Compact U

We propose a bosonic U^{κ}(1) rotor model on a three dimensional spacetime lattice. With the inclusion of a Maxwell term, we show that the low-energy properties of our model can be obtained reliably via a semiclassical approach. Those properties are the same as that of the Chern-Simons field theory, S=∫d^{3}x(K_{IJ}/4π)A_{I}dA_{J}. We require the lattice variables on each link to be compact (i.e., take values on circles), which enforces the quantization of the K matrix as a symmetric integer matrix with even diagonals. Our lattice model also has exact 1-symmetries, which gives rise to the 1-form symmetry in the Chern-Simons field theory. In particular, some of those 1-symmetries are anomalous (i.e., non-on-site) in the expected way. The anomaly can be probed via the breaking of those lattice 1-symmetries by the boundaries.

Continuous Topological Phase Transition between Two 1D Antiferromagnetic Spin-1 Boson Superfluids with the Same Symmetry.

Spin-1 bosons on a one-dimensional chain, at incommensurate filling with an antiferromagnetic spin interaction between neighboring bosons, may form a spin-1 boson condensed state that contains both a gapless charge and spin excitations. We argue that the spin-1 boson condensed state is unstable, and will become one of two superfluids by opening a spin gap. One superfluid must have a spin-1 ground state on a ring if it contains an odd number of bosons and has no degenerate states at the chain end. The other superfluid has a spin-0 ground state on a ring for any number of bosons and has a spin-1/2 degeneracy at the chain end. The two superfluids have the same symmetry and only differ by a spin-SO(3) symmetry protected topological order. Although Landau theory forbids a continuous phase transition between two phases with the same symmetry, the phase transition between the two superfluids can be generically continuous, which is described by conformal field theory (CFT) su(2)_{2}⊕u(1)_{4}⊕su(2)[over ¯]_{2}⊕u(1)[over ¯]_{4}. Such a CFT has a spin fractionalization: spin-1 excitation can decay into a spin-1/2 right mover and a spin-1/2 left mover. We determine the critical theory by solving the partition function based on emergent symmetries and modular invariance condition of CFTs.

Choreographed entanglement dances: Topological states of quantum matter.

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

1/2(e

We address the question about the origin of the 1/2(e^{2}/h) conductance plateau observed in a recent experiment on an integer quantum Hall (IQH) film covered by a superconducting (SC) film. Since one-dimensional (1D) chiral Majorana fermions on the edge of the above device can give rise to the half quantized plateau, such a plateau is regarded as conclusive evidence for the chiral Majorana fermions. However, in this Letter we give another mechanism for the 1/2(e^{2}/h) conductance plateau. We find the 1/2(e^{2}/h) conductance plateau to be a general feature of a good electric contact between the IQH film and the SC film, and cannot distinguish the existence or the nonexistence of 1D chiral Majorana fermions. We also find that the contact conductance between a superconductor and an IQH edge channel has a non-Ohmic form σ_{SC-Hall}∝V^{2} in the k_{B}T≪eV limit, if the SC and IQH bulks are fully gapped.

Loop Optimization for Tensor Network Renormalization.

We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.

Hierarchy Construction and Non-Abelian Families of Generic Topological Orders.

We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one. We show that such construction is reversible and leads to a new equivalence relation between topological orders. We refer to the corresponding equivalence class (the orbit of the hierarchy construction) as "the non-Abelian family." Each non-Abelian family has one or a few root topological orders with the smallest number of anyon types. All the Abelian topological orders belong to the trivial non-Abelian family whose root is the trivial topological order. We show that Abelian anyons in root topological orders must be bosons or fermions with trivial mutual statistics between them. The classification of topological orders is then greatly simplified, by focusing on the roots of each family: those roots are given by non-Abelian modular extensions of representation categories of Abelian groups.

[Removal of AOX, Chroma and TOC in Chemical Dyestuff Wastewater with Iron Scraps-Fenton-Coagulation Combined Process].

