Choreographed entangle dances: topological states of quantum matter

Abstract

For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at zero temperature, even symmetric disordered liquids can have features, which give rise to topological phases of quantum matter. Some of the topological phases are highly entangled (i.e. have topological order), while others are weakly entangled (i.e. have SPT order). In this article, we will briefly introduce those new zero-temperature states of matter and their amazing emergent properties. We will also discuss their significance in unifying some most basic concepts in nature.

8 pages 5 figures

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• Realization of fractional quantum Hall state with interacting photons
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• Topological edge states at Floquet quantum criticality
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• Role of alkaline metal in the rare-earth triangular antiferromagnet KYbO${}_2$
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• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
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• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
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• Gauge symmetry of excited states in projected entangled-pair state simulations
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• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Robust translational invariance in topological bands against lattice potentials and disorders
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• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Manipulating Topological Polaritons in Optomechanical Ladders
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Universal fluctuating regime in triangular chromate antiferromagnets
• Topological Order of Quantum Gravity in $Ad{S}_3$ Spacetime