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At least 415 records · Page 23

The role of deviatoric stress and dislocations on the α to ω phase transformation in Ti

Under extreme conditions, α-Ti becomes unstable and transforms either into β-Ti at high temperature or into ω-Ti at high pressure. In what concerns the α to ω phase transformation (PT), there has been a wide range of experimentally reported transition pressures from approximately 2 to 15 GPa at room temperature. Deviatoric stresses and internal defects are often assumed to be the root cause of this variation. Here, in this study, these postulates are revisited using both continuum mechanics and molecular dynamics (MD) simulations. First, a simple continuum model, assuming linear elasticity and isotropic plasticity, is developed to describe the effects of applied stress and dislocations on the stability of an ω nucleus in an infinite α domain. Second, a new MD simulation method is developed to generate an ω nucleus in the α domain utilizing the displacement field identified from the topological analysis. Results from MD simulations show that despite the fact that phase diagrams typically delineate the limits between two phases in terms of only P and T, deviatoric stress promotes the α to ω phase transformation by reducing the critical radius above which an ω nucleus is stable. Furthermore, the required deviatoric stress to nucleate and stabilize a nanoscale ω nucleus is likely emanating from the internal stress of defects such as dislocations. The MD-informed micromechanics models are used to identify favorable configurations where dislocations help favor the α to ω transformation. These configurations show that the interaction with a basal or prismatic dislocation reduces the critical radius of a ω nucleus by about 10 or 16 %, respectively. In addition, prismatic edge dislocations are found to promote the growth of ω nucleus when interacting with the ($\bar{1}$$\bar{1}$20) α //(0001) ω interface. Importantly, a simple model of the arrival of dislocation at an ω nucleus suggests that PT does not necessarily require a pile-up to be present but could alternatively be mediated by a constant rapid flow of dislocations.

36 MATERIALS SCIENCE↗

Intrinsic even-odd thickness-driven anomalous Hall effect in epitaxial MnBi2⁢Te4 thin films

We demonstrate precise control of magnetism in MnBi2⁢Te4 thin films through careful synthesis by molecular beam epitaxy, achieving minimal defects and accurate layer thickness control. By optimizing Mn-Bi-Te ratios and growth temperatures, we minimize detrimental self-doping effects and accurately target integer-layer films. X-ray diffraction and reflectivity provide quantitative measures of film quality and thickness. When these macroscale probes of structure and thickness are integrated with magnetotransport measurements, a striking even-odd layer dependence of the anomalous Hall effect is revealed. Odd-layer films exhibit a large hysteresis up to the Néel temperature (∼25K), consistent with noncompensated antiferromagnetism, while even-layer films show minimal response, as expected for an antiferromagnet. The sign of the anomalous Hall effect exhibits a sign reversal for intrinsic magnetism versus magnetism associated with defects. This work identifies critical factors for inducing pure, noncompensated ferromagnetism and reveals the characteristics of the intrinsic anomalous Hall effect in MnBi2⁢Te4, which together is a step toward realizing the zero-field quantum anomalous Hall effect in topological materials.

Mallick, Deb [ORNL] (ORCID:000900005806411X)↗

Neutron diffraction study of magnetism in van der Waals layered MnBi 2n Te 3n+1

Two-dimensional van der Waals MnBi 2 n Te 3 n +1 ( n = 1, 2, 3, 4) compounds have been recently found to be intrinsic magnetic topological insulators rendering quantum anomalous Hall effect and diverse topological states. Here, we summarize and compare the crystal and magnetic structures of this family, and discuss the effects of chemical composition on their magnetism. We found that a considerable fraction of Bi occupies at the Mn sites in MnBi 2 n Te 3 n +1 ( n = 1, 2, 3, 4) while there is no detectable Mn at the non-magnetic atomic sites within the resolution of neutron diffraction experiments. The occupancy of Mn monotonically decreases with the increase of n . The polarized neutron diffraction on the representative MnBi 4 Te 7 reveals that its magnetization density is exclusively accumulated at the Mn site, in good agreement with the results from the unpolarized neutron diffraction. The defects of Bi at the Mn site naturally explain the continuously reduced saturated magnetic moments from n = 1 to n = 4. The experimentally estimated critical exponents of all the compounds generally suggest a three-dimensional character of magnetism. Our work provides material-specified structural parameters that may be useful for band structure calculations to understand the observed topological surface states and for designing quantum magnetic materials through chemical doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Manipulating Ferroelectric Topological Polar Structures with Twisted Light

