Sine-Gordon Model: Renormalization Group Solution and Applications

Malard, Mariana

doi:10.1007/s13538-013-0123-4

Cited by 14 publications

(14 citation statements)

References 28 publications

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“…There are a large number of good reviews [8,9,10,11]. A lot of work has been done on the RG of the Sine-Gordon model over the last few years and many computations have been carried out analytically and numerically [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. This paper primarily studies the application of ERG mainly to two dimensional field theories -the emphasis being on a simple way of writing down the solution to the ERG in terms of an evolution operator.…”

Section: Introductionmentioning

confidence: 99%

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Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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Abstract:The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional φ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating cfunctions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact renormalization group and Sine Gordon theory

Oak¹,

Sathiapalan²

2017

J. High Energ. Phys.

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“…Quantization of soliton [5] discuss the two vector solutions. A Ketaeve chain [6] with interaction studied using bosonization, Jordon-Wigner Transformation, and cumulant expansion showed standard BKT physics.The perturbative RG schemes have captured the robust coupling regime in SG field expansion [7] Flow equation renormallization(FeQRG) is carried out on the SG model [8].Functional renormallization(FRG) and numerical renormallization(NRG) is carried out on the SG model [9,10] to show a dissipative transition in Josephson junctions.…”

Section: Introductionmentioning

confidence: 99%

Derivation of $\mathcal{PT}$-symmetric Sine-Gordon model and its relevance to non-equilibrium

Kulkarni¹

2022

Preprint

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The Parity-Time PT -symmetric non-Hermitian Sine-Gordon(nhSG) model derived from the nonequilibrium spin-boson model. We have derived the Keldysh rotation for spin operators, from which the SG model can be derived. We perform renormalization group calculations in the Keldysh fields and compare the fixed points and the flow of the effective couplings of nonequilibrium and non-Hermitian models. Also, we explicitly find the self-energies and compare the two methods to understand the regimes where PT symmetry preserved regime, and nonequilibrium regimes persist.RG flow of couplings of nonequilibrium model and non-hermitian model both capture the standard Berezinskii-Kosterlitz-Thouless(BKT) physics in a strong coupling regime.

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“…Notice that the value of η for temperatures between T = 0 (at which η = 1) and the BKT critical temperature, T = T BKT (at which η = 1/4) is not universal, and it depends on the specific model. A complete understanding of this critical behaviour can be obtained by mapping in 2D the XY model -or more precisely, its low temperature limit, the Villain model, which is in the same universality [13,15,16] -into the 2D Coulomb gas [17], which in turn can exactly be mapped onto the 2D sine-Gordon model [18]. The latter is a field theory with an interaction term proportional to cos(βφ) where β is the frequency.…”

Section: Introductionmentioning

confidence: 99%

Topological phase transitions in four dimensions

Defenu,

Trombettoni,

Zappalà

2020

Preprint

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We show that four-dimensional systems may exhibit a topological phase transition analogous to the well-known Berezinskii-Kosterlitz-Thouless vortex unbinding transition in two-dimensional systems. The realisation of an engineered quantum system, where the predicted phase transition shall occur, is also presented. We study a suitable generalization of the sine-Gordon model in four dimensions and the renormalization group flow equation of its couplings, showing that the critical value of the frequency is the square of the corresponding value in 2D. The value of the anomalous dimension at the critical point is determined (η = 1/32) and a conjecture for the universal jump of the superfluid stiffness (4/π 2 ) presented.

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Sine-Gordon Model: Renormalization Group Solution and Applications

Abstract: The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is carried out through a decomposi-

Cited by 14 publications

References 28 publications

Exact renormalization group and Sine Gordon theory

Exact renormalization group and Sine Gordon theory

Derivation of $\mathcal{PT}$-symmetric Sine-Gordon model and its relevance to non-equilibrium

Topological phase transitions in four dimensions

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