REVIEW 3 cited by
Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
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
abstract
For any locality-preserving action of a group $G$ on a quantum spin chain one can define an anomaly index taking values in the group cohomology of $G$. The anomaly index is a kinematic quantity, it does not depend on the Hamiltonian. We prove that a nonzero anomaly index prohibits any $G$-invariant Hamiltonian from having $G$-invariant gapped ground states. Lieb-Schultz-Mattis-type theorems are a special case of this result when $G$ involves translations. In the case when the symmetry group $G$ is a Lie group, we define an anomaly index which takes values in the differentiable group cohomology as defined by J.-L. Brylinski and prove a similar result.
Forward citations
Cited by 3 Pith papers
-
Exactly Solvable 1+1d Chiral Lattice Gauge Theories
Anomaly-free chiral U(1) gauge theories in 1+1 dimensions can be written as quadratic, exactly solvable lattice Hamiltonians, with the 34-50 model as an explicit example.
-
Anomaly-free symmetries with obstructions to gauging and onsiteability
A new class of two-dimensional lattice symmetries is anomaly-free yet obstructs both gauging and on-site realization, with the obstruction classified by H^2(G,Q+).
-
Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems
A symmetry-restriction procedure computes the H^4(G,U(1)) anomaly class of any finite unitary symmetry acting by finite-depth circuits on a 2D lattice, with nontrivial class forbidding a symmetric invertible gapped state.
Discussion (0). Sign in to comment.