The S=(1)/(2) XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities

2024/12/24 by Shiraishi, Naoto, Tasaki, Hal · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2412.18504

Abstract

We study the S=(1)/(2) quantum spin system on the d-dimensional hypercubic lattice with d≥2 with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently developed for quantum spin chains, we prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian. This result strongly suggests that the model is non-integrable. We note that our result applies to the XX model without a magnetic field, which is one of the easiest solvable models in one dimension.

Cited by

• Absence of local conserved charges of the Fredkin spin chain and its truncated versions
• Absence of nontrivial local conserved quantities in the Hubbard model on the two or higher dimensional hypercubic lattice

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