A Generalized Duality Transformation of the Anisotropic Xy Chain in a Magnetic Field

TL;DR

This paper introduces a generalized duality transformation for the anisotropic XY chain in a magnetic field, revealing a symmetry that connects different parameter regimes and extends the known Ising duality.

Contribution

It presents a new generalized duality transformation for the anisotropic XY chain, broadening the understanding of symmetries in quantum spin chains.

Findings

The duality transformation relates different parameter sets of the XY chain.

In a special limit, the transformation reduces to the well-known Ising duality.

The transformation preserves the form of the Hamiltonian under parameter exchange.

Abstract

We consider the anisotropic $XY$ chain in a magnetic field with special boundary conditions described by a two-parameter Hamiltonian. It is shown that the exchange of the parameters corresponds to a similarity transformation, which reduces in a special limit to the Ising duality transformation.