Topological Entanglement Research Articles

Physical proof of the topological entanglement entropy inequality

Physical proof of the topological entanglement entropy inequality

Human Topoisomerase IIα Promotes Chromatin Condensation Via a Phase Transition.

Topoisomerase II (topo II) enzymes are essential enzymes known to resolve topological entanglements during DNA processing. Curiously, while yeast expresses a single topo II, humans express two topo II isozymes, topo IIα and topo IIβ, which share a similar catalytic domain but differ in their intrinsically disordered C-terminal domains (CTDs). During mitosis, topo IIα and condensin I constitute the most abundant chromosome scaffolding proteins essential for chromosome condensation. However, how topo IIα enables this function is poorly understood. Here, we discovered a new and functionally distinct role for human topo IIα - it condenses DNA and chromatin at a low topo IIα concentration (100 pM or less) during a polymer-collapse phase transition. The removal of the topo IIα CTDs effectively abolishes its condensation ability, indicating that the condensation is mediated by the CTDs. Although topo IIβ can also perform condensation, it is about 4-fold less effective. During the condensation, topo IIα-DNA condensates form along DNA, working against a DNA tension of up to 1.5 pN, greater than that previously reported for yeast condensin. In addition, this condensation does not require ATP and thus is independent of topo IIα's catalytic activity. We also found that condensation and catalysis can concurrently proceed with minimal mutual interference. Our findings suggest topo IIα may directly participate in chromosome condensation during mitosis.

Long-lived topological time-crystalline order on a quantum processor

Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

Variational MonteCarlo Study of the 1/9-Magnetization Plateau in Kagome Antiferromagnets.

Motivated by very recent experimental observations of the 1/9-magnetization plateaus in YCu_{3}(OH)_{6+x}Br_{3-x} and YCu_{3}(OD)_{6+x}Br_{3-x}, our study delves into the magnetic-field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational MonteCarlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9-magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number, and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral Z_{3} topological quantum spin liquid and elucidate its diverse physical properties.

Force and the α-C-terminal domains bias RNA polymerase recycling

After an RNA polymerase reaches a terminator, instead of dissociating from the template, it may diffuse along the DNA and recommence RNA synthesis from the previous or a different promoter. Magnetic tweezers were used to monitor such secondary transcription and determine the effects of low forces assisting or opposing translocation, protein roadblocks, and transcription factors. Remarkably, up to 50% of Escherichia coli (E. coli) RNA polymerases diffused along the DNA after termination. Force biased the direction of diffusion (sliding) and the velocity increased rapidly with force up to 0.7 pN and much more slowly thereafter. Sigma factor 70 (σ70) likely remained associated with the DNA promoting sliding and enabling re-initiation from promoters in either orientation. However, deletions of the α-C-terminal domains severely limited the ability of RNAP to turn around between successive rounds of transcription. The addition of elongation factor NusG, which competes with σ70 for binding to RNAP, limited additional rounds of transcription. Surprisingly, sliding RNA polymerases blocked by a DNA-bound lac repressor could slowly re-initiate transcription and were not affected by NusG, suggesting a σ-independent pathway. Low forces effectively biased promoter selection suggesting a prominent role for topological entanglements that affect RNA polymerase translocation.

Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi Point Strange Correlators

In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications, such as secret-sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., linelike subsystems in the two-dimensional cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is that has either fractal and linelike subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in a square lattice can be locally simulated by an HOCA-generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call . We propose a universal procedure to design the spatial configuration of the multi point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long-range behavior in a short-range entangled state. Our HOCA approaches and multi point strange correlators pave the way for a unified paradigm to design, classify, and detect phases of matter with symmetries supported on a great variety of subsystems, and also provide potential useful perspective in surpassing the computational irreducibility of HOCA in a quantum mechanical way. Published by the American Physical Society 2024

A hemoadhican-based sponge with anti-heparin interference for treating uncontrollable massive hemorrhage

