Wuppertal University

摘要:

This talk explores the intriguing physical properties of integrable low-dimensional models, specifically focusing on 1D quantum systems and 2D classical systems such as the spin-1/2 Heisenberg chain and the 1D Hubbard model. The classical six-vertex model on the square lattice and its generalizations also play a crucial role in understanding these prototypes.

The first part of the talk elucidates the connection between 2D classical models and 1D quantum systems. By exploring the Yang-Baxter equation for local Boltzmann weights, we unveil a family of commuting transfer matrices. These matrices operate in the Hilbert space of the 1D quantum system, ultimately leading to a lattice path integral formulation of the Heisenberg and Hubbard Hamiltonians at arbitrary temperatures. The practical implications include a compact representation of thermodynamic quantities based on a finite set of non-linear integral equations, a departure from the traditional TBA approach involving infinitely many equations.

Transitioning to the second part, we delve into seminal results in integrable systems and touch upon current research topics, such as thermal and spin transport in the Heisenberg chain. A special focus is placed on the staggered Heisenberg spin chain, where we present results on the finite-size spectrum for varying sizes, ranging from $L = 10$ to $L = 10^{24}$.

邀请人：张鑫