Abstract The dynamic control of non‐equilibrium states represents a central challenge in condensed matter physics. While intense terahertz fields drive metal‐insulator transitions and ferroelectricity via soft phonon modes, recent theory suggests that twisted light with orbital angular momentum (OAM) offers a distinct route to manipulate ferroelectric order and stabilize topological excitations including skyrmions, vortices, and Hopfions. Control of ferroelectric polarization in quasi‐2D CsBiNb 2 O 7 (CBNO) is demonstrated using non‐resonant twisted ultra‐violet (UV) light (375 nm, 800 THz). Combining in situ X‐ray Bragg coherent diffractive imaging (BCDI), twisted optical Raman spectroscopy, and density functional theory (DFT), three‐dimensional (3D) ionic displacements, strain fields, and polarization changes are resolved in single crystals. Operando measurements reveal light‐induced strain hysteresis under twisted light–a hallmark of nonlinear, history‐dependent ferroelastic switching driven by OAM. Discrete, irreversible domain transitions emerge as the topological charge ℓ is cycled, stabilizing non‐trivial domain textures including vortex‐antivortex pairs, Bloch/anti‐Bloch points, and merons. These persist after OAM removal, indicating a memory effect. Competing mechanisms are discussed, including multiphoton absorption, strain‐mediated polarization switching, and defect‐wall interactions. The findings establish structured light as a tool for deterministic, reversible control of ferroic states, enabling optically reconfigurable non‐volatile devices.

Chemistry↗

Degradation of Carbon Fiber Microstructures Due to Oxidative Etch Pitting

In order to understand the influence of etch pits on the material properties of carbon fiber microstructures, we use the Porous Microstructure Analysis (PuMA) software to create realistic pitted structures from virgin fiber structures and then analyze their degradation as the degree of pitting increases. For that purpose, we developed a pitting module within PuMA that creates pits with user-defined geometry (shape, size) and distribution (defect density) on the surface of arbitrary microstructures. In this work, we consider FiberForm microstructures, which are commonly used as the base material for ablative thermal protection systems (TPS). Using the new pitting module, we mimic the evolution of etch pits on FiberForm as it occurs from oxidation in ablative heating environments, by first importing the virgin FiberForm structure from a micrograph scan and then imposing different pitting conditions by varying pit radii and defect densities. We then leverage PuMA’s capabilities to calculate material properties for each structure. The results clearly show the degradation of thermal conductivity and structural integrity as etch pits grow, and furthermore highlight the complex evolution of the surface topology, which results in significant changes of the flowgeometry and chemical gas-surface interactions. Furthermore, a comparison of these changes with the case of shrinking fibers, which has heretofore been the standard for modelling ablation of carbon structures, yields significant differences. For example, we observe the formation of small chunks of fibers as pits grow in size, which could be released into the surrounding flow environment as spallation particles. This motivates us to continue our efforts of modelling pitting as an integral part of the structural degradation of carbon fiber structures in oxidation environments, which will ultimately improve our understanding of failure mechanisms in those materials.