Iron scraps-Fenton-coagulation process was applied to chemical dyestuff wastewater. The removal performance of absorbable organic halogens(AOX), chroma and total organic carbon (TOC) was investigated at different molar ratios of Fe2+ to H2O2 (1:3-1:15), iron scraps reaction time (2-5 h) and Fenton reaction time (20-80 min). The results showed that the removal ratios of AOX, chroma and TOC firstly increased and then decreased with the decrease of the molar ratio of Fe2+ to H2O2, while continuously increased with the increase of iron scraps and Fenton reaction time. The optimal condition was determined as Fe2+:H2O2 ratio of 1:8, iron scraps reaction time of 4 h and Fenton reaction time of 60 min, under which 94.2% of AOX, 93.7% of chroma and 27.2% of TOC were removed. A comparison study revealed that the iron scraps-Fenton-coagulation combined process could achieve much better removal of AOX, chroma and TOC than any other single or combined processes of iron treatment, Fenton oxidation and coagulation. GC-MS analysis revealed that halogenated compounds and anilines were efficiently removed, as well as nitrobenzenes, phenols, benzaldehydes, ethers, nitriles and heterocyclic compounds.·OH was found to devote much in the Fenton reaction according to the tert-butyl alcohol trapping hydroxyl radicals test.

Topological degeneracy (Majorana zero-mode) and 1 + 1D fermionic topological order in a magnetic chain on superconductor via spontaneous Z2(f) symmetry breaking.

We study a chain of ferromagnetic sites, ie nano-particles, molecules or atoms, on a substrate of fully gapped superconductors. We find that under quite realistic conditions, the fermion-number-parity symmetry Z2(f) can spontaneously break. In other words, such a chain can realize a 1 + 1D fermionic topologically ordered state and the corresponding two-fold topological degeneracy on an open chain. Such a topological degeneracy becomes the so called Majorana zero mode in the non-interacting limit.

Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States.

We propose a way-universal wave-function overlap-to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M^{d}) of closed spatial manifold M^{d}. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations.

Gapped domain walls, gapped boundaries, and topological degeneracy.

Gapped domain walls, as topological line defects between (2+1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which (2+1)D topological orders must have gapless edge modes, namely, which (1+1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix W, whose entries are the fusion-space dimensions W(ia), to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

[Advanced Treatment of Incineration Leachate with O3-BAC and Double O3-BAC].

Ozone-biological activated carbon (O3-BAC) process and double O3-BAC process were respectively used for advanced treatment of the biologically treated effluent of incineration leachate, and their pollutant removal performances were compared. The results showed that the double O3-BAC removed 75.9% ± 2.1% of chemical oxygen demand (COD), 78.8% ± 2.9% of UV254 and 96.8% ± 0.9% of color at ozone dosage of 200 mg x L(-1). The treated effluent was with COD of below 100 mg x L(-1) and color of below 40 times, meeting the emission requirements of GB 16889-2008. At the same ozone dosage, however, the O3-BAC removed 68.2% ± 1.3% of COD, 69.7% ± 0.5% of UV254 and 92.5% ± 1.1% of color. The treated effluent was with COD of around 150 mg x L(-1) and color of about 60 times, failing to meet the emission requirements. Namely, ozone of 290 mg x L(-1) was required by O3-BAC in order to achieve similar pollutant removals as those in double O3-BAC at O3 dosage of 200 mg x L(-1). In double O3-BAC at ozone dosage of 200 mg x L(-1), total phosphorus was removed by 63.5% ± 4.4%, and the phosphorus concentration in the effluent was remained 1 mg x L(-1) or less, directly meeting the emission requirement of GB 16889-2008.

[Study on the quality of digested piggery wastewater in large-scale farms in Jiaxing].