Hemoadhican (HD) is an exopolysaccharide with a branched structure that has been reported for its high hemostatic ability. In this study, a HD-based hemostatic sponge was prepared through ultrasonic dissolution and freeze-drying without using any cross-linking agent. The sponge could spontaneously cross-link using hydrogen bonds to form adhesive mud within 3 s upon contact with blood. This sponge-mud mixture adhered tightly to the wound tissue, forming a pressure-resistant physical barrier that captures and locks in blood cells and platelets. Simultaneously, the hydrophobic methyl groups of HD sponges repel blood inwardly, effectively sealing the wound. The brush-like structure of HD molecules was suspected to penetrate wet tissues through topological entanglement, thereby enhancing wet adhesion. Compared with gauze and gelatin sponges, HD sponges achieved more effective hemostasis in animal models using rat and rabbit femoral arteries. In particular, HD sponges showed excellent hemostasis in heparin-induced hemorrhage models in mice and pigs. The in vivo experiment demonstrated the excellent biosafety of the HD sponge. Conclusively, the HD sponge is a safe and efficient rapid hemostatic material that is expected to become an alternative material for clinical hemostatic procedures.

An Algorithm for Computing Entanglements in an Ensemble of Linear Polymers

AbstractThe entanglement length plays a key role in deciding many important properties of thermoplastics. A number of computational techniques exist for the determination of entanglement length. In Ahmad et al.,[1] a method is proposed that treats a macromolecular chain as a 1D open curve and identifies entanglements by computing the linking number between two such interacting curves. If the curves wind around each other, a topological entanglement is detected. However, the entanglement length that is measured in experiments is assumed to be between rheological entanglements, which are clusters of such topological entanglements that collectively anchor the interacting chains strongly. In this article, the method of clustering topological entanglements into rheological ones is further elaborated and the robustness of the method is assessed. It is shown that this method estimates an entanglement length that depends on the forcefield chosen and is reasonably constant for chain lengths longer than the entanglement length. For shorter chain lengths, the method returns an infinite value of entanglement length indicating that the sample is unentangled. Moreover, in spite of using a geometry‐based algorithm for clustering topological entanglements, the estimated entanglement length retains known empirical connections with physical attributes associated with the ensemble.

Topological Polymer Networks-Enabled Mechanically Strong Polyamide-Imide Aerogel Fibers for Thermal Insulation in Harsh Environments.

Aerogel fibers have sparked substantial interest as attractive candidates for thermal insulation materials. Developing aerogel fibers with the desired porous structure, good knittability, flame retardancy, and high- and low-temperature resistance is of great significance for practical applications; however, that is very challenging, especially by using an efficient method. Herein, mechanically strong and flexible aerogel fibers with remarkable thermal insulation performance are reported, which are achieved by constructing stiff-soft topological polymer networks and a multilevel hollow porous structure. The combination of polyamide-imide (PAI) with stiff chains and polyurethane (PU) with soft chains is first found to be able to form a topological entanglement architecture. More importantly, multilevel hollow pores can be constructed synchronously through just a one-step and green wet-spinning process. The resultant PAI/PU@340 aerogel fibers show an ultrahigh breaking strength of 94.5 MPa and superelastic property with a breaking strain of 20%. Furthermore, they can be knitted into fabrics with a low thermal conductivity of 25 mW/(m·K) and exhibit attractive thermal insulation property under extremely high (300 °C) and low temperatures (-191 °C), implying them as promising candidates for next-generation thermal insulation materials.

Rigid-flexible mediated Co-polyimide enabling stable silicon anode in lithium-ion batteries

Silicon is considered as a promising electrode materials for the next generation of lithium-ion batteries. However, it’s commercial applications are hindered by significant volume changes. In this study, copolyimide binders with adjustable rigidity and flexibility were synthesized through simple copolymerization. The rigid segments containing adenine groups (p-APA) provide excellent mechanical strength and interface interaction, while flexible segments containing siloxane bonds and alkane chains (DS-NH2) can buffer volume changes through enhanced mobility and topological entanglement of molecular segments. Optimizing the copolymerization ratio helps minimize damage to the silicon electrode structure and stabilizes solid electrolyte interphase (SEI) growth. Compared to the rigid polyimide binders, rigid-flexible coupling strategy improves cycling stability, remaining a capacity of 2170 mAh/g at 2 A/g after 200 cycles and exhibiting stable cycling for over 750 cycles with a capacity limitation of 1500 mAh/g. The high mass loading silicon anodes, micron-sized silicon oxide electrodes and the full cells also exhibit favorable electrochemical performance. This research provides valuable insights for designing high-performance aromatic polymer binders for high energy density lithium-ion batteries.

Non-Abelian braiding of Fibonacci anyons with a superconducting processor

Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.

Knotted artifacts in predicted 3D RNA structures.

