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}.

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.

Application of Auto-regressive Linear Model in Understanding the Effect of Climate on Malaria Vectors Dynamics in the Three Gorges Reservoir.

It is important to understand the dynamics of malaria vectors in implementing malaria control strategies. Six villages were selected from different sections in the Three Gorges Reservoir for exploring the relationship between the climatic factors and its malaria vector density from 1997 to 2007 using the auto-regressive linear model regression method. The result indicated that both temperature and precipitation were better modeled as quadratic rather than linearly related to the density of Anopheles sinensis.

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.

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.

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.

[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.

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).

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.

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.

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.

[Morphology and habits of An. anthropophagus and its role in malaria transmission in Hengqin Island of Zhuhai City].

OBJECTIVE: To study the morphology and ecological habits of An. anthropophagus and its role in malaria transmission in Hengqin Island of Zhuhai City, Guangdong Province. METHODS: Mosquitoes were captured through overnight/semi-overnight trapping with human and cattle baits as well as lamp-trapping. The specimens were morphologically identified through describing the adult mosquitoes, eggs and pupae. The relevant parameters were collected to calculate the vectorial capacity of both An. anthropophagus and An. sinensis. RESULTS: There is no morphological difference between the isolate of An. aothropophagus from Hengqin Island and that from Jiangsu Province. Its human blood preference ratio and human blood index was 0.94 and 0.75 respectively, and the vectorial capacity of An. anthropophagus was 7.36 times higher than that of An.sinensis (5.1914/0.7052). CONCLUSION: The isolate of An. anthropophagus from Hengqin Island belongs same species to that from the mainland, which prefers to human blood and shows higher malaria transmission potential.

[Sequence difference of ribosomal DNA second internal transcribed spacer in Anopheles minimus in different localities].

OBJECTIVE: To compare the sequence difference of the ribosomal DNA second internal transcribed spacer (ITS2) in Anopheles minimus from Yunnan, Hainan, Guangxi of China and from Thailand. METHODS: Single mosquito's legs were digested to extract DNA; the rDNA-ITS2 region was amplified by specific primers and the PCR products were purified, sequenced and analysed. RESULTS: Two different kinds of ITS2 sequences, temporarily named as An. minimus A and An. minimus C, were found in this study. The length and GC contents of ITS2 region in species A and species C are 481 bp, 54.04% and 483 bp, 54.23%, respectively. Two species differed by 5.8% in the ITS2 sequences owing to 22 fixed nucleotide substitutions and indels. CONCLUSION: Two cryptic species, An. minimus A and An. minimus C, were found in the research localities.

[Malaria situation in the People's Republic of China in 2002].

