New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions

Non-additive fusion, Hubbard models and non-locality

In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable one-dimensional spin-chain Hamiltonians. Here fusion is shown to generalize naturally to non-additive R-matrices, which therefore do not have a quantum group symmetry. This method is then applied to the generalized Hubbard models. Although the resulting integrable models are not as simple as the starting ones, the general structure is that of two spin-(s times s') sl(2) models coupled at the free-fermio…

Integrable three-state vertex models with weights lying on genus five curves

We investigate the Yang-Baxter algebra for $\mathrm{U}(1)$ invariant three-state vertex models whose Boltzmann weights configurations break explicitly the parity-time reversal symmetry. We uncover two families of regular Lax operators with nineteen non-null weights which ultimately sit on algebraic plane curves with genus five. We argue that these curves admit degree two morphisms onto elliptic curves and thus they are bielliptic. The associated $\mathrm{R}$-matrices are non-additive in the spectral parameters and it has been checked that they satisfy the Yang-Baxter equation. The respective i…

KPZ方程在非可积空间相关下的标度极限

Scaling limit of the KPZ equation with non-integrable spatial correlations

本文证明在$d\geq3$中，由非可积空间相关噪声驱动的KPZ方程的标度极限为加性随机热方程，且噪声保留相关性，收敛以概率方式成立。

离散可积系统与随机 Lax 矩阵

Discrete integrable systems and random Lax matrices

本文通过 Lax 表示研究具有随机初始数据的 Hamiltonian 可积系统，在自由度趋于无穷大时，精确或数值推导了多种离散可积系统的极限态密度，并显式给出了基态下的态密度。