Exact and simple results for the XYZ and strongly interacting fermion chains

TL;DR

This paper conjectures exact formulas for physical quantities in specific quantum chains, including the XYZ and strongly interacting fermion chains, revealing new analytical results in these models.

Contribution

It introduces novel conjectures for exact formulas in the XYZ and fermion chains under special conditions, extending classical results to new models.

Findings

Exact formulas for magnetization and gap in the XYZ chain.

Exact formulas for staggered density in the fermion chain.

Independence of certain quantities from finite-size effects.

Abstract

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects.