Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice

There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-1/2 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux-smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED$_3$) with an emergent $\mathrm{SU}(8)$ flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.Comment: 14 pages, 8 figure

Interlayer coherent composite Fermi liquid phase in quantum Hall bilayers

Composite fermions have played a seminal role in understanding the quantum Hall effect, particularly the formation of a compressible `composite Fermi liquid' (CFL) at filling factor nu = 1/2. Here we suggest that in multi-layer systems interlayer Coulomb repulsion can similarly generate `metallic' behavior of composite fermions between layers, even if the electrons remain insulating. Specifically, we propose that a quantum Hall bilayer with nu = 1/2 per layer at intermediate layer separation may host such an interlayer coherent CFL, driven by exciton condensation of composite fermions. This phase has a number of remarkable properties: the presence of `bonding' and `antibonding' composite Fermi seas, compressible behavior with respect to symmetric currents, and fractional quantum Hall behavior in the counterflow channel. Quantum oscillations associated with the Fermi seas give rise to a new series of incompressible states at fillings nu = p/[2(p \pm 1)] per layer (p an integer), which is a bilayer analogue of the Jain sequence.Comment: 4 pages, 3 figure

Phase diagram of bismuth in the extreme quantum limit

Elemental bismuth provides a rare opportunity to explore the fate of a three-dimensional gas of highly mobile electrons confined to their lowest Landau level. Coulomb interaction, neglected in the band picture, is expected to become significant in this extreme quantum limit with poorly understood consequences. Here, we present a study of the angular-dependent Nernst effect in bismuth, which establishes the existence of ultraquantum field scales on top of its complex single-particle spectrum. Each time a Landau level crosses the Fermi level, the Nernst response sharply peaks. All such peaks are resolved by the experiment and their complex angular-dependence is in very good agreement with the theory. Beyond the quantum limit, we resolve additional Nernst peaks signaling a cascade of additional Landau sub-levels caused by electron interaction

High affinity binding of H3K14ac through collaboration of bromodomains 2, 4 and 5 is critical for the molecular and tumor suppressor functions of PBRM1.

Polybromo-1 (PBRM1) is an important tumor suppressor in kidney cancer. It contains six tandem bromodomains (BDs), which are specialized structures that recognize acetyl-lysine residues. While BD2 has been found to bind acetylated histone H3 lysine 14 (H3K14ac), it is not known whether other BDs collaborate with BD2 to generate strong binding to H3K14ac, and the importance of H3K14ac recognition for the molecular and tumor suppressor function of PBRM1 is also unknown. We discovered that full-length PBRM1, but not its individual BDs, strongly binds H3K14ac. BDs 2, 4, and 5 were found to collaborate to facilitate strong binding to H3K14ac. Quantitative measurement of the interactions between purified BD proteins and H3K14ac or nonacetylated peptides confirmed the tight and specific association of the former. Interestingly, while the structural integrity of BD4 was found to be required for H3K14ac recognition, the conserved acetyl-lysine binding site of BD4 was not. Furthermore, simultaneous point mutations in BDs 2, 4, and 5 prevented recognition of H3K14ac, altered promoter binding and gene expression, and caused PBRM1 to relocalize to the cytoplasm. In contrast, tumor-derived point mutations in BD2 alone lowered PBRM1\u27s affinity to H3K14ac and also disrupted promoter binding and gene expression without altering cellular localization. Finally, overexpression of PBRM1 variants containing point mutations in BDs 2, 4, and 5 or BD2 alone failed to suppress tumor growth in a xenograft model. Taken together, our study demonstrates that BDs 2, 4, and 5 of PBRM1 collaborate to generate high affinity to H3K14ac and tether PBRM1 to chromatin. Mutations in BD2 alone weaken these interactions, and this is sufficient to abolish its molecular and tumor suppressor functions

Parafermionic edge zero modes in Z_n-invariant spin chains

A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss their presence in spin chains with Z_n symmetry, and prove that for appropriate coupling they are exact, even in this strongly interacting system. These modes are naturally expressed in terms of parafermions, generalizations of fermions to the Z_n case. I show that parafermionic edge zero modes do not occur in the usual ferromagnetic and antiferromagnetic cases, but rather only when the interactions are chiral, so that spatial-parity and time-reversal symmetries are broken.Comment: 22 pages. v2: small changes, added reference

Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.Comment: 34 pages, 17 figures; v4: minor changes, final versio

Topological orbital ladders

We unveil a topological phase of interacting fermions on a two-leg ladder of unequal parity orbitals, derived from the experimentally realized double-well lattices by dimension reduction. $Z_2$ topological invariant originates simply from the staggered phases of $sp$-orbital quantum tunneling, requiring none of the previously known mechanisms such as spin-orbit coupling or artificial gauge field. Another unique feature is that upon crossing over to two dimensions with coupled ladders, the edge modes from each ladder form a parity-protected flat band at zero energy, opening the route to strongly correlated states controlled by interactions. Experimental signatures are found in density correlations and phase transitions to trivial band and Mott insulators.Comment: 12 pages, 5 figures, Revised title, abstract, and the discussion on Majorana numbe

Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor

Bulk electronic state of superconducting topological insulator

We study electronic properties of a superconducting topological insulator whose parent material is a topological insulator. We calculate the temperature dependence of the specific heat and spin susceptibility for four promising superconducting pairings proposed by L. Fu and E. Berg (Phys. Rev. Lett. 105, 097001). Since the line shapes of temperature dependence of specific heat are almost identical among three of the four pairings, it is difficult to identify them simply from the specific heat. On the other hand, we obtain wide varieties of the temperature dependence of spin susceptibility for each pairing reflecting the spin structure of Cooper pair. We propose that the pairing symmetry of superconducting topological insulator can be determined from measurement of Knight shift by changing the direction of applied magnetic field.Comment: 12 pages, 15 figures. Accepted for publication in J. Phys. Soc. Jp