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.
Quasiadia- batic continuation of quantum states: The stabil- ity of topological ground-state degeneracy and emer- gent gauge invariance,
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k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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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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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.