Conformal invariance in the quantum Ising model

TL;DR

This paper extends classical Ising model results to the quantum case by introducing Kadanoff-Ceva operators, demonstrating conformal invariance in the (1+1)D quantum Ising model using a loop expansion approach.

Contribution

It introduces a novel operator representation for the quantum Ising model, enabling the extension of classical conformal invariance results to the quantum setting.

Findings

Conformal invariance of correlations in the quantum Ising model.

Equivalence of the operator approach to fermionic loop expansions.

Extension of classical results to quantum (1+1)D case.

Abstract

We introduce Kadanoff-Ceva order-disorder operators in the quantum Ising model. This approach was first used for the classical planar Ising model and recently put back to the stage. This representation turns out to be equivalent to the loop expansion of Sminorv's fermionic observables and is particularly interesting due to its simple and compact formulation. Using this approach, we are able to extend different results known in the classical planar Ising model, such as the conformal invariance/covariance of correlations and the energy-density, to the spin-representation of the (1+1) dimensional quantum Ising model.