Pollution characteristics of digested piggery wastewater (DPW), including not only the chemical oxygen demand (COD), nitrogen and phosphorus but also the veterinary antibiotics and heavy metals, were investigated in ten large-scale pig farms in Jiaxing City. Results showed that the water quality of DPW greatly varied with farms and seasons. DPW in the spring group showed the highest pollutant concentration, with seven of the ten pig farms demonstrating COD of over 2 000 mg x L(-1), total nitrogen and ammonia nitrogen of over 1 000 mg x L(-1) and total phosphorus of over 60 mg x L(-1). Pollutant concentrations of DPW were lower in the autumn and winter groups, while the lowest was observed in the summer group. Unbalanced nutrient was observed in DPW, the carbon nitrogen ratio showed the lowest value of 0.8-4.3 in the autumn group. Four classes (tetracyclines, quinolones, macrolides and sulfonamides) of ten antibiotics and six heavy metals (Cu, Zn, Pb, Cd, Ni and Cr) were detectable in DPW from all the ten farms. Cu and Zn were the top two dominant heavy metals, with an average concentration of 1.88 mg x L(-1) and 7.63 mg L(-1), respectively. Tetracyclines (including Tetracycline, Oxytetracycline and Chlortetracycline) were always the dominant antibiotics. The total concentration of the ten antibiotics was in the range of 10.1 microg x L(-1) to 1090 microg x L(-1), far exceeding the antibiotics limit of 10 ng x L(-1) in the water environment specified by EU. Efficient but low cost treatment technologies are in urgent need in order to deal with the pollution by DPW, a wastewater that is not only difficult to remove nitrogen and phosphorus, but also seriously polluted by heavy metals and antibiotics.

Microscopic realization of two-dimensional bosonic topological insulators.

It is well known that a bosonic Mott insulator can be realized by condensing vortices of a boson condensate. Usually, a vortex becomes an antivortex (and vice versa) under time reversal symmetry, and the condensation of vortices results in a trivial Mott insulator. However, if each vortex or antivortex interacts with a spin trapped at its core, the time reversal transformation of the composite vortex operator will contain an extra minus sign. It turns out that such a composite vortex condensed state is a bosonic topological insulator (BTI) with gapless boundary excitations protected by U(1)⋊Z2(T) symmetry. We point out that in BTI, an external π-flux monodromy defect carries a Kramers doublet. We propose lattice model Hamiltonians to realize the BTI phase, which might be implemented in cold atom systems or spin-1 solid state systems.

[Study on chlorinated disinfection byproducts and the relevant health risk in tap water of J City].

J City lies in the downstream of Taihu Lake and its water source was micro-polluted by the well-developed industry and agriculture inside the city and in the upper stream. Tap water of J City is characterized as high concentrations of organics and ammonia nitrogen, and chlorinated disinfection byproducts (CDBPs), which has drawn many public concerns for the health risk. Tap water was sampled in May, August, October of 2012 and January of 2013. Four trihalomethanes (THMs) and five haloacetic acids (HAAs) were determined with the gas chromatography. Results revealed that THMs accounted for 88.1% of the sum of THMs and HAAs, with higher concentrations in May, August and January (39.34, 50.37 and 28.02 microg x L(-1), respectively) while obviously lower in October (19.19 microg x L(-1)), which were significantly higher than that of HAAs (2.58-4.02 microg x L(-1)). After boiled for three minutes, THMs were removed over 92.3% but HAAs were largely increased. The health risk of CDBPs was then calculated based on the health risk assessment model recommended by the USEPA. The health risk caused by carcinogenic CDBPs was within a range of 3.1 x 10(-6) - 7. 3 x 10(-6) in the tap water, all over the recommended level of 1 x 10(-6), but after boiled, the value significantly decreased to 7.9 x 10(-7), which is below the recommended level. The health risk caused by non-carcinogenic CDBPs absolutely increased from 2.1 x 10(-11) to 3.4 x 10(-9) after boiled, which is below the reference value of 10(-5).

Constructing a gapless spin-liquid state for the spin-1/2 J(1)-J(2) Heisenberg model on a square lattice.

