Finite Size Formula in the XYZ Spin Chain

TL;DR

This paper derives a finite size formula for magnetizations in the boundary XYZ spin chain using vertex operators and geometric symmetries, enabling explicit calculations of spontaneous magnetization.

Contribution

It introduces a novel finite size formula for the XYZ spin chain with boundaries, constructed via vertex operators and geometric symmetries.

Findings

Finite size formula for magnetizations derived

Explicit calculation of spontaneous magnetization achieved

Method applicable to bounded and half-infinite chains

Abstract

The XYZ spin chain with boundaries is studied. We construct the vacuum state by the vertex operators in the level one modules of the elliptic algebra, and compact it through a geometric symmetry of the model called the turning symmetry. From this simplified expression the ``finite size formula'' for magnetizations in the bounded and in the half-infinite chains is deduced. Applying this formula we calculate the spontaneous magnetization in the bounded XYZ model.