Unlike proteins, RNAs deposited in the Protein Data Bank do not contain topological knots. Recently, admittedly, the first trefoil knot and some lasso-type conformations have been found in experimental RNA structures, but these are still exceptional cases. Meanwhile, algorithms predicting 3D RNA models have happened to form knotted structures not so rarely. Interestingly, machine learning-based predictors seem to be more prone to generate knotted RNA folds than traditional methods. A similar situation is observed for the entanglements of structural elements. In this paper, we analyze all models submitted to the CASP15 competition in the 3D RNA structure prediction category. We show what types of topological knots and structure element entanglements appear in the submitted models and highlight what methods are behind the generation of such conformations. We also study the structural aspect of susceptibility to entanglement. We suggest that predictors take care of an evaluation of RNA models to avoid publishing structures with artifacts, such as unusual entanglements, that result from hallucinations of predictive algorithms.

Anyon quantum dimensions from an arbitrary ground state wave function

Realizing topological orders and topological quantum computation is a central task of modern physics. An important but notoriously hard question in this endeavor is how to diagnose topological orders that lack conventional order parameters. A breakthrough in this problem is the discovery of topological entanglement entropy, which can be used to detect nontrivial topological order from a ground state wave function, but is far from enough for fully determining the topological order. In this work, we take a key step further in this direction: We propose a simple entanglement-based protocol for extracting the quantum dimensions of all anyons from a single ground state wave function in two dimensions. The choice of the space manifold and the ground state is arbitrary. This protocol is both validated in the continuum and verified on lattices, and we anticipate it to be realizable in various quantum simulation platforms.

Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization effects

We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits significant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization effects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, both e−/2 solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonic e−/2 fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.

The Jones polynomial in systems with periodic boundary conditions

Entanglement of collections of filaments arises in many contexts, such as in polymer melts, textiles and crystals. Such systems are modeled using periodic boundary conditions (PBCs), which create an infinite periodic system whose global entanglement may be impossible to capture and is repetitive. We introduce two new methods to assess topological entanglement in PBC: the Periodic Jones polynomial and the Cell Jones polynomial. These tools capture the grain of geometric/topological entanglement in a periodic system of open or closed chains, by using a finite link as a representative of the global system. These polynomials are topological invariants in some cases, but in general are sensitive to both the topology and the geometry of physical systems. For a general system of 1 closed chain in 1 PBC, we prove that the Periodic Jones polynomial is a recurring factor, up to a remainder, of the Jones polynomial of a conveniently chosen finite cutoff of arbitrary size of the infinite periodic system. We apply the Cell Jones polynomial and the Periodic Jones polynomial to physical PBC systems such as 3D realizations of textile motifs and polymer melts of linear chains obtained from molecular dynamics simulations. Our results demonstrate that the Cell Jones polynomial and the Periodic Jones polynomial can measure collective geometric/topological entanglement complexityin such systems of physical relevance.

Low modulus ultra-ductility ionic skin by highly entangled PAM-co-UPyMA hydrogel

This work primarily discusses the construction of physically cross-linked polyacrylamide copolymer containing 2-(3-(6-methyl-4-oxo-1,4-dihydropyrimidin-2-yl)ureido)ethyl methacrylate (PAM-co-UPyMA, short for PAU) hydrogels with topological entanglement by designing high concentrations of acrylamide (AM) monomers and introducing “bridging” flexible non-covalent bonds. This method overcomes the poor stretchable performance of chemically cross-linked hydrogels, as well as the limited improvement in mechanical properties due to the low dissipation energy of physically cross-linked hydrogel (non-covalent bonding) under an external force. This new hydrogel exhibits low modulus (0.12 MPa), a certain fracture strength (0.2 MPa), and high toughness with an elongation at a break of 5700 %, demonstrating excellent tensile strain sensitivity with a gauge factor (GF) of 16.14, capable of detecting tiny deformations of 0.2 %. It also exhibits fast strain response, long-term stability, and performs well in applications such as human joints and voice monitoring. Furthermore, this work elucidates the relationship between the microstructure of PAU hydrogels and sensing performance, proving that the rate of microstructure change serves as an essential mechanism. The less cross-linked and highly entangled PAU hydrogel strain sensor increases the cross-linked domain size under tensile load, leading to ion channel blockade with a rapid increase in resistance during deformation, thus resulting in an improved sensitivity.

