REVIEW 3 cited by
Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
read the original abstract
We prove that the Ising models with transverse and longitudinal fields on the hypercubic lattices with dimensions higher than one have no local conserved quantities other than the Hamiltonian. This holds for any value of the longitudinal field, including zero, as far as the transverse field and the Ising interactions are nonzero. The conserved quantity considered here is ``local'' in a very weak sense: it can be written as a linear combination of operators whose side lengths of the supports in one direction do not exceed half the system size, while the side lengths in the other directions are arbitrary. We also prove that the above result holds even in the ladder system. Our results extend the recently developed technique of the proof of absence of local conserved quantities in one-dimensional systems to higher dimensions and to the ladder.
Forward citations
Cited by 3 Pith papers
-
Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
Only two models in the class of S=1/2 zigzag spin chains are integrable (one classical, one Bethe-ansatz solvable); all others are non-integrable, with no missing integrable models and no intermediate cases having fin...
-
The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
-
Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.