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Register a new userPhase diagram of $ u=frac{1}{2}+frac{1}{2}$ bilayer bosons with inter-layer couplings
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We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ u=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.
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Recent low temperature heat capacity (C$_P$) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$ have shown a strong sensitivity to the precise Tb concentration $x$, with a large anomaly exhibited for $x sim 0.005$ at $T_C sim 0.5$ K and no such anomaly and corresponding phase transition for $x le 0$. We have grown single crystal samples of Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$, with approximate composition $x=-0.001, +0.0042$, and $+0.0147$, where the $x=0.0042$ single crystal exhibits a large C$_P$ anomaly at $T_C$=0.45 K, but neither the $x=-0.001$ nor the $x=+0.0147$ single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the $x=-0.001$ and the $x=+0.0147$ samples which show strong $left(frac{1}{2},frac{1}{2},frac{1}{2}right)$ quasi-Bragg peaks at low temperatures characteristic of short range antiferromagnetic spin ice (AFSI) order at zero magnetic field but only under field-cooled conditions, as was previously observed in our $x = 0.0042$ single crystal. These results show that the strong $left(frac{1}{2},frac{1}{2},frac{1}{2}right)$ quasi-Bragg peaks and gapped AFSI state at low temperatures under field cooled conditions are robust features of Tb$_2$Ti$_2$O$_7$, and are not correlated with the presence or absence of the C$_P$ anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the C$_P$ anomaly is confined to $0 leq x leq 0.01$ for Tb$_{2+x}$Ti$_{2-x}$O$_{7+delta}$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.
The past few years have witnessed increased attention to the quest for Majorana-like excitations in the condensed matter community. As a promising candidate in this race, the one-dimensional chiral Majorana edge mode (CMEM) in topological insulator-superconductor heterostructures has gathered renewed interests during recent months after an experimental breakthrough. In this paper, we study the quantum transport of topological insulator-superconductor hybrid devices subject to light-matter interaction or general time-periodic modulation. We report half-integer quantized conductance plateaus at $frac{1}{2}frac{e^2}{h}$ and $frac{3}{2}frac{e^2}{h}$ upon applying the so-called sum rule in the theory of quantum transport in Floquet topological matter. In particular, in a photoinduced topological superconductor sandwiched between two Floquet Chern insulators, it is found that for each Floquet sideband, the CMEM admits equal probability for normal transmission and local Andreev reflection over a wide range of parameter regimes, yielding half-integer quantized plateaus that resist static and time-periodic disorder. The $frac{3}{2}frac{e^2}{h}$ plateau has not yet been computationally or experimentally observed in any other superconducting system, and indicates the possibility to simultaneously create and manipulate multiple pairs of CMEMs by light. The robust half-quantized conductance plateaus, due to CMEMs at quasienergies zero or half the driving frequency, are both fascinating and subtle because they only emerge after a summation over contributions from all Floquet sidebands. Such a distinctive transport signature can thus serve as a hallmark of photoinduced CMEMs in topological insulator-superconductor junctions.
The frustrated XY model on the honeycomb lattice has drawn lots of attentions because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this work, we study the extended spin-$frac{1}{2}$ XY model with nearest-neighbor ($J_1$), and next-nearest-neighbor ($J_2$) interactions in the presence of a three-spins chiral ($J_{chi}$) term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin CSL is shown to emerge under a small $J_{chi}$ perturbation due to the interplay of the magnetic frustration and chiral interactions. The CSL, which is a non-magnetic phase, is identified by the scalar chiral order, the finite spin gap on a torus, and the chiral entanglement spectrum described by chiral $SU(2)_{1}$ conformal field theory.
We study the zero-temperature phase diagram of the spin-$frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.
The zero-temperature quantum phase diagram of the spin-$frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{perp}$ model on an $AA$-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} equiv kappa J_{1}>0$. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_{1}^{perp} equiv delta J_{1}$. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the N{e}el and N{e}el-II phases, are calculated in the $kappa delta$ half-plane with $kappa > 0$. Whereas on each monolayer in the N{e}el state all NN pairs of spins are antiparallel, in the N{e}el-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter $M$ and the excitation energy $Delta$ from the $s^{z}_{T}=0$ ground state to the lowest-lying $|s^{z}_{T}|=1$ excited state (where $s^{z}_{T}$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders ($n leq 10$) in a systematic series of approximations involving $n$-spin clusters. The sole approximation made is then to extrapolate the sequences of $n$th-order results for $M$ and $Delta$ to the exact limit, $n to infty$.
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