10,990 research outputs found

    Topological Z2\mathbb{Z}_2 Resonating-Valence-Bond Spin Liquid on the Square Lattice

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    A one-parameter family of long-range resonating valence bond (RVB) state on the square lattice was previously proposed to describe a critical spin liquid (SL) phase of the spin-1/21/2 frustrated Heisenberg model. We provide evidence that this RVB state in fact also realises a topological (long-range entangled) Z2\mathbb{Z}_2 SL, limited by two transitions to critical SL phases. The topological phase is naturally connected to the Z2\mathbb{Z}_2 gauge symmetry of the local tensor. This work shows that, on one hand, spin-1/21/2 topological SL with C4vC_{4v} point group symmetry and SU(2)SU(2) spin rotation symmetry exists on the square lattice and, on the other hand, criticality and nonbipartiteness are compatible. We also point out that, strong similarities between our phase diagram and the ones of classical interacting dimer models suggest both can be described by similar Kosterlitz-Thouless transitions. This scenario is further supported by the analysis of the one-dimensional boundary state.Comment: v2: improve presentation, present new evidence and add reference

    SU(3) trimer resonating-valence-bond state on the square lattice

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    We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with C4vC_{4v} point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular SS and TT matrices by constructing all nine topological sectors on a torus and establish the existence of Z3\mathbb{Z}_3 topological order in this SU(3) tRVB state.Comment: 6 pages, 6 figure

    Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

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    We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the Z2\mathbb{Z}_2-topological order (or toric code type), which has a long correlation length Ο∌10\xi\sim 10 unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long Ο\xi explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure

    Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

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    Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice π/2\pi/2-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results.Comment: 10 pages, 12 figures. V2: reference added. V3: reference added, published versio

    Occupation Life Cycle

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    This paper explores the evolution of occupations within the context of industry and technology life cycles, highlighting the critical yet underexplored intersection between occupational trends and broader economic dynamics. Introducing the Occupation Life Cycle (OLC) model, we delineate five stages (i.e., growth, peak, fluctuation, maturity, and decline) to systematically explore the trajectory of occupations. Utilizing job posting data from one of China's largest recruitment platforms as a novel proxy, our study meticulously tracks the fluctuations and emerging trends in the labor market from 2018 to 2023. Through a detailed examination of representative roles, such as short video operators and data analysts, alongside emerging occupations within the artificial intelligence (AI) sector, our findings allocate occupations to specific life cycle stages, revealing insightful patterns of occupational development and decline. Our findings offer a unique perspective on the interplay between occupational evolution and economic factors, with a particular focus on the rapidly changing Chinese labor market. This study not only contributes to the theoretical understanding of OLC but also provides practical insights for policymakers, educators, and industry leaders facing the challenges of workforce planning and development in the face of technological advancement and market shifts
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