Symmetry Protected Topological Phases in Spin Ladders with Two-body Interactions

TL;DR

This paper identifies new symmetry protected topological phases in spin-1/2 two-legged ladders with specific symmetries, revealing unique edge state behaviors and proposing quantum simulation methods for these phases.

Contribution

It introduces novel SPT phases in spin ladders respecting certain symmetries and demonstrates how to realize and simulate these phases experimentally.

Findings

Three new SPT phases with distinct edge states

Edge states respond differently to magnetic fields

Proposed quantum simulation schemes for specific phases

Abstract

Spin-1/2 two-legged ladders respecting inter-leg exchange symmetry and D2 spin rotation symmetry have new symmetry protected topological (SPT) phases which are different from the Haldane phase. Three of the new SPT phases are tx,ty,tz, which all have symmetry protected two-fold degenerate edge states on each end of the open boundaries. However, the edge states in different phases have different response to magnetic field. For example, the edge states in the tz phase will be split by the magnetic field along the z-direction, but not by the fields in the x- and y-directions. We give the Hamiltonian that realizes each SPT phase and demonstrate a proof-of-principle quantum simulation scheme for Hamiltonians of the t0 and tz phases based on coupled-QED-cavity ladder.