A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field

TL;DR

This paper introduces a two-parameter deformation of the SU(1/1) superalgebra and explores its invariance in the XY quantum chain under a magnetic field, extending algebraic structures and discussing their physical implications.

Contribution

It presents a novel two-parameter deformation of the SU(1/1) superalgebra and connects it to the invariance of the XY quantum chain in a magnetic field.

Findings

Extension of the braid group and Hecke algebra with two parameters

Reduction to known algebraic structures when parameters coincide

Discussion of the physical significance of the deformation

Abstract

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the SU(1/1) superalgebra. One is led to an extension of the braid group and the Hecke algebra which reduce to the known ones when the two parameter coincide. The physical significance of the two parameters is discussed.