Free Fermion Conditions and the Symmetries of Integrability

1997 ◽  
Vol 11 (01n02) ◽  
pp. 213-221 ◽  
Author(s):  
Claude-M. Viallet
Keyword(s):  
Free Fermion ◽  
Vertex Models ◽  
Inversion Relations

We show that free-fermion conditions on vertex models amount to degeneration conditions for the inversion relations and the symmetries of the Yang-Baxter equations. We also show how solutions of the tetrahedron equations enjoy a similar property, and analyze the phenomenon.

TAXONOMY OF THE SIXTEEN-VERTEX MODELS

1992 ◽  
Vol 06 (14) ◽  
pp. 2559-2574 ◽  
Author(s):  
S. BOUKRAA ◽  
J.-M. MAILLARD
Keyword(s):  
Symmetry Group ◽  
Parameter Space ◽  
Vertex Model ◽  
Vertex Models ◽  
Exact Calculations ◽  
Inversion Relations

A classification of the subcases of the sixteen-vertex model compatible with the infinite symmetry group generated by the inversion relations of the model is performed. The elliptic parameterization of these models is recalled, emphasizing the subvarieties of the parameter space for which this parameterization degenerates into a rational one. This situation corresponds to the vanishing of some discriminant and is deeply related to the critical and disorder manifolds for these models. We concentrate on subcases of the sixteen-vertex model for which factorizations of this discriminant occur, allowing further exact calculations.

Solvable nineteen-vertex models and quantum spin chains of spin one

1994 ◽  
Vol 4 (8) ◽  
pp. 1151-1159 ◽  
Author(s):  
Makoto Idzumi ◽  
Tetsuji Tokihiro ◽  
Masao Arai
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Vertex Models

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

scholarly journals Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

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