Characterizing the ambiguity in topological entanglement entropy

Topological entanglement entropy (TEE), the sub-leading term in the entanglement entropy of topological order, is the direct evidence of the long-range entanglement. While effective in characterizing topological orders on closed manifolds, TEE is model-dependent when entanglement cuts intersect with physical gapped boundaries. In this paper, we study the origin of this model-dependence by introducing a model-independent picture of partitioning the topological orders with gapped boundaries. In our picture, the entanglement boundaries (EBs), i.e. the virtual boundaries of each subsystem induced by the entanglement cuts, are assumed to be gapped boundaries with boundary defects. At this model-independent stage, there are two choices one has to make manually in defining the bi-partition: the boundary condition on the EBs, and the coherence between certain boundary states. We show that TEE appears because of a constraint on the defect configurations on the EBs, which is choice-dependent in the cases where the EBs touch gapped boundaries. This choice-dependence is known as the ambiguity in entanglement entropy. Different models intrinsically employ different choices, rendering TEE model-dependent. For D(ℤ2) topological order, the ambiguity can be fully characterized by two parameters that respectively quantifies the EB condition and the coherence. In particular, calculations compatible with the folding trick naturally choose EB conditions that respect electric-magnetic duality and set specific parameter values.

Bicolor loop models and their long range entanglement

Quantum loop models are well studied objects in the context of lattice gauge theories and topological quantum computing. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider generalization of the toric code model to bicolor loop models and show that the long range entanglement can be reflected in three different ways: a topologically invariant constant, a sub-leading logarithmic correction to the area law, or a modified bond dimension for the area-law term. The Hamiltonians are not exactly solvable for the whole spectra, but admit a tower of area-law exact excited states corresponding to the frustration free superposition of loop configurations with arbitrary pairs of localized vertex defects. The continuity of color along loops imposes kinetic constraints on the model and results in Hilbert space fragmentation, unless plaquette operators involving two neighboring faces are introduced to the Hamiltonian.

Topological entanglement entropy for torus-knot bipartitions and the Verlinde-like formulas

The topological Rényi and entanglement entropies depend on the bipartition of the manifold and the choice of the ground states. However, these entanglement quantities remain invariant under a coordinate transformation when the bipartition also undergoes the identical transformation. In topological quantum field theories (TQFTs), these coordinate transformations reduce to representations of the mapping class group on the manifold of the Hilbert space. We employ this invariant property of the Rényi and entanglement entropies under coordinate transformations for TQFTs in (2 + 1) dimensions on a torus with various bipartitions. By utilizing the replica trick and the surgery method to compute the topological Rényi and entanglement entropies, the invariant property results in Verlinde-like formulas. Furthermore, for the bipartition with interfaces as two non-intersecting torus knots, an SL(2, ℤ) transformation can untwist the torus knots, leading to a simple bipartition with an effective ground state. This invariant property allows us to demonstrate that the topological entanglement entropy has a lower bound −2 ln D, where D is the total quantum dimensions of the system.

In Situ Polymerization of Hydrogel Electrolyte on Electrodes Enabling the Flexible All-Hydrogel Supercapacitors with Low-Temperature Adaptability.

All-hydrogel supercapacitors are emerging as promising power sources for next-generation wearable electronics due to their intrinsic mechanical flexibility, eco-friendliness, and enhanced safety. However, the insufficient interfacial adhesion between the electrode and electrolyte and the frozen hydrogel matrices at subzero temperatures largely limit the practical applications of all-hydrogel supercapacitors. Here, an all-hydrogel supercapacitor is reported with robust interfacial contact and anti-freezing property, fabricated by in situ polymerizing hydrogel electrolyte onto hydrogel electrodes. The robust interfacial adhesion is developed by the synergistic effect of a tough hydrogel matrix and topological entanglements. Meanwhile, the incorporation of zinc chloride (ZnCl2) in the hydrogel electrolyte prevents the freezing of water solvents and endows the all-hydrogel supercapacitor with mechanical flexibility and fatigue resistance across a wide temperature range of 20°C to -60°C. Such all-hydrogel supercapacitor demonstrates satisfactory low-temperature electrochemical performance, delivering a high energy density of 11mWhcm-2 and excellent cycling stability with a capacitance retention of 90% over 10000 cycles at -40°C. Notably, the fabricated all-hydrogel supercapacitor can endure dynamic deformations and operate well under 2000 tension cycles even at -40°C, without experiencing delamination and electrochemical failure. This work offers a promising strategy for flexible energy storage devices with low-temperature adaptability.