Multispecies TASEP and the tetrahedron equation

Kuniba, Atsuo; Maruyama, Shouya; Okado, Masato

doi:10.1088/1751-8113/49/11/114001

Cited by 25 publications

(40 citation statements)

References 18 publications

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“…Its formulation is another important result in this paper which contrasts with the simpler situation of continuous time models on a ring (cf. [22,1,6,16]) where the ZF algebra alone sufficed together with its derivative. We find in the proof of Proposition 6 that the U q (A (1) n ) stochastic R matrix fits the auxiliary condition perfectly by an intriguing mechanism.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Matrix product formula for ${{U}_{q}}(A_{2}^{(1)})$ -zero range process

Kuniba¹,

Okado²

2016

J. Phys. A: Math. Theor.

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The U q (A (1) n )-zero range processes introduced recently by Mangazeev, Maruyama and the authors are integrable discrete and continuous time Markov processes associated with the stochastic R matrix derived from the well-known U q (A (1) n ) quantum R matrix. By constructing a representation of the relevant Zamolodchikov-Faddeev algebra, we present, for n = 2, a matrix product formula for the steady state probabilities in terms of q-boson operators.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Matrix product formula for ${{U}_{q}}(A_{2}^{(1)})$ -zero range process

Kuniba¹,

Okado²

2016

J. Phys. A: Math. Theor.

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“…which are just (18) and (17) without an overall scalar for simplicity. In order to describe the elements of K(z)K(w), we prepare two copies of (16) and their product:…”

Section: Discussionmentioning

confidence: 99%

Quantum spin chains from Onsager algebras and reflection K-matrices

Kuniba

Pasquier

2019

Nuclear Physics B

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We present a representation of the generalized p-Onsager algebras O p (An ) in which the generators are expressed as local Hamiltonians of XXZ type spin chains with various boundary terms reflecting the Dynkin diagrams. Their symmetry is described by the reflection K matrices which are obtained recently by a q-boson matrix product construction related to the 3D integrability and characterized by Onsager coideals of quantum affine algebras. The spectral decomposition of the K matrices with respect to the classical part of the Onsager algebra is described conjecturally. We also include a proof of a certain invariance property of boundary vectors in the q-boson Fock space playing a key role in the matrix product construction.

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“…The transition rate r i,j of |i, j → |j, i satisfies r i,j : r j,i = 1 : q 2 for 1 ≤ i < j ≤ n + 1. Many results have been obtained for the n-species ASEP with general n including, for example, matrix product stationary states [40], spectral duality with respect to the Hasse diagram of sectors [2], solutions to stochastic initial value problem on infinite lattice [47], connection to the tetrahedron equation at q = 0 [30], application to generalized Macdonald polynomials [20] and so on.…”

Section: Models Associated With S(z)mentioning

confidence: 99%

Integrable Structure of Multispecies Zero Range Process

Kuniba¹,

Okado²,

Watanabe³

2017

SIGMA

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Abstract. We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic R matrices of quantum affine algebra U q A(1) n , matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc. We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.

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Multispecies TASEP and the tetrahedron equation

Cited by 25 publications

References 18 publications

Matrix product formula for ${{U}_{q}}(A_{2}^{(1)})$ -zero range process

Matrix product formula for ${{U}_{q}}(A_{2}^{(1)})$ -zero range process

Quantum spin chains from Onsager algebras and reflection K-matrices

Integrable Structure of Multispecies Zero Range Process

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