Islands for entanglement negativity

We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.

Effect of Dilute Magnetism in a Topological Insulator

Three-dimensional (3D) topological insulator (TI) has emerged as a unique state of quantum matter and generated enormous interests in condensed matter physics. The surfaces of a 3D TI consist of a massless Dirac cone, which is characterized by the Z2 topological invariant. Introduction of magnetism on the surface of a TI is essential to realize the quantum anomalous Hall effect and other novel magneto-electric phenomena. Here, by using a combination of first-principles calculations, magneto-transport and angle-resolved photoemission spectroscopy (ARPES), we study the electronic properties of gadolinium (Gd)-doped Sb2Te3. Our study shows that Gd doped Sb2Te3 is a spin-orbit-induced bulk band-gap material, whose surface is characterized by a single topological surface state. Our results provide a new platform to investigate the interactions between dilute magnetism and topology in magnetic doped topological materials.

Geometric frustration produces long-sought Bose metal phase of quantum matter

Two of the most prominent phases of bosonic matter are the superfluid with perfect flow and the insulator with no flow. A now decades-old mystery unexpectedly arose when experimental observations indicated that bosons could organize into the formation of an entirely different intervening third phase: the Bose metal with dissipative flow. The most viable theory for such a Bose metal to date invokes the use of the extrinsic property of impurity-based disorder; however, a generic intrinsic quantum Bose metal state is still lacking. We propose a universal homogeneous theory for a Bose metal in which geometric frustration confines the essential quantum coherence to a lower dimension. The result is a gapless insulator characterized by dissipative flow that vanishes in the low-energy limit. This failed insulator exemplifies a frustration-dominated regime that is only enhanced by additional scattering sources at low energy and therefore produces a Bose metal that thrives under realistic experimental conditions.

Novel topological end modes and breaking of bulk boundary correspondence in skin-effect absent superconductive chain

Topological nontrivial systems feature isolated gapless edge modes, and play a key role in advancing our understanding of quantum matter. A most profound way to characterize edge modes above is through bulk topological invariants, which is known as bulk boundary correspondence. Recent studies on non-Hermitian physics have pronounced the broken bulk-boundary correspondence with the presence of skin effect. Here, we propose a new type of fermionic topological edge modes η, satisfying η+= iη,η2=-i. Remarkably, we demonstrate that for both two cases: superconductive chain with purely η modes and quantum chain with η, Majorana modes γ on different ends, fermion parity can be well defined. Interestingly, for the latter case, broken bulk boundary correspondence is observed despite the absence of skin effects . The phenomenon above is unique to open quantum systems. For the junction with both η,γ modes, the current will not remain sinusoid form but decay exponentially. The exchange of η modes obeys the rules of non-abelian statistics, and can find its applications in topological quantum computing.

Exact holographic tensor networks for the Motzkin spin chain

The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated via a tensor-network description. The tensor network's utility in studying short range correlated states in 1D have been thoroughly investigated, with numerous examples where the treatment is essentially exact. Yet, despite the large number of works investigating these networks and their relations to physical models, examples of exact correspondence between the ground state of a quantum critical system and an appropriate scale-invariant tensor network have eluded us so far. Here we show that the features of the quantum-critical Motzkin model can be faithfully captured by an analytic tensor network that exactly represents the ground state of the physical Hamiltonian. In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice. We discuss connections to renormalization and holography.

An allgravity as a grand unification of forces

Each type of Coulomb (Newton) charge corresponds to a kind of Coulomb (Newton) mass. Such a mass-charge duality principle explains the availability of the united rest mass and charge in a neutrino equal to all its mass and charge consisting of the electric, weak, and strong components and the range of other innate components. A neutrino itself, similarly to all other quantum matter with Coulomb (Newton) mass and charge, testifies hereby in favor of a kind of mononeutrino with magnetocoulomb (magnetonewton) rest mass and charge equal to all its mass and charge including the magnetoelectric, magnetoweak, and magnetostrong parts and the range of other innate parts. We discuss a theory in which symmetry between electricity and magnetism comes forward at the level of a grand unification mathematical logic as the defined symmetry between gravity and magnetogravity within the same allgravity responsible for all that in a curved space-time. This allgravity relates a graviton and a monograviton as a consequence of force unification forming a single allgraviton. Thereby, it establishes a set of forces and the role of mass and charge in their formation and thus directly reveals the most diverse properties of a curved space that have remained hitherto latent.