Dimer XXZ Spin Ladders: Phase diagram and a Non-Trivial Antiferromagnetic Phase

TL;DR

This paper explores the phase diagram of dimer XXZ spin ladders, revealing a non-trivial antiferromagnetic phase with time-reversal symmetry through analytical and numerical methods, relevant for ultracold atom experiments.

Contribution

It provides a comprehensive phase diagram of the dimer XXZ spin ladder, identifying a novel non-trivial antiferromagnetic phase with detailed analytical and numerical analysis.

Findings

Identification of a non-trivial antiferromagnetic phase with gap and time-reversal symmetry.

Verification of phase transitions using quantum Monte Carlo and exact diagonalization.

Detailed characterization of multiple phases including Luttinger liquid and triplon solid.

Abstract

We study the dimer $XXZ$ spin model on two-leg ladders with isotropic Heisenberg interactions on the rung and anisotropic $XXZ$ interactions along the rail in an external field. Combining both analytical and numerical methods, we set up the ground state phase diagram and investigate the quantum phase transitions and the properties of rich phases, including the full polarized, singlet dimer, Luttinger liquid, triplon solid, and a non-trivial antiferromagnetic phases with gap. The analytical analyses based on solvable effective Hamiltonians are presented for clear view of the phases and transitions. Quantum Monte Carlo and exact diagonalization methods are employed on finite system to verify the exact nature of the phases and transitions. Of all the phases, we pay a special attention to the gapped antiferromagnetic phase, which is disclosed to be a non-trivial one that exhibits the time-reversal symmetry. We also discuss how our findings could be detected in experiment in the light of ultracold atoms technology advances.