Gapped Z2Z_2 spin liquid in the breathing kagome Heisenberg antiferromagnet

We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries $Z_2$ topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy

Semionic resonating valence bond states

The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a Z_2 topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic Resonating Valence Bond (RVB) states, this is, Resonating Valence Bond states which are in the Z_2 ordered double-semion phase, and study them using Projected Entangled Pair States (PEPS). We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the Toric Code Z_2 topological phase. In particular, we find that a suitably optimized "semionic simplex RVB" outperforms the equally optimized conventional "simplex RVB" state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests to use the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space group symmetry breaking in valence bond wavefunctions with double-semion topological order.Comment: 14 pages, 21 figures. v2: minor correction

Study of anyon condensation and topological phase transitions from a Z4\mathbb{Z}_4 topological phase using Projected Entangled Pair States

We use Projected Entangled Pair States (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons, and serve as a substitute for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a $\mathbb Z_4$ symmetry, which contains $\mathbb Z_4$ quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.Comment: 21+6 page

Detecting subsystem symmetry protected topological order via entanglement entropy

Subsystem symmetry protected topological (SSPT) order is a type of quantum order that is protected by symmetries acting on lower-dimensional subsystems of the entire system. In this paper, we show how SSPT order can be characterized and detected by a constant correction to the entanglement area law, similar to the topological entanglement entropy. Focusing on the paradigmatic two-dimensional cluster phase as an example, we use tensor network methods to give an analytic argument that almost all states in the phase exhibit the same correction to the area law, such that this correction may be used to reliably detect the SSPT order of the cluster phase. Based on this idea, we formulate a numerical method that uses tensor networks to extract this correction from ground-state wave functions. We use this method to study the fate of the SSPT order of the cluster state under various external fields and interactions, and find that the correction persists unless a phase transition is crossed, or the subsystem symmetry is explicitly broken. Surprisingly, these results uncover that the SSPT order of the cluster state persists beyond the cluster phase, thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss the correction to the area law found in three-dimensional cluster states on different lattices, indicating rich behavior for general subsystem symmetriesComment: 17 pages. v2: Published version, minor changes throughou

Entanglement order parameters and critical behavior for topological phase transitions and beyond

Topological phases are exotic quantum phases which are lacking the characterization in terms of order parameters. In this paper, we develop a unified framework based on variational iPEPS for the quantitative study of both topological and conventional phase transitions through entanglement order parameters. To this end, we employ tensor networks with suitable physical and/or entanglement symmetries encoded, and allow for order parameters detecting the behavior of any of those symmetries, both physical and entanglement ones. First, this gives rise to entanglement-based order parameters for topological phases. These topological order parameters allow to quantitatively probe topological phase transitions and to identify their universal behavior. We apply our framework to the study of the Toric Code model in different magnetic fields, which in some cases maps to the (2+1)D Ising model. We identify 3D Ising critical exponents for the entire transition, consistent with those special cases and general belief. However, we moreover find an unknown critical exponent beta=0.021. We then apply our framework of entanglement order parameters to conventional phase transitions. We construct a novel type of disorder operator (or disorder parameter), which is non-zero in the disordered phase and measures the response of the wavefunction to a symmetry twist in the entanglement. We numerically evaluate this disorder operator for the (2+1)D transverse field Ising model, where we again recover a critical exponent hitherto unknown in the model, beta=0.024, consistent with the findings for the Toric Code. This shows that entanglement order parameters can provide additional means of characterizing the universal data both at topological and conventional phase transitions, and altogether demonstrates the power of this framework to identify the universal data underlying the transition.Comment: v2: Significantly extended; added new Section IV with construction and study of disorder parameters for conventional phase transition

Smokeless Tobacco Use: A Risk Factor for Hyperhomocysteinemia in a Pakistani Population