PuMA↗

Degradation of Carbon Fiber Microstructures Due to Oxidative Etch Pitting

In order to understand the influence of etch pits on the material properties of carbon fiber microstructures, we use the Porous Microstructure Analysis (PuMA) software to create realistic pitted structures from virgin fiber structures and then analyze their degradation as the degree of pitting increases. For that purpose, we developed a pitting module within PuMA that creates pits with user-defined geometry (shape, size) and distribution (defect density) on the surface of arbitrary microstructures. In this work, we consider FiberForm microstructures, which are commonly used as the base material for ablative thermal protection systems (TPS). Using the new pitting module, we mimic the evolution of etch pits on FiberForm as it occurs from oxidation in ablative heating environments, by first importing the virgin FiberForm structure from a micrograph scan and then imposing different pitting conditions by varying pit radii and defect densities. We then leverage PuMA’s capabilities to calculate material properties for each structure. The results clearly show the degradation of thermal conductivity and structural integrity as etch pits grow, and furthermore highlight the complex evolution of the surface topology, which results in significant changes of the flowgeometry and chemical gas-surface interactions. Furthermore, a comparison of these changes with the case of shrinking fibers, which has heretofore been the standard for modelling ablation of carbon structures, yields significant differences. For example, we observe the formation of small chunks of fibers as pits grow in size, which could be released into the surrounding flow environment as spallation particles. This motivates us to continue our efforts of modelling pitting as an integral part of the structural degradation of carbon fiber structures in oxidation environments, which will ultimately improve our understanding of failure mechanisms in those materials.

PuMA↗

Large bandgap observed on the surfaces of EuZn 2 As 2 single crystals

EuM 2 As 2 (M = Zn, Cd, In, Sn etc.) is an excellent material system for studying magnetism-tuned topological properties. However, discrepancies exist between experimental data and theoretical calculations regarding the bulk and surface bandgaps. In this work, cleaved EuZn 2 As 2 crystals are studied using scanning tunneling microscopy/spectroscopy and density functional theory calculations. Triangular-shaped defect-induced modifications in the local density of states help distinguish between Eu-terminated and AsZn-terminated surfaces. While large bandgaps (~1.5 eV at 77 K) are observed on both pristine surfaces, the bandgap size is found to be highly sensitive to local heterogeneity, tending to decrease. By combining experimental observations with theoretical simulations, we conclude that the reduced bandgap in heterogeneous regions arises from Zn vacancies and/or substitution by As atoms, both impacting greater in the Eu surface electronic properties than those in the AsZn surface. This demonstrates the intimate relationship between the electronic structure and magnetism in EuZn 2 As 2 .

interfaces↗

In Situ Visualization of Local Distortions in the High- T c Molecule-Intercalated Li x (C 5 H 5 N) y Fe 2– z Se 2 Superconductor

A time-resolved synchrotron X-ray total scattering study sheds light on the evolution of the different structural length scales involved during the intercalation of the layered iron–selenide host by organic molecular donors, aiming at the formation of the expanded-lattice Li x (C 5 H 5 N) y Fe 2– z Se 2 hybrid superconductor. The intercalates are found to crystallize in the tetragonal ThCr 2 Si 2 -type structure at the average level, however, with an enhanced interlayer iron–selenide spacing ( d = 16.2 Å) that accommodates the heterocyclic molecular spacers. Quantitative atomic pair distribution function (PDF) analysis at variable times suggests distorted FeSe 4 tetrahedral local environments that appear swollen with respect to those in the parent β-FeSe. Simultaneously acquired in situ synchrotron X-ray powder diffraction data disclose that secondary phases (α-Fe and Li 2 Se) grow significantly when a higher lithium concentration is used in the solvothermal reaction or when the solution is aged. These observations are in line with the strongly reducing character of the intercalation medium’s solvated electrons that mediate the defect chemistry of the expanded-lattice superconductor. In the latter, intralayer correlated local distortions indicate electron-donating aspects that reflect in somewhat enlarged Fe–Se bonds. Additionally, they also reveal a degree of relief of chemical pressure associated with a large distance between Fe and Se sheets (“taller” anion height) and a stretched Fe–Fe square planar topology. The elongation of the latter, derived from the in situ PDF study, speaks for a plausible increase in the Fe-site vacancy concentration. The evolution of the local structural parameters suggests an optimum reaction window where kinetically stabilized phases resemble the distortions of the edge-sharing Fe–Se tetrahedra, required for a high- T c in expanded-lattice iron-chalcogenides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A plant-specific cytochrome b 5 –like protein is essential for phytosterol biosynthesis