This summary was made on the basis of the annual reports of malaria control from the professional institutions in the 21 Provinces/Municipality/Autonomous Region (P/M/A). The number of malaria cases reported in the country was 35,298 in the year 2002 and the incidence rate was 0.348/10,000, an increase of 68.2% than that of the last year and the largest increase since 1994. The total number of suspected cases was 136,902, and the death toll due to malaria was 42. Based on the numbers of malaria cases and suspected cases from the case reporting system of P/M/A, and on the field investigations of the cases missed (failed to report), the estimated total number of malaria cases was 387,000 in 2002. In the South, the provinces of Yunnan and Hainan have been the major area of malaria historically. About 50% of the reported cases in the country were from the two provinces in 2002. There were 12,218 cases reported from Yunnan with 33 deaths, the incidence was 3.026/10,000, 31.6% increase than that in the last year. Among the reported cases, 2,922 were cases of falciparum malaria. The estimated number of malaria cases was 18 times more than that reported. The number of reported cases in Hainan was 5,354 with an incidence of 6.645/10,000, 15.5% increase than that of the last year; there were 1,210 cases of falciparum malaria, and 1 death. The estimated number of malaria cases was 100,000. Covered were also the other P/M/A in the South: Fujian, Guizhou, Guangxi, Guangdong, Sichuan and Chongqing. In Fujian province, 92 malaria cases were reported, all imported, with an incidence of 0.028/10,000 which increased by 272.8% than that in the last year. There were 713 cases reported in Guizhou with an incidence of 0.193/10,000, increased by 17.1%. The number of reported malaria cases was 392 in Guangxi, with an incidence rate of 0.082/10,000, increased by 14.0%. The incidence slightly decreased in Sichuan, Guangdong and Chongqing, and the case number was 443, 403 and 130 respectively. The cases from the 6 provinces/municipality occupied 6.2% of all cases reported from the country. The 5 provinces in central China were also important in malaria control program. Hubei province reported 5,101 malaria cases (incidence 0.895/10,000), increased by 161.6% than that of the last year; plus suspected cases of 5,614, the total number of malaria cases was estimated to be 11,000. The number of reported cases in Anhui province was 5,999 (0.958/10,000), second largest to that of Yunnan province, increased by 123.6%; with 22,615 suspected cases, the total number of malaria cases was estimated to be 28,000. The case number reported in Henan and Jiangsu provinces was 2,921 and 686 respectively, the incidence decreased by 35.1% and 41.7% respectively, but in Shandong province, 52 cases reported with an increase of 23.8%. Focal outbreaks occurred in 81 villages of 17 counties in the provinces of Hubei, Anhui, Henan and Jiangsu, where Anopheles sinensis is the principal transmitting vector. Malaria cases reported from the 5 provinces in central China accounted for 42% of the national figure. Three hundred and thirteen and 229 cases respectively reported from Hunan and Zhejiang provinces, the incidence increased by 44.2% and 288.1% with 3 and 1 death respectively. There were 28 cases in Jiangxi province with a little fluctuation situation. In Shanghai, 135 cases were recorded with an increase of incidence by 66.7%; 16 were infected locally and others all imported. In the provinces of Shaanxi, Shanxi, Liaoning and Gansu, sporadical malaria cases were still reported. The number of Plasmodium falciparum malaria cases was 4,319, accounting for 12.2% of the total cases; of which 13.4% (556) were imported cases. The locally infected falciparum malaria was found in 61 counties/cities of Hainan, Yunnan, Guangxi, and Shaanxi; of which 42 counties/cities were in Yunnan, increased by 11, 16 counties/cities in Hainan, increased by 5, 2 counties in Guangxi and 1 county in Shaanxi. Imported falciparum malaria cases were reported in 114 counties of 14 P/M/A, 2 provinces less but 6 counties more than that in 2001. Due to the strengthening of surveillance and effective management of dubious epidemic conditions, there was no local transmission of falciparum malaria in the above provinces except 2 locally infected cases in Guangxi and 1 in Shaanxi. In areas where the transmission of falciparum malaria has been interrupted but vectors and transmission conditions exist, it is of great importance to prevent the transmission of falciparum malaria by imported source of infection. The main reasons for the considerable increase of malaria transmission in 2002 were as follows: the provinces of Yunnan and Hainan still faced a severe situation of malaria epidemic with a spread of Plasmodium falciparum, especially in the mountainous area of Hainan and the 25 frontier counties in the south and west of Yunnan. Following the development of economy and trade, more frequent population movement occurred among the provinces and between Yunnan and bordering countries, malaria situation becomes more challenging. In central part of the country including Hubei, Anhui, Henan and Jiangsu, where Anopheles sinensis was the principal vector, the malaria situation was highly unstable and local outbreaks took place from time to time. Meanwhile, the increase of the floating population brought more imported cases into Guangdong, Guangxi, Guizhou, Hunan, Fujian, Jiangxi, Chongqing, Shangdong, Zhejiang, and Shanghai, which accounted for 47%-100% of the cases reported in the P/M/A. Furthermore, because of the faultiness in the public health system and the network of the case reporting system, more malaria cases failed to be reported and it is therefore a challenge in implementing the program of malaria control and prevention.

[Study on the thresholds of malaria transmission by Anopheles anthropophagus in Hubei Province].

OBJECTIVE: To study the thresholds and potential of malaria transmission by Anopheles anthropophagus in Hubei Province and provide indicators for the disease surveillance, early warning, prevention and control in the locality. METHODS: From July to August 2001, field investigations on vectors and malaria situation were carried out in the village of Yanjiafan, Suizhou City, where the malaria incidence was high. The entomological investigations included the man-biting rate, the proportion of parous anophelines, the human blood index and the blood preference. The others included malaria incidence and parasite rate in human population, the intervals from episode to treatment of the cases, and collection of data on the mean temperature in the area. Based on the formula of basic reproductive rate, the critical man-biting rate was estimated. RESULTS: 92.6% (63/68) of An. anthropophagus were found to have human blood meals, it occupied 91.5% (97/106) of the mosquitoes in human dwellings, its human blood index and vectorial capacity were 12.5 times (0.50/0.04) and 6.5 times (0.9448/0.1449) higher than those of An. sinensis. The critical man-biting rate was 0.2823 and the adjusted man-biting rate was 3.5 times of its critical man-biting rate (0.9892/0.2823). The malaria incidence was 0.65% (12/1844) and the parasite rate in pupils was 0.51%(1/198). CONCLUSION: A reduction of the adjusted man-biting rate of An. anthropophagus by 71.5% is needed for interrupting malaria transmission by this vector in the study area.

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.