Bayesian critical points in classical lattice models

(2025)

Authors:

Adam Nahum, Jesper Lykke Jacobsen

A closed band-projected density algebra must be Girvin-MacDonald-Platzman

Physical Review Letters American Physical Society 134 (2025) 136502

Authors:

Ziwei Wang, Steven Simon

Abstract:

The band-projected density operators in a Landau level obey the Girvin-MacDonald-Platzman (GMP) algebra, and a large amount of effort in the study of fractional Chern insulators has been directed toward approximating this algebra in a Chern band. In this Letter, we prove that the GMP algebra, up to form factors, is the only closed algebra that projected density operators can satisfy in two and three dimensions, highlighting the central place it occupies in the study of Chern bands in general. A number of interesting corollaries follow.

Solvable Quantum Circuits in Tree+1 Dimensions

(2025)

Authors:

Oliver Breach, Benedikt Placke, Pieter W Claeys, SA Parameswaran

Odd electrical circuits

ArXiv 2503.14383 (2025)

Authors:

Harry Walden, Alexander Stegmaier, Jörn Dunkel, Alexander Mietke

Pivoting through the chiral-clock family

SciPost Physics SciPost 18 (2025) 094

Authors:

Nick G Jones, Abhishodh Prakash, Paul Fendley

Abstract:

The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this family of chiral Hamiltonians. These Hamiltonians have an anti-unitary CPT symmetry that when combined with the usual $\mathbb{Z}_N$ clock symmetry gives a non-abelian dihedral symmetry group $D_{2N}$. We show that this symmetry gives rise to symmetry-protected topological (SPT) order in this family for all even $N$, and representation-SPT (RSPT) physics for all odd $N$. The simplest such example is a next-nearest-neighbour chain generalising the spin-1/2 cluster model, an SPT phase of matter. We derive a matrix-product state representation of its fixed-point ground state along with the ensuing entanglement spectrum and symmetry fractionalisation. We analyse a rich phase diagram combining this model with the Onsager-integrable chiral Potts chain, and find trivial, symmetry-breaking and (R)SPT orders, as well as extended gapless regions. For odd $N$, the phase transitions are "unnecessarily" critical from the SPT point of view.