Quantum XX chain with interface

TL;DR

This paper investigates the quantum XX chain with an interface, revealing how interface patterns induce localized states, degeneracies, and potential qubit candidates near a quantum phase transition.

Contribution

It introduces a detailed analysis of interface effects in the quantum XX chain, highlighting the emergence of localized midgap states and a Majorana-like symmetry linking degenerate ground states.

Findings

Localized midgap states appear near the interface.

Degeneracy arises from a global symmetry, not band occupancy.

Potential for protected qubits from superpositions of degenerate states.

Abstract

The quantum XX chain - or rather ring - is studied as a toy model of an interface. Two transverse field patterns are used to define the interface, on the one hand a staggered field, on the other hand a step-like configuration, from -h to +h. The interface leads to Friedel oscillations and proximity effects, in particular close to the quantum phase transition of the bulk, which is a metal-insulator transition in the fermionic language. The most prominent interface effects appear for odd-numbered rings, for which - in contrast to even chains - the ground state is doubly degenerate. In the regime where the bulk energy spectrum is gapped a level appears close to midgap, with a wave function localized in the region of the interface. The two members of the ground state doublet have two different particle number parities and spin components S_z=+-1/2. They also have different energy levels and thus the degeneracy does not originate from different occupancies of a rigid band structure, but rather from a global symmetry. The unitary transformation linking the two degenerate ground states resembles a Majorana operator. Coherent superpositions of the two states may be suitable candidates for well protected qubits.