In the X-Q model the Néel-VBS transition is strongly first-order for N>2 because the X term cannot generate enough U(1) fluctuations of the dimer pattern.
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Quantum quenches in the Ising chain exhibit qualitatively distinct out-of-equilibrium dynamics when crossing continuous versus first-order quantum transitions depending on the transverse field strength.
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SU($N$) Quantum Spin Model with Weak and Strong First-Order N\'eel to Valence-Bond Solid Transitions
In the X-Q model the Néel-VBS transition is strongly first-order for N>2 because the X term cannot generate enough U(1) fluctuations of the dimer pattern.
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Quantum quenches across continuous and first-order quantum transitions in one-dimensional quantum Ising models
Quantum quenches in the Ising chain exhibit qualitatively distinct out-of-equilibrium dynamics when crossing continuous versus first-order quantum transitions depending on the transverse field strength.