10,990 research outputs found
Topological Resonating-Valence-Bond Spin Liquid on the Square Lattice
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- frustrated Heisenberg model. We provide evidence
that this RVB state in fact also realises a topological (long-range entangled)
SL, limited by two transitions to critical SL phases. The
topological phase is naturally connected to the gauge symmetry
of the local tensor. This work shows that, on one hand, spin- topological
SL with point group symmetry and 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
We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state
with 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
and matrices by constructing all nine topological sectors on a torus
and establish the existence of topological order in this SU(3)
tRVB state.Comment: 6 pages, 6 figure
Gapped spin liquid with -topological order for kagome Heisenberg model
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 -topological order (or toric code type), which has a long
correlation length unit cell length. We justify that the TRG
method can handle very large systems with over thousands of spins. Such a long
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
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 -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
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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