Integrable Chain Models With Staggered R-Matrices

Sedrakyan, A.

doi:10.1007/978-94-010-0514-2_7

Cited by 5 publications

(12 citation statements)

References 18 publications

(39 reference statements)

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“…[73] in connection with the string representation of the 3D Ising model, and further studied in Refs. [74][75][76][77][78]. Following these works, we connect the midpoint of each edge e "forward" to two other midpoints by two vectors ξ e .…”

Section: 69mentioning

confidence: 99%

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Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

et al. 2017

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Recent results for the critical exponent of the localization length at the integer quantum Hall transition differ considerably between experimental (νexp ≈ 2.38) and numerical (νCC ≈ 2.6) values obtained in simulations of the Chalker-Coddington (CC) network model. The difference is at least partially due to effects of the electron-electron interaction present in experiments. Here we propose a mechanism that changes the value of ν even within the single-particle picture. We revisit the arguments leading to the CC model and consider more general networks with structural disorder. Numerical simulations of the new model lead to the value ν ≈ 2.37. We argue that in a continuum limit the structurally disordered model maps to free Dirac fermions coupled to various random potentials (similar to the CC model) but also to quenched two-dimensional quantum gravity. This explains the possible reason for the considerable difference between critical exponents for the CC model and the structurally disordered model. We extend our results to network models in other symmetry classes.

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Section: 69mentioning

confidence: 99%

“…[71,72 is only suitable for single-particle problems, while the approach of Refs. [74][75][76][77][78] is able, in principle, to describe interacting particles. To this end one uses the second quantization, and the scattering matrices at the nodes are "promoted" to R-matrices acting in the Fock spaces attached to edges of the network (see Fig.…”

Section: 69mentioning

confidence: 99%

Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

et al. 2017

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“…Examples include representation of the R matrix in the Fock space of the scalar fermions and in a space with the basis of fermionic coherent-states, developed in Refs. 26,27,28,30 . These reformulations are fully equivalent, and they allow developing a field theory corresponding to the model.…”

Section: Fermionic Realization Of Boltzmann Weightsmentioning

confidence: 99%

“…The developed theory utilizes the graded R operator formalism 26,27,28,29,30 and allows the generalization to other integrable models, which is demonstrated in this work by operating with rather general R operator.…”

Section: Introductionmentioning

confidence: 99%

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Khachatryan

Sedrakyan

2009

Phys. Rev. B

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We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and XY Z model, which is simple to apply for calculation of various correlation functions. We calculate the partition function of 2DIM and XY model within the developed framework. Determinant representation of spin-spin correlation functions is derived using fermionic realization for the Boltzmann weights. The approach also allows formulation of the partition function of 2DIM in the presence of an external magnetic field.

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“…In this article, developing the results obtained in our previous works [21,22,23], we give the exact action (Lagrangian) formulation of the original CC Transfer Matrix model as a field theory on 2D lattice. First we show, that before the disorder over U (1) phases is taken into account the CC model is equivalent to some inhomogeneous modification of the XX model in the background of U (1) field.…”

mentioning

confidence: 99%

Action formulation of the network model of plateau-plateau transitions in the quantum Hall effect

Sedrakyan

2003

Phys. Rev. B

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The Lagrangian (action) formulation of the Chalker-Coddington network model for plateauplateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice (M L). The dimensionless Landauer resistance is considered and its average is calculated over the random U (1) phases with constant distribution on the circle. The Lagrangian of the resultant model on M L is found and the corresponding R-matrix is written down. It appeared, that this model is integrable, rising hope to investigate physics of plateauplateau transitions by the exact method of powerful Algebraic Bethe Ansatz (ABA).

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Integrable Chain Models With Staggered R-Matrices

Cited by 5 publications

References 18 publications

Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Action formulation of the network model of plateau-plateau transitions in the quantum Hall effect

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