Quantum Criticality with Emergent Symmetry in the Extended Shastry-Sutherland Model.

Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.

Emergent symmetry in quantum phase transition: From deconfined quantum critical point to gapless quantum spin liquid.

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the J1x-J1y-J2 model, which contains anisotropic nearest-neighbor couplings J1x,J1y and the next nearest neighbor coupling J2. For small J1y/J1x, by tuning J2, a direct continuous transition between the AFM and valence bond solid phase is observed. With growing J1y/J1x, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM-VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL-VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

Preparation and Density Functional Theory Studies of Aluminosilicate-Based Ceramic Solidified Products for Sr Immobilization.

Strontium is a common radionuclide in radioactive waste, and its release into the environment can cause enormous damage to the ecosystem environment. In this study, the natural mineral allophane was selected as the substrate to prepare solidified ceramic products by cold pressing/sintering to solve the problem of the final disposal of radioactive strontium. Ceramic solidified products with various crystal structures were successfully prepared, and the microscopic morphology and energy-dispersive spectroscopy images of the samples showed a uniform distribution of Sr in the solidified products. Sr2Al2SiO7 and SrAl2Si2O8, which can stably solidify strontium, were formed in the solidified products, and the structural characteristics and stability of the above-mentioned substances were analyzed from the perspective of quantum chemical calculations using density functional theory. The calculation results showed that the overall deformation resistance of Sr2Al2SiO7 was higher than that of SrAl2Si2O8. Considering the isomorphic substitution effect of CaO impurities, we inferred that a mixed-crystalline structure of Ca2-xSrxAl2SiO7 may be present in the solidified products.

Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1-J2 square antiferromagnetic Heisenberg model.

The nature of the zero-temperature phase diagram of the spin-1/2J1-J2 Heisenberg model on a square lattice has been debated in the past three decades, and it remains one of the fundamental problems unsettled in the study of quantum many-body theory. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of the J1-J2 Heisenberg model up to 24×24 sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region 0.56≲J2/J1≤0.61 before the system enters the well known collinear antiferromagnetic phase. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems. Finally, an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point (DQCP).

Non-Abelian three-loop braiding statistics for 3D fermionic topological phases.

Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing topological quantum computation. Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics. In this work, we systematically study the so-called three-loop braiding statistics for 3D interacting fermion systems. Most surprisingly, we discover new types of non-Abelian three-loop braiding statistics that can only be realized in fermionic systems (or equivalently bosonic systems with emergent fermionic particles). On the other hand, due to the correspondence between gauge theories with fermionic particles and classifying fermionic symmetry-protected topological (FSPT) phases with unitary symmetries, our study also gives rise to an alternative way to classify FSPT phases. We further compare the classification results for FSPT phases with arbitrary Abelian unitary total symmetry Gf and find systematical agreement with previous studies.

Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity.

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

Anomalous Symmetry Protected Topological States in Interacting Fermion Systems.

The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We first demonstrate the essential idea by considering an anomalous topological superconductor with time-reversal symmetry T^{2}=1 in 2D. The physical reason for this is that the fermion parity might be changed locally by certain symmetry action, but it is conserved if we introduce a bulk. Then we discuss the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry G_{f}=G_{b}×Z_{2}^{f}. Finally, potential experimental realizations of ASPT states are also addressed.

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.

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.

Topological response theory of Abelian symmetry-protected topological phases in two dimensions.

It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with Zm symmetry and find the classification of SPT phases depends on the parity of m: for even m there are 2m classes, m out of which is intrinsically fermionic SPT phases and cannot be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.

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.

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 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.

[Impact of pesticide use on the density of Anopheles anthropophagus and malaria incidence].