We construct a class of projected entangled pair states which is exactly the resonating valence bond wave functions endowed with both short range and long range valence bonds. With an energetically preferred resonating valence bond pattern, the wave function is simplified to live in a one-parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin-1/2 J(1)-J(2) antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with an even or odd number of fluxes penetrating the cylinder and an even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin-liquid phase at the optimum parameter.

Symmetry-protected quantum spin Hall phases in two dimensions.

Symmetry-protected topological (SPT) states are short-range entangled states with symmetry. Nontrivial SPT states have symmetry-protected gapless edge excitations. In 2 dimension (2D), there are an infinite number of nontrivial SPT phases with SU(2) or SO(3) symmetry. These phases can be described by SU(2) or SO(3) nonlinear-sigma models with a quantized topological θ term. At an open boundary, the θ term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. Only the left movers (if θ>0) carry the SU(2) or SO(3) quantum numbers. As a result, the SU(2) SPT phases have a half-integer quantized spin Hall conductance and the SO(3) SPT phases have an even-integer quantized spin Hall conductance. Both the SU(2) and SO(3) SPT phases are symmetric under their U(1) subgroup and can be viewed as U(1) SPT phases with even-integer quantized Hall conductance.

Symmetry-protected topological orders in interacting bosonic systems.

Symmetry-protected topological (SPT) phases are bulk-gapped quantum phases with symmetries, which have gapless or degenerate boundary states as long as the symmetries are not broken. The SPT phases in free fermion systems, such as topological insulators, can be classified; however, it is not known what SPT phases exist in general interacting systems. We present a systematic way to construct SPT phases in interacting bosonic systems. Just as group theory allows us to construct 230 crystal structures in three-dimensional space, we use group cohomology theory to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry, leading to the discovery of bosonic topological insulators and superconductors.

[Implementation of a pretreatment device for an electronic nose].

A pretreament device was implemented for removing the interference of humidity on the baseline signal response of sensors in an electronic nose, which was used for rapid detection and real-time monitoring of volatile chlorinated hydrocarbons (VCHs) pollution in soil. The desiccant material was optimized, and the humidity removal performance and adsorpiton of VCHs was studied. The pretreatment device was evaluated by both the electronic nose and gas chromatography (GC) for its applicability in monitoring the PCE concentration in the desorption gas during the soil ventilation process. The following results were obtained: 1) A desiccant tube with anhydrous calcium chloride followed by a halogenated hydrocarbon separation tube was the best device, with a humidity removal rate of over 99%, and the baseline values of each sensor in the electronic nose were close to that of the control. 2) The desiccant device described above could continuously remove almost all the humidity from air with 75% humidity within 90 min, and the humidity removal rate remained above 95% within 120 min, while little interference was observed on the baseline of each sensor. 3) Little adsorption was observed by the pretreatment device, the relative error being only 3% - 5% between the concentration of VCHs before and after the filtration by the pretreatment device. 4) When applied for monitoring the remediation progress in a soil ventilation process, 99% of humidity was removed within 120 min from air with humidity of over 98%, and the data determined with the electronic nose and GC fitted each other very well, with R2 > 0.99. From the above, the pretreatment device connected with the electronic nose was considered to be applicable for monitoring the soil remediation process.

Interacting one-dimensional fermionic symmetry-protected topological phases.

In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z2, or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S(z) spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z4. Using group cohomology, one can additionally show that there are only four distinct phases for such one-dimensional superconductors even with strong interactions. Comparing their projective representations, we find that all these four symmetry-protected topological phases can be realized with free fermions. Further, we show that one-dimensional fermionic superconducting phases with Z(n) discrete S(z) spin rotation and time-reversal symmetries are classified by Z4 when n is even and Z2 when n is odd; again, all these strongly interacting topological phases can be realized by noninteracting fermions. Our approach can be applied to systems with other symmetries to see which one-dimensional topological phases can be realized with free fermions.