REVIEW 8 cited by
Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
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
We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of "on-site action.") In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the $c=1$ compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an 't Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states.
Forward citations
Cited by 8 Pith papers
-
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
-
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.
-
Disjoint additivity and local quantum physics
Local quantum systems should obey disjoint additivity plus Haag duality, a combination that survives higher-form symmetries and fails for known nonlocal constructions.
-
Bosonization versus the Nielsen-Ninomiya theorem
The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.
-
Integrability and lattice discretizations of all Topological Defect Lines in minimal CFTs
In integrable RSOS models, all Verlinde lines of diagonal minimal models are realized by spectral-parameter insertions: (1,s) lines are exactly topological on the lattice, (r>=2,s) lines only in the continuum limit, w...
-
Irrational CFTs from coupled anyon chains with non-invertible symmetries?
DMRG evidence from three coupled Fibonacci anyon chains points to a conformal phase with c=2.10±0.03, proposed as a candidate irrational CFT, though small system sizes leave a weakly first-order alternative open.
-
2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
The 2d Cardy-Rabinovici model is constructed on a modified Villain lattice, making rescaled theta periodicity and strong-weak duality exact at finite spacing and giving a symmetry-based phase classification.
-
To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories
A review showing that if a QCD-like theory with enough massless flavors is fully color-screened in the infrared, then chiral symmetry must be spontaneously broken.
Discussion (0). Sign in to comment.