OBJECTIVE: To investigate the impact of the application of chemical pesticides on the distribution of Anopheles anthropophagus in rice fields and the malaria incidence. METHOD: Twenty-four villages from 16 counties in the provinces of Zhejiang, Sichuan and Guangxi were chosen for the surveys in the period of 1983-1987. For the survey of An. anthropophagus, indoor human bait trapping until midnight and catching the mosquitoes in all the nets in early morning were carried out to get the density and population ratio of the mosquitoes. Historical data on Anopheles spp., malaria incidence, acreage of the single or double season cropping of rice and on the quantity of chemical pesticide used in rice fields were collected from the study areas. RESULTS: In Hang-jia-hu region of Zhejiang Province, double season rice cropping was performed at that time, the quantity of pesticides used in 1973 was 45 kg/hm2, which was as high as 50 times than that in the 1950s. The density of An. anthropophagus decreased yearly, no An. anthropophagus could be found at 11 survey points in late 1980s. The malaria incidence dropped to less than 1 per 10000. In Leshan and Yibin areas of Sichuan Province, the major cultivation was single cropping, pesticides were applied in paddy fields since 1960s, and the average quantity of pesticides used was 8.6 kg/hm2 during 1970s-1980s. No significant difference on the density of An. anthropophagus was revealed between 1980s (86.2%) and 1960s (82.2%) (chi2=0.63, P>0.05). After mid-1980s, pesticide use gradually increased, and reached to 18.18 kg/hm2 in average in the years after 2000. The density of An. anthropophagus decreased, no An. anthropophagus was found in 2010 in the area surveyed and no malaria cases were reported as well. With double season cropping in Huanjiang County of Guangxi, the pesticide amount consumed was 1.79kg/hm2, 25.13 kg/hm2 and 7.68 kg/hm2 in paddy fields in 1960s, 1970s, and 1980s, respectively. The proportion of An. anthropophagus in anophelines was 52%(1 747/3 392) in the beginning of the 1980s. After the year 2000, the average pesticide use increased to 20.38 kg/hm2 in paddy fields. It was difficult to find An. anthropophagus in human dwellings after 2008. The average annual malaria incidence dropped to 0.14 per 10 000. CONCLUSION: Change of farming activities and especially use of chemical pesticides in high quantity at the rice fields undermine the breeding environments of An. anthropophagus, greatly reduce the mosquito population and therefore the malaria incidence.

[Investigation on anopheline species in Chayu County, Linzhi Prefecture of Tibet Autonomous Region].

OBJECTIVE: To investigate Anopheline species in Chayu County of Linzhi Prefecture, Tibet. METHODS: Four natural villages in Chayu County were selected in this study in 2010. The methods of overnight/semi-overnight trapping indoor and outdoor human-bait, and overnight trapping with light traps were used, and all the Anopheline mosquitoes were confirmed by morphological characteristics. RESULTS: Totally 2 991 Anopheline mosquitoes were captured, with 76.36% (2 284/2 291) of An. peditaeniatus, 22.30% (667/2 291) of An. maculates group. The average densities of An. peditaeniatus by semi-overnight trapping were 56.2/per person indoor and 4/per person outdoor respectively, and the average densities of An. maculatus group by semi-overnight trapping were 17.8/per person indoor and 17.9/per person outdoor respectively. The man-biting rates of An. peditaeniatus by overnight trapping were 28.1/per person indoor and 2/per person outdoor respectively, and were both 8.9/per person to An. maculatus group. CONCLUSION: An. peditaeniatus and An. maculatus group are the possible transmission vectors of malaria in Chayu County.

Non-abelian quantum Hall effect in topological flat bands.

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.

Fractional quantum Hall effect of hard-core bosons in topological flat bands.

Recent proposals of topological flat band models have provided a new route to realize the fractional quantum Hall effect without Landau levels. We study hard-core bosons with short-range interactions in two representative topological flat band models, one of which is the well-known Haldane model (but with different parameters). We demonstrate that fractional quantum Hall states emerge with signatures of an even number of quasidegenerate ground states on a torus and a robust spectrum gap separating these states from the higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.

Fractional quantum Hall effect in the absence of Landau levels.

It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.

Nearly flatbands with nontrivial topology.

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

Gapped two-body hamiltonian whose unique ground state is universal for one-way quantum computation.

Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be remarkably valuable, if only it were thermodynamically stable and experimentally accessible, by virtue of being the unique ground state of a physically reasonable Hamiltonian made of two-body, nearest-neighbor interactions. We introduce such a state, composed of six-state particles on a hexagonal lattice, and describe a general method for analyzing its properties based on its projected entangled pair state representation.