“Not-
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>
”, representation symmetry-protected topological, and Potts phases in an 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>
-invariant chain

O’Brien, E.; Vernier, Éric; Fendley, Paul

doi:10.1103/physrevb.101.235108

Cited by 15 publications

(38 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Writing H(θ ) in terms of Temperley-Lieb generators (see e.g. [4]) gives the same expression as in Ref. [8] but in a different representation with different physics.…”

Section: The Model and The Phase Diagrammentioning

confidence: 87%

“…Duality here is neither unitary nor invertible, as for example it maps the ordered ground states of the Potts chain to the unique ground state of the disordered phase. For the self-dual couplings we study, this non-triviality allows for novel phase transitions to occur [4]. Here we study the entire self-dual line and find a rich variety of previously unknown critical and gapped phases.…”

Section: The Model and The Phase Diagrammentioning

confidence: 99%

“…The Hamiltonian we study is self-dual under Kramers-Wannier duality, with duality-broken cases analyzed in [4]. The action of duality on the Hilbert space is given in a convenient and general form by using topological defects [5].…”

Section: The Model and The Phase Diagrammentioning

confidence: 99%

“…This Hamiltonian is the quantum spin-chain limit of the integrable self-dual 3-state Potts model [6,7]. Another nearest-neighbor self-dual Hamiltonian is [4]…”

Section: The Model and The Phase Diagrammentioning

confidence: 99%

“…Both the ferromagnet H P and and antiferromagnet −H P extend to critical phases. The former is described by the well-known c = 4 5 three-state Potts CFT [15], a phase we dub "Potts 1". The latter is described by a c =1 CFT, and below we explain why it describes a full region, not immediately obvious as the corresponding critical point in the classical squarelattice antiferromagnet is unstable [16].…”

Section: The Model and The Phase Diagrammentioning

confidence: 99%

See 4 more Smart Citations

Self-dual $S_3$-invariant quantum chains

O’Brien

Fendley

2020

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and S_3S3, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1)U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct “Fermi velocities”. The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.

show abstract

“…Writing H(θ ) in terms of Temperley-Lieb generators (see e.g. [4]) gives the same expression as in Ref. [8] but in a different representation with different physics.…”

Section: The Model and The Phase Diagrammentioning

confidence: 87%

Section: The Model and The Phase Diagrammentioning

confidence: 99%

Section: The Model and The Phase Diagrammentioning

confidence: 99%

“…This Hamiltonian is the quantum spin-chain limit of the integrable self-dual 3-state Potts model [6,7]. Another nearest-neighbor self-dual Hamiltonian is [4]…”

Section: The Model and The Phase Diagrammentioning

confidence: 99%

Section: The Model and The Phase Diagrammentioning

confidence: 99%

See 3 more Smart Citations

Self-dual $S_3$-invariant quantum chains

O’Brien

Fendley

2020

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

Z3 and (×Z3)3 symmetry protected topological paramagnets

Topchyan,

Iugov,

Mirumyan

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by (×Z3)3 ≡ Z3 × Z3 × Z3 symmetry and smaller Z3 symmetry. We derive microscopic models for the gapless edge, uncover their symmetries and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue, that the low energy limit of our edge modes defined by the SUk(3)/SUk(2) coset conformal field theory with the level k = 2. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.

show abstract

Onsager symmetries in $U(1)$ -invariant clock models

Vernier¹,

O’Brien²,

Fendley³

2019

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a U (1) symmetry. We describe in detail the example of nearest-neighbour n-state clock chains whose Z n symmetry is enhanced to U (1). As a consequence of the Onsager-algebra symmetry, the spectrum of these models possesses degeneracies with multiplicities 2 N for positive integer N . We construct the elements of the algebra explicitly from transfer matrices built from nonfundamental representations of the quantum-group algebra U q (sl 2 ). We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. We also find a family of commuting chiral Hamiltonians that break the degeneracies and allow an integrable interpolation between ferro-and antiferromagnets. arXiv:1812.09091v2 [cond-mat.stat-mech] 21 Jun 2019Jordan-Wigner transformation [4]. This fermionic method is even easier, and so for the most part the Onsager algebra itself was no longer exploited. Moreover, the elements of the Onsager algebra in the Ising model are all free-fermion bilinears, and their commutation relations are nice because any commutator of such fermion bilinears yields a linear combination of bilinears.It thus seemed sensible to expect that the Onsager algebra is merely one of the many marvellous properties of free-fermionic systems, and so only occurs in such. This expectation, however, is simply wrong. Motivated by some curious observations by Howes, Kadanoff and den Nijs [5], von Gehlen and Rittenberg made the remarkable observation that the Onsager algebra is obeyed by operators in an n-state clock model [6]. They then show that the algebra allows construction of an infinite series of commuting local conserved charges, strongly suggesting a certain chiral clock model commuting with them is integrable. 2 This model is indeed integrable, and now bears the name of the superintegrable chiral Potts model. The integrability allows many of its properties to be computed [9], but the Onsager algebra is not heavily utilised in this analysis.The Onsager algebra cannot be used to solve chiral clock models directly because its elements here do not have the simple periodicity property that the Ising presentation has. Thus what is free-fermionic about Onsager's original solution is the periodicity property, not the algebra itself. However, while progress has been made in understanding how the Onsager algebra relates to more standard approaches to integrability (see [10] and references therein), the question remains: what more can the Onsager algebra tell us about properties of clock models?The purpose of this paper is to define and analyse a series of clock models that have the Onsager algebra as a symmetry algebra: all its elements commute with the Hamiltonian and transfer matrix. We believe this is the simplest set of such models. W...

show abstract

“Not- A ”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

Cited by 15 publications

References 49 publications

Self-dual $S_3$-invariant quantum chains

Self-dual $S_3$-invariant quantum chains

Z3 and (×Z3)3 symmetry protected topological paramagnets

Onsager symmetries in $U(1)$ -invariant clock models

Contact Info

Product

Resources

About