉 ( G ) symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.

Pace, Salvatore D. (ORCID:0000000306093335)↗