Sterols are essential isoprenoid derivatives that contribute to membrane structure and function. In plants, they also serve as precursors to phytohormones and specialized metabolites important for development, defense, and health. Although the sterol biosynthetic pathway is considered well-characterized, we report the discovery of a plant-specific cytochrome b 5 –like protein, CB5LP, as a critical component of phytosterol biosynthesis. Loss of CB5LP in Arabidopsis causes embryonic defects, seedling lethality, and accumulation of 14α-methyl-sterols, with reduced levels of sitosterol and stigmasterol—indicating a defect in sterol 14α-demethylation. TurboID-based proximity labeling and in vitro assays show that CB5LP physically and functionally interacts with CYP51, a cytochrome P450 enzyme catalyzing this demethylation step. Unlike canonical cytochrome b 5 proteins, CB5LP has a reversed topology and is exclusive to plants, acting as an evolutionarily distinct electron donor. This discovery reveals an uncharacterized redox partnership essential for sterol biosynthesis and highlights a promising target for the development of selective herbicide.

59 BASIC BIOLOGICAL SCIENCES↗

Doping transition-metal atoms in graphene for atomic-scale tailoring of electronic, magnetic, and quantum topological properties

Atomic-scale fabrication is an outstanding challenge and overarching goal for the nanoscience community. The practical implementation of moving and fixing atoms to a structure is non-trivial considering that one must spatially address the positioning of single atoms, provide a stabilizing scaffold to hold structures in place, and understand the details of their chemical bonding. Free-standing graphene offers a simplified platform for the development of atomic-scale fabrication and the focused electron beam in a scanning transmission electron microscope can be used to locally induce defects and sculpt the graphene. In this scenario, the graphene forms the stabilizing scaffold and the experimental question is whether a range of dopant atoms can be attached and incorporated into the lattice using a single technique and, from a theoretical perspective, we would like to know which dopants will create technologically interesting properties. Here in this paper, we demonstrate that the electron beam can be used to selectively and precisely insert a variety of transition metal atoms into graphene with highly localized control over the doping locations. We use first-principles density functional theory calculations with direct observation of the created structures to reveal the energetics of incorporating metal atoms into graphene and their magnetic, electronic, and quantum topological properties.

36 MATERIALS SCIENCE↗

Anomalies of non-invertible symmetries in (3+1)d

Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form gauge theories, with a 0-form permutation symmetry. Gauging the 0-form symmetry gives the 4+1d “inflow” symmetry topological field theory for the non-invertible symmetry. We find a two levels of anomalies: (1) the bulk may fail to have an appropriate set of loop excitations which can condense to trivialize the boundary dynamics, and (2) the “Frobenius-Schur indicator” of the non-invertible symmetry (generalizing the Frobenius-Schur indicator of 1+1d fusion categories) may be incompatible with trivial boundary dynamics. As a consequence we derive conditions for non-invertible symmetries in 3+1d to be compatible with symmetric gapped phases, and invertible gapped phases. Along the way, we see that the defects characterizing \mathbb{Z}_{4} ℤ 4 ordinary symmetry host worldvolume theories with time-reversal symmetry \mathsf{T} 𝖳 obeying the algebra \mathsf{T}^{2}=C 𝖳 2 = C or \mathsf{T}^{2}=(-1)^{F}C, 𝖳 2 = ( − 1 ) F C , with C C a unitary charge conjugation symmetry. We classify the anomalies of this symmetry algebra in 2+1d and further use these ideas to construct 2+1d topological orders with non-invertible time-reversal symmetry that permutes anyons. As a concrete realization of our general discussion, we construct new lattice Hamiltonian models in 3+1d with non-invertible symmetry, and constrain their dynamics.

