AWhat changed
Watanabe connected a gap within a fixed conserved-charge sector to the static response of that charge at zero temperature. For local quantum systems with a U(1) symmetry, a subregion charge fluctuation creates a neutral variational excitation. The boundary cost of this excitation forces charge fluctuations per volume to vanish when the neutral gap stays positive. Combining this with a susceptibility bound gives zero charge susceptibility, without translation symmetry or a quasiparticle description. The result clarifies part of the connection between magnetization plateaus and neutral-excitation constraints.
Scientific scope
Watanabe connected a gap within a fixed conserved-charge sector to the static response of that charge at zero temperature. For local quantum systems with a U(1) symmetry, a subregion charge fluctuation creates a neutral variational excitation. The boundary cost of this excitation forces charge fluctuations per volume to vanish when the neutral gap stays positive. Combining this with a susceptibility bound gives zero charge susceptibility, without translation symmetry or a quasiparticle description. The result clarifies part of the connection between magnetization plateaus and neutral-excitation constraints. The argument uses local Hamiltonian and charge densities, a well-defined reservoir and thermodynamic response limit, and a unique ground state within the selected charge sector. Its extension to symmetry-breaking degeneracy relies on suppressed matrix elements between the distinct states. The conclusion is zero susceptibility at the specified chemical potential; it does not by itself prove a plateau on a finite interval or a gap to charged excitations. The converse fails: gapless neutral excitations can coexist with zero susceptibility or a magnetization plateau.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The argument uses local Hamiltonian and charge densities, a well-defined reservoir and thermodynamic response limit, and a unique ground state within the selected charge sector. Its extension to symmetry-breaking degeneracy relies on suppressed matrix elements between the distinct states. The conclusion is zero susceptibility at the specified chemical potential; it does not by itself prove a plateau on a finite interval or a gap to charged excitations. The converse fails: gapless neutral excitations can coexist with zero susceptibility or a magnetization plateau.
Contributors
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