One-Dimensional Models

Ralph E. Christoffersen

Huan-Qiang Zhou, Lin-Jie Jiang, Jian-Gang Tang

Ambiguities in the Lax pairs for a one-dimensional small-polaron model and the one-dimensional Hubbard model are discussed.

Chandrima B. Pushpan, K. J. Harikrishnan, Prithvi Narayan +1 more

In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on the leading order in perturbation, for arbitrary size of the lattice, we show how the one-dimensional effective description emerges. We point out specific states in the low-energy sector of the two-dimensional model that are well-approximated by the one-dimensional spin-1/2 XXZ model. We propose a systematic approach for mapping matrix-elements of operators defined on the two-dimensional model to their low-energy counterparts on the one-dimensional XXZ model. We also show that partial trace-based description of entanglement in the two-dimensional model can be satisfactorily approximated using the one-dimensional XXZ model as a substitute. We further show numerically that the one-dimensional XXZ model performs well in estimating entanglement quantified using a measurement-based approach in the two-dimensional model for specific choices of measured Hermitian operators.

Edgard Elbaz

RADHIKA VATHSAN

The two-dimensional anyon system, when reduced to one dimension, yields models related to the Calogero–Sutherland model. One such reduction leads to a new model with a class of exact solutions. This model is one of a family of models obtained upon dimensional reduction of spherically symmetric models in arbitrary dimensions.

Alberto Galindo, P. Pascual