Córdova, Clay↗

Exploration of two surfaces observed in Weyl semimetal BaMnSb 2

Single crystalline BaMnSb 2 is considered as a 3D Weyl semimetal with the 2D electronic structure containing Dirac cones from the Sb sheet. We report experimental investigation of low-temperature cleaved BaMnSb 2 surfaces using scanning tunneling microscopy/spectroscopy and low energy electron diffraction. By natural cleavage, we find two terminations: one is Ba (above the orthorhombically distorted Sb sheet) and another Sb2 (at the surface of the Sb/Mn/Sb sandwich layer). Both terminations show the 2×1 surface reconstructions, with drastically different morphologies and electronic properties, however. The reconstructed structures, defect types and nature of the electronic structures of the two terminations are extensively studied. The quasiparticle interference (QPI) analysis is conducted at the energy range between -2 V and 2 V, although no interesting states are observed near the Fermi level, the surface-projected electronic band structures strongly depend on the surface termination above 1.6 V. The existence of defects can greatly modify the local density of states to create electronic phase separations on the surface in the order of tens of nm scale. Our observation on the atomic structures of the terminations and the corresponding electronic structures provides critical information towards an understanding of topological properties of BaMnSb 2 .

36 MATERIALS SCIENCE↗

Enhancing MnBi 2 Te 4 Stability by Doping

MnBi 2 Te 4 (MBT) is an intrinsically magnetic topological material that possesses unique properties due to the quantum Hall effect. However, the low Mn–Bi mixed antisite formation energy is detrimental to these properties as it alters the long-range magnetic ordering in the Mn layer. Therefore, it is crucial to destabilize the antisite defects in MBT while preserving the favorable electronic properties. Here, to this end, we utilized a screening approach to understand the role of dopants in the Mn and Bi sites. We find that Sc, Y, and La dopings prefer substitutions on the Bi site and significantly increase the Mn–Bi antisite defect formation energy. We find that the contribution from the empty s and d states of Sc, Y, and La around the Fermi level is insignificant. However, at the high concentration limit, the Bi–Te octahedra are significantly modified with doping, leading to important changes in the band structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A small-box approach to the local crystal structure of Y 3 NbO 7

The local crystal structure of Y 3 NbO 7 was probed using neutron total scattering. Five different structural models were fit to the experimental pair distribution function of this material up to 15 Å. Fits of defect fluorite (Fm$\overline{3}$m), pyrochlore (Fd$\overline{3}$m), and orthorhombic C weberite models (C222 1 ) were attempted based on prior structural investigations of Y 3 NbO 7 and related fluorite-based materials. Orthorhombic P weberite (P222 1 ) and monoclinic weberite models (P112 1 ) were derived via symmetry reduction of the orthorhombic C weberite structure. All models except monoclinic weberite failed to reproduce the experimental pair distribution function. Misfits were clearly visible for peaks arising from atom pairs within the first coordination shell (defect fluorite and pyrochlore) and beyond (orthorhombic C and P weberite). By contrast, monoclinic weberite (γ ≈ 91.8°) provided an excellent fit, with no major misfits observed. This unit cell features distorted YO 8 dodecahedra, YO 7 monocapped octahedra, and NbO 6 octahedra as building blocks. Comparison between the topologies of the cationic and anionic substructures in monoclinic weberite and its parent orthorhombic C structure revealed displacements of the metal atoms along the [100] direction and a less compact spatial distribution of oxygen atoms along the a axis. In conclusion, the monoclinic weberite model presented herein may serve as a starting point to revisit structural modeling of fluorite-based materials with challenging local structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomic scale interface engineering for realizing a perpendicularly magnetized CoFeB-based skyrmion hosting material