Background Smokeless tobacco (ST) use is highly prevalent in the South Asian populations. While there have been a number of reports on association of ST consumption with cancer, very few studies have been conducted to investigate its relationship with cardiovascular disease. Hyperhomocysteinemia is a well-recognized risk factor for cardiovascular disease; however, its association with ST use has never been investigated. The objective of this study was to evaluate the relationship of ST use with hyperhomocysteinemia in an urban Pakistani population. Methodology/Principal Findings In a cross-sectional study for assessment of risks of hyperhomocysteinemia, 872 healthy adults (355 males and 517 females of age range 18–60 years) were recruited from a low-income population in Karachi, Pakistan. A detailed questionnaire was administered which included information about smoking, non-smoking, use of ST alone (chewing as well as sniffing) and use of ST with betel nuts. Fasting serum/plasma levels of homocysteine, folate, vitamin B12 and pyridoxal phosphate (PLP; a coenzymic form of vitamin B6) were analyzed. In this population, 43.4% males and 15.5% females were found to be regular users of ST products. Laborers and vendors were the major ST consumers. Smoking was not found to be associated with plasma/serum concentrations of homocysteine, folate, vitamin B12 and PLP. However, homocysteine concentrations in the group which consumed ST alone and the group which consumed ST along with betel nut were significantly higher compared to the non-user group (17.7±7.5 µmol/L, 25.48 µmol/L vs. 11.95 µmol/L, respectively; p\u3c0.01). Odds ratio for the association of hyperhomocysteinemia (\u3e15 µmol/L) was 11-fold higher in the ST-consumer group compared to the non-user group, [OR (95%CI) =11.34 (7.58–16.96); p\u3c0.001], when the model was adjusted for age, gender, folate and vitamin B12 status. Conclusion This study shows a positive association between ST consumption and hyperhomocysteinemia in a low-income urban Pakistani population

Entanglement phases as holographic duals of anyon condensates

Anyon condensation forms a mechanism which allows to relate different topological phases. We study anyon condensation in the framework of Projected Entangled Pair States (PEPS) where topological order is characterized through local symmetries of the entanglement. We show that anyon condensation is in one-to-one correspondence to the behavior of the virtual entanglement state at the boundary (i.e., the entanglement spectrum) under those symmetries, which encompasses both symmetry breaking and symmetry protected (SPT) order, and we use this to characterize all anyon condensations for abelian double models through the structure of their entanglement spectrum. We illustrate our findings with the Z4 double model, which can give rise to both Toric Code and Doubled Semion order through condensation, distinguished by the SPT structure of their entanglement. Using the ability of our framework to directly measure order parameters for condensation and deconfinement, we numerically study the phase diagram of the model, including direct phase transitions between the Doubled Semion and the Toric Code phase which are not described by anyon condensation.Comment: 20+7 page

Physico-Chemical Properties and Fertility Status of District Rahim Yar Khan, Pakistan

Physico-chemical properties of soils in Rahim Yar Khan district of Punjab Province, Pakistan, were determined for better management. A total of 3198 soil samples collected from all tehsils of Rahim Yar Khan district (662 samples from Khan Pur, 800 samples from Liaquat Pur, 866 samples from Rahim Yar Khan and 870 soil samples from Sadiq Abad) were tested in Soil and Water Testing Laboratory, Bahawalpur, Pakistan during 2011-2013. Soil characteristics of Rahim Yar Khan district were evaluated through physical and chemical analyses. Representative soil samples received/collected from farmers fields were analyzed for texture, electrical conductivity (EC), pH, organic matter (OM), available phosphorus (P) and potassium (K) contents. Texture of the soils varied from sandy loam to loam. About 53% soils had EC values within the normal range (< 4 dS m-1). The pH values of 92% soils ranged from 7.5 to 8.5 with an average of 8.06 and 7% soils had pH > 8.5. About 93% soils were poor (< 0.86%) in organic matter and only 7% soil samples had satisfactory level of organic matter (0.86-1.29%). About 47% soils were poor( < 7 ppm) in available phosphorus,33 % samples had satisfactory level of  available phosphorus (7-14 ppm) and only 20 % samples had adequate level of  available phosphorus (>14 ppm) contents. The K status of most of soils was in satisfactory (50%) and adequate range (43%). The objective of present study is to assess the soil fertility and salinity status of Rahim Yar Khan district for formulation of optimum fertilizer recommendations for different crops grown in the area. Keywords: Soil Analysis, EC, pH, SOM, P, K, Rahim Yar Kha

Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the Resonating Valence Bond wavefunctions to a trimer and SU(3) setting. We demonstrate that these models carry a Z_3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological 9-fold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers -- it can display either Z_3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior. Our results accordingly hold for the SU(3) model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and SU(3)-singlet ansatzes to model SU(3) topological spin liquids on the kagome lattice