Related papers: Yang-Baxter integrable Lindblad equations
Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the set…
In this article, we introduce endocabling as a technique to deform involutive, non-degenerate set-theoretic solutions to the Yang-Baxter equation (``solutions'', for short) by means of $\lambda$-endomorphisms of their associated permutation…
We construct invertible spectral parameter dependent Yang-Baxter solutions ($R$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using…
In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate…
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians…
We present a multi-spin solution to the Yang-Baxter equation. The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights and parameterized in terms of the basic hypergeometric…
The Lindblad quantum master equation is one of the central approaches to the physics of open quantum systems. In particular, boundary driving enables the study of transport, where a steady state emerges in the long-time limit, which…
A detailed study of an $S={1\over2}$ spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown…
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As…
We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and multipermutation solutions. We introduce and study graphs of…
A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of…
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are…
A scheme suitable for describing quantum nonultralocal models including supersymmetric ones is proposed. Braided algebras are generalised to be used through Baxterisation for constructing braided quantum Yang--Baxter equations.…
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…
Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Yang-Baxter equation having specific imprimitivity blocks.…
The dimer model on a strip is considered as a Yang-Baxter \mbox{integrable} six vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$ and quantum group invariant boundary conditions. A one-to-many mapping…
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random hoppings that are induced by a Markovian…