The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit

Schroer, Bert; Truong, T.T.

doi:10.1016/0550-3213(78)90499-6

Cited by 101 publications

(122 citation statements)

References 15 publications

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“…It should be mentioned that the formulas equivalent to (4.50)-(4.51) were first obtained by Schroer and Truong [32]. In a context similar to ours, they were rediscovered by Palmer in [27].…”

Section: Local Expansions and Deformation Equationssupporting

confidence: 60%

On Painlevé VI transcendents related to the Dirac operator on the hyperbolic disk

Lisovyy

2008

Journal of Mathematical Physics

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Dirac hamiltonian on the Poincaré disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincaré disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painlevé VI equation with γ = 0. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painlevé VI transcendents as s → 1. Considering the limit of flat space, we also obtain a class of solutions of the Painlevé V equation with β = 0.

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Section: Local Expansions and Deformation Equationssupporting

confidence: 60%

On Painlevé VI transcendents related to the Dirac operator on the hyperbolic disk

Lisovyy

2008

Journal of Mathematical Physics

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“…By uniqueness of the branch-point twist field, the factorisation above must be the correct one. We checked in the case n = 2 that our form factors agree with formula (B.7) along with the known form factors form U (1)-twist fields [43]. For n odd, similar calculations show that there are many lowest-dimension factorized operators, and that their dimension does not agree with the CFT prediction (it is higher).…”

Section: B Vacuum Expectation Values Of Branch-point Twist Fields In mentioning

confidence: 59%

Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy

2007

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In this paper we compute the leading correction to the bipartite entanglement entropy at large sub-system size, in integrable quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle spectrum of the theory and not on the details of the scattering matrix. We employ the "replica trick" whereby the entropy is obtained as the derivative with respect to n of the trace of the n th power of the reduced density matrix of the sub-system, evaluated at n = 1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are naturally related to branch points in an n-sheeted Riemann surface. Their two-point function directly gives the scaling limit of the trace of the n th power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this two-point function in terms of form factors of the twist fields, in order to evaluate it at large distances in the two-particle approximation. Although this is a well-known technique, the new geometry of the problem implies a modification of the form factor equations satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide solutions, which we specialize both to the Ising and sinh-Gordon models.

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“…They have a scalar diagonal S-matrix and three soliton super-selection sectors: A bosonic, a fermionic and a disorder sector, reflecting an underlying Z 2 -symmetry. Some major references in the context of form factors are [3,26,20,32,1,9] for the Ising model and [11,17,19,25,18] for the Sinh-Gordon theory.…”

Section: Form Factors In the Deformed Ising And Sinh-gordon Modelmentioning

confidence: 99%

Varying the Unruh temperature in integrable quantum field theories

Niedermaier¹

1998

Nuclear Physics B

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A computational scheme is developed to determine the response of a quantum field theory (QFT) with a factorized scattering operator under a variation of the Unruh temperature. To this end a new family of integrable systems is introduced, obtained by deforming such QFTs in a way that preserves the bootstrap S-matrix. The deformation parameter β plays the role of an inverse temperature for the thermal equilibrium states associated with the Rindler wedge, β = 2π being the QFT value. The form factor approach provides an explicit computational scheme for the β = 2π systems, enforcing in particular a modification of the underlying kinematical arena. As examples deformed counterparts of the Ising model and the Sinh-Gordon model are considered.

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The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit

Cited by 101 publications

References 15 publications

On Painlevé VI transcendents related to the Dirac operator on the hyperbolic disk

On Painlevé VI transcendents related to the Dirac operator on the hyperbolic disk

Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy

Varying the Unruh temperature in integrable quantum field theories

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