Boson Condensation in Topologically Ordered Quantum Liquids

Boson condensation in topological quantum field theories (TQFT) has been previously investigated through the formalism of Frobenius algebras and the use of vertex lifting coefficients. While general, this formalism is physically opaque and computationally arduous: analyses of TQFT condensation are practically performed on a case by case basis and for very simple theories only, mostly not using the Frobenius algebra formalism. In this paper we provide a new way of treating boson condensation that is computationally efficient. With a minimal set of physical assumptions, such as commutativity of lifting and the definition of confined particles, we can prove a number of theorems linking Boson condensation in TQFT with chiral algebra extensions, and with the factorization of completely positive matrices over the nonnegative integers. We present numerically efficient ways of obtaining a condensed theory fusion algebra and S matrices; and we then use our formalism to prove several theorems for the S and T matrices of simple current condensation and of theories which upon condensation result in a low number of confined particles. We also show that our formalism easily reproduces results existent in the mathematical literature such as the noncondensability of 5 and 10 layers of the Fibonacci TQFT.Comment: 29 page

Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter

We study the entanglement entropy of gapped phases of matter in three spatial dimensions. We focus in particular on size-independent contributions to the entropy across entanglement surfaces of arbitrary topologies. We show that for low energy fixed-point theories, the constant part of the entanglement entropy across any surface can be reduced to a linear combination of the entropies across a sphere and a torus. We first derive our results using strong sub-additivity inequalities along with assumptions about the entanglement entropy of fixed-point models, and identify the topological contribution by considering the renormalization group flow; in this way we give an explicit definition of topological entanglement entropy $S_{\mathrm{topo}}$ in (3+1)D, which sharpens previous results. We illustrate our results using several concrete examples and independent calculations, and show adding "twist" terms to the Lagrangian can change $S_{\mathrm{topo}}$ in (3+1)D. For the generalized Walker-Wang models, we find that the ground state degeneracy on a 3-torus is given by $\exp(-3S_{\mathrm{topo}}[T^2])$ in terms of the topological entanglement entropy across a 2-torus. We conjecture that a similar relationship holds for Abelian theories in $(d+1)$ dimensional spacetime, with the ground state degeneracy on the $d$-torus given by $\exp(-dS_{\mathrm{topo}}[T^{d-1}])$.Comment: 34 pages, 16 figure

No-go theorem for boson condensation in topologically ordered quantum liquids

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. This includes (as the case k = 3) the noncondensability of any number of layers of the Fibonacci TQFT

Roles of brca2 (fancd1) in Oocyte Nuclear Architecture, Gametogenesis, Gonad Tumors, and Genome Stability in Zebrafish

Mild mutations in BRCA2 (FANCD1) cause Fanconi anemia (FA) when homozygous, while severe mutations cause common cancers including breast, ovarian, and prostate cancers when heterozygous. Here we report a zebrafish brca2 insertional mutant that shares phenotypes with human patients and identifies a novel brca2 function in oogenesis. Experiments showed that mutant embryos and mutant cells in culture experienced genome instability, as do cells in FA patients. In wild-type zebrafish, meiotic cells expressed brca2; and, unexpectedly, transcripts in oocytes localized asymmetrically to the animal pole. In juvenile brca2 mutants, oocytes failed to progress through meiosis, leading to female-to-male sex reversal. Adult mutants became sterile males due to the meiotic arrest of spermatocytes, which then died by apoptosis, followed by neoplastic proliferation of gonad somatic cells that was similar to neoplasia observed in ageing dead end (dnd)-knockdown males, which lack germ cells. The construction of animals doubly mutant for brca2 and the apoptotic gene tp53 (p53) rescued brca2-dependent sex reversal. Double mutants developed oocytes and became sterile females that produced only aberrant embryos and showed elevated risk for invasive ovarian tumors. Oocytes in double-mutant females showed normal localization of brca2 and pou5f1 transcripts to the animal pole and vasa transcripts to the vegetal pole, but had a polarized rather than symmetrical nucleus with the distribution of nucleoli and chromosomes to opposite nuclear poles; this result revealed a novel role for Brca2 in establishing or maintaining oocyte nuclear architecture. Mutating tp53 did not rescue the infertility phenotype in brca2 mutant males, suggesting that brca2 plays an essential role in zebrafish spermatogenesis. Overall, this work verified zebrafish as a model for the role of Brca2 in human disease and uncovered a novel function of Brca2 in vertebrate oocyte nuclear architecture

Simulation of Near-Infrared Light Absorption Considering Individual Head and Prefrontal Cortex Anatomy: Implications for Optical Neuroimaging

