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Arnaudon, D.; Sedrakyan, A.; Sedrakyan, Tigran; Sorba, P.

doi:10.1023/a:1014504526934

Cited by 8 publications

(12 citation statements)

References 10 publications

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“…The result is written in terms of two type (spin up and spin down) Fermi fields. It appeared, that the R-matrix we have found is fulfilling the Yang-Baxter Equations (Y BE), which were defined in the article [22] for the models with staggered disposition of Rmatrices. This means that the resultant model is integrable.…”

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confidence: 95%

“…In the second line (marked T 2 in the Fig.3b) the R-matrices have minus sign in front of vertical hopping parameters of one of fermions (say spin-up), which we marked by the subscript ι in the expression (17). But this is precisely the ι operation defined in the articles [22]. We have an inhomogeneous model.…”

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confidence: 98%

“…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.…”

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confidence: 99%

“…The R-matrices (16) define an integrable model of the type developed recently in a chain of articles [22,23]. First, it is easy to make an U (1) gauge transformation and pass from the distribution of hopping parameters of the model as it defined by the formula (16) and shown on the Fig.3a, to the one, which is drown on Fig.3b.…”

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confidence: 99%

“…Besides of the ι operation differing neighbor chains, the R matrices are staggered along of each chain. It was shown in [22], that this Z 2 graded structure demands two sets of Yang-Baxter's Equation (Y BE) in order to ensure the commutativity of the Transfer Matrices with different spectral parameters u and v. have a solution of the same form as (16) with…”

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confidence: 99%

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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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confidence: 95%

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confidence: 98%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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

Sedrakyan

2003

Phys. Rev. B

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Integrable Chain Models With Staggered R-Matrices

Sedrakyan

2002

Statistical Field Theories

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The technique of construction on Manhattan lattice (M L) the fermionic action for Integrable models is presented. The Sign-Factor of 3D Ising model (SF of 3DIM ) and Chalker-Coddington-s phenomenological model (CCM ) for the edge excitations in Hall effect are formulated in this way.The second one demonstrates the necessity to consider the inhomogeneous models with staggered R-matrices. The disorder over the U (1) phases is taken into account and staggered Hubbard type of model is obtained. The technique is developed to construct the integrable models with staggered disposition of R-matrices.

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Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

Wei,

Mkhitaryan,

Sedrakyan

2024

J. High Energ. Phys.

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We study the low-energy properties of the one-dimensional spin-1/2 XXZ chain with time-reversal symmetry-breaking pseudo-scalar chiral interaction and propose a phase diagram for the model. In the integrable case of the isotropic Heisenberg model with the chiral interaction, we employ the thermodynamic Bethe ansatz to find “chiralization”, the response of the ground state versus the strength of the pseudo-scalar chiral interaction of a chiral Heisenberg chain. Unlike the magnetization case, the chirality of the ground state remains zero until the transition point corresponding to critical coupling αc = 2J/π with J being the antiferromagnetic spin-exchange interaction. The central-charge c = 1 conformal field theories (CFTs) describe the two phases with zero and finite chirality. We show for this particular case and conjecture more generally for similar phase transitions that the difference between two emergent CFTs with identical central charges lies in the symmetry of their ground state (lightest weight) primary fields, i.e., the two phases are symmetry-enriched CFTs. At finite but small temperatures, the non-chiral Heisenberg phase acquires a finite chirality that scales with the temperature quadratically. We show that the finite-size effect around the transition point probes the transition.

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Cited by 8 publications

References 10 publications

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

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

Integrable Chain Models With Staggered R-Matrices

Unveiling chiral states in the XXZ chain: finite-size scaling probing symmetry-enriched c = 1 conformal field theories

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