Néel-type magnetic skyrmions in perpendicularly magnetized systems have attracted considerable interest due to their potential in fundamental research on topological objects and spintronics applications. Various systems have been explored to study Néel-type magnetic skyrmions, including repeated magnetic multilayers, two-dimensional materials, and single magnetic thin-films. Among these, single magnetic thin-films, especially a CoFeB single layer, offers multiple benefits, such as reduced defect energy, high mobility, and easy integration with existing magnetoresistive random access memory technology. However, optimizing CoFeB-based skyrmion hosting materials remains challenging and requires further systematic and comprehensive investigation. Here, in this study, we examine the effect of atomic-scale interface engineering by inserting a Ta layer between the CoFeB/MgO interface on perpendicular magnetic anisotropy, saturation magnetization, and Dzyaloshinskii–Moriya interaction. Moreover, we provide a guideline for engineering material parameters and demonstrate the validity of atomic-scale interface engineering. Our findings contribute to the development of optimized CoFeB-based skyrmion hosting materials.

36 MATERIALS SCIENCE↗

Two-Dimensional Uranyl Borates: From Conventional to Extreme Synthetic Conditions: Two-Dimensional Uranyl Borates: From Conventional to Extreme Synthetic Conditions

A systematic investigation of uranyl borates under different synthetic conditions resulted in five new 2D compounds, namely, (H 3 O)[(UO 2 )(BO 3 )], Li[(UO 2 )(BO 3 )] · (H 2 O), α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ], β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] and K 2.5 [(UO 2 ) 5 (BO 3 ) 2 O 2.5 (OH) 1.5 ] · (H 2 O) 2.5 . (H 3 O)[(UO 2 )(BO 3 )] and Li[(UO 2 )(BO 3 )] · (H 2 O) were obtained from hydrothermal reactions at 220 °C using the same mineralizer. Both materials possess the uranophane sheet topology with different symmetry of the unit cells. In the structure of (H 3 O)[(UO 2 )(BO 3 )] and Li[(UO 2 )(BO 3 )] · (H 2 O), UO 7 pentagonal bipyramids share edges and vertexes with four BO 3 planar triangles. α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] and β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] are polytypes. α-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] was synthesized from a high-temperature solid-state reaction under ambient pressure; whereas β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] was obtained from a high-temperature/high-pressure (HT/HP) reaction. Both structures have an identical anion topology, but β-K 4 [(UO 2 ) 5 (BO 3 ) 2 O 4 ] crystallizes in space group with higher symmetry. In K 2.5 [(UO 2 ) 5 (BO 3 ) 2 O 2.5 (OH) 1.5 ] · (H 2 O) 2.5 , which was obtained from a hydrothermal reaction, UO 7 polyhedra share vertexes and edges with two independent BO 3 triangles, forming the most complex uranyl borate layers among all five compounds. The different synthetic routes, novel topologies, thermal behavior and Raman spectra are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Double-Crucible Vertical Bridgman Technique for Stoichiometry-Controlled Chalcogenide Crystal Growth

Precise stoichiometry control in single-crystal growth is essential for both technological applications and fundamental research. However, conventional growth methods often face challenges such as non-stoichiometry, compositional gradients, and phase impurities, particularly in non-congruent melting systems. Even in congruent melting systems like Bi₂Se₃, deviations from the ideal stoichiometric composition can lead to significant property degradation, such as excessive bulk conductivity, which limits its topological applications. In this study, we introduce the double-crucible vertical Bridgman (DCVB) method, a novel approach that enhances stoichiometry control through the combined use of continuous source material feeding, traveling-solvent growth, and liquid encapsulation, which suppresses volatile element loss under high pressure. Using Bi₂Se₃ as a model system, we demonstrate that crystals grown via DCVB exhibit enhanced stoichiometric control, significantly reducing defect density and achieving much lower carrier concentrations compared to those produced by conventional Bridgman techniques. Moreover, the continuous feeding of source material enables the growth of large crystals. As a result, this approach presents a promising strategy for synthesizing high-quality, large-scale crystals, particularly for metal chalcogenides and pnictides that exhibit challenging non-congruent melting behaviors.

Crystal structure↗

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