Functional near-infrared spectroscopy (fNIRS) is an established optical neuroimaging method for measuring functional hemodynamic responses to infer neural activation. However, the impact of individual anatomy on the sensitivity of fNIRS measuring hemodynamics within cortical gray matter is still unknown. By means of Monte Carlo simulations and structural MRI of 23 healthy subjects (mean age: years), we characterized the individual distribution of tissue-specific NIR-light absorption underneath 24 prefrontal fNIRS channels. We, thereby, investigated the impact of scalp-cortex distance (SCD), frontal sinus volume as well as sulcal morphology on gray matter volumes () traversed by NIR-light, i.e. anatomy-dependent fNIRS sensitivity. The NIR-light absorption between optodes was distributed describing a rotational ellipsoid with a mean penetration depth of considering the deepest of light. Of the detected photon packages scalp and bone absorbed and absorbed of the energy. The mean volume was negatively correlated () with the SCD and frontal sinus volume () and was reduced by in subjects with relatively large compared to small frontal sinus. Head circumference was significantly positively correlated with the mean SCD () and the traversed frontal sinus volume (). Sulcal morphology had no significant impact on . Our findings suggest to consider individual SCD and frontal sinus volume as anatomical factors impacting fNIRS sensitivity. Head circumference may represent a practical measure to partly control for these sources of error variance

Fermion-boson many-body interplay in a frustrated kagome paramagnet

Kagome-net, appearing in areas of fundamental physics, materials, photonic and cold-atom systems, hosts frustrated fermionic and bosonic excitations. However, it is extremely rare to find a system to study both fermionic and bosonic modes to gain insights into their many-body interplay. Here we use state-of-the-art scanning tunneling microscopy and spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet. Our results reveal the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through a combination of self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice analog of kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.Comment: To appear in Nature Communications (2020

Discovery of unconventional chiral charge order in kagome superconductor KV3Sb5

Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2x2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2x2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. At impurity-pinning free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral CDW in the frustrated kagome lattice, which can not only lead to large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.Comment: Orbital magnetism calculation adde

Roles of brca2 (fancd1) in Oocyte Nuclear Architecture, Gametogenesis, Gonad Tumors, and Genome Stability in Zebrafish

Mild mutations in BRCA2 (FANCD1) cause Fanconi anemia (FA) when homozygous, while severe mutations cause common cancers including breast, ovarian, and prostate cancers when heterozygous. Here we report a zebrafish brca2 insertional mutant that shares phenotypes with human patients and identifies a novel brca2 function in oogenesis. Experiments showed that mutant embryos and mutant cells in culture experienced genome instability, as do cells in FA patients. In wild-type zebrafish, meiotic cells expressed brca2; and, unexpectedly, transcripts in oocytes localized asymmetrically to the animal pole. In juvenile brca2 mutants, oocytes failed to progress through meiosis, leading to female-to-male sex reversal. Adult mutants became sterile males due to the meiotic arrest of spermatocytes, which then died by apoptosis, followed by neoplastic proliferation of gonad somatic cells that was similar to neoplasia observed in ageing dead end (dnd)-knockdown males, which lack germ cells. The construction of animals doubly mutant for brca2 and the apoptotic gene tp53 (p53) rescued brca2-dependent sex reversal. Double mutants developed oocytes and became sterile females that produced only aberrant embryos and showed elevated risk for invasive ovarian tumors. Oocytes in double-mutant females showed normal localization of brca2 and pou5f1 transcripts to the animal pole and vasa transcripts to the vegetal pole, but had a polarized rather than symmetrical nucleus with the distribution of nucleoli and chromosomes to opposite nuclear poles; this result revealed a novel role for Brca2 in establishing or maintaining oocyte nuclear architecture. Mutating tp53 did not rescue the infertility phenotype in brca2 mutant males, suggesting that brca2 plays an essential role in zebrafish spermatogenesis. Overall, this work verified zebrafish as a model for the role of Brca2 in human disease and uncovered a novel function of Brca2 in vertebrate oocyte nuclear architecture

Three dimensional electron microscopy reveals changing axonal and myelin morphology along normal and partially injured optic nerves

Following injury to the central nervous system, axons and myelin distinct from the initial injury site undergo changes associated with compromised function. Quantifying such changes is important to understanding the pathophysiology of neurotrauma; however, most studies to date used 2 dimensional (D) electron microscopy to analyse single sections, thereby failing to capture changes along individual axons. We used serial block face scanning electron microscopy (SBF SEM) to undertake 3D reconstruction of axons and myelin, analysing optic nerves from normal uninjured female rats and following partial optic nerve transection. Measures of axon and myelin dimensions were generated by examining 2D images at 5 µm intervals along the 100 µm segments. In both normal and injured animals, changes in axonal diameter, myelin thickness, fiber diameter, G-ratio and percentage myelin decompaction were apparent along the lengths of axons to varying degrees. The range of values for axon diameter along individual reconstructed axons in 3D was similar to the range from 2D datasets, encompassing reported variation in axonal diameter attributed to retinal ganglion cell diversity. 3D electron microscopy analyses have provided the means to demonstrate substantial variability in ultrastructure along the length of individual axons and to improve understanding of the pathophysiology of neurotrauma