In disordered 1D quantum spin ensembles with Ising symmetry, gapped phases exhibit a strict trade-off: they have either long-range Edwards-Anderson order or even-parity disorder, but not both.
Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Combined with Laughlin's argument on the quantized Hall conductivity, Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number, on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength and particle statistics (bose/fermi), a finite excitation gap is possible only when the particle number per unit cell of the groundstate is an integer.
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Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Develops local diagnostics for strong symmetries and strong-to-weak symmetry breaking via infinite-volume definitions and local charge coherence, introduces von Neumann symmetries, and derives an LSM-type anomaly constraint for quantum spin chains.
U(3) infrared parton theory unifies a ν=1/3 FCI with topological superconductors (SC* preserving U(1)_3, chiral TSC with c_-=3/2, strong-pairing with c_-=3) and a σ_xy=0 CDW.
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
citing papers explorer
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Order-disorder trade-off in dirty quantum systems
In disordered 1D quantum spin ensembles with Ising symmetry, gapped phases exhibit a strict trade-off: they have either long-range Edwards-Anderson order or even-parity disorder, but not both.
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Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems
Develops local diagnostics for strong symmetries and strong-to-weak symmetry breaking via infinite-volume definitions and local charge coherence, introduces von Neumann symmetries, and derives an LSM-type anomaly constraint for quantum spin chains.
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Topological superconductivity from Abelian fractional Chern insulators
U(3) infrared parton theory unifies a ν=1/3 FCI with topological superconductors (SC* preserving U(1)_3, chiral TSC with c_-=3/2, strong-pairing with c_-=3) and a σ_xy=0 CDW.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.