Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice -- A perturbative point of view

2024/02/16 by Jan Alexander Koziol, Koziol, J. A., Matthias Mühlhauser +3
Physics and Astronomy · #FOS: Physical sciences #Opinion Dynamics and Social Influence #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2402.10584

openalex publication_date 2024/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the low-field ground-state (GS) properties of the antiferromagnetic transverse-field Ising model with long-range interactions (afLRTFIM) on the triangular lattice. We use the method of perturbative continuous unitary transformations (pCUT) to derive an effective model for the degenerate GS space of the antiferromagnetic nearest-neighbour (NN) Ising model on a finite system, by treating the transverse-field (TF) and the long-range interactions (LRI) as a perturbation. We determine a level-crossing between the plain stripe phase at small TF and the clock-ordered phase at intermediate TF at h≅0.129 for α=6, N=36 spins in order three perturbation theory. We discuss the qualitative layout of the quantum phase diagram of the afLRTFIM on the triangular lattice.

Related

• Geometry of the order-disorder surface of the mean-field square lattice Ising model with up to third-neighbor interactions
• Antiferromagnetic Long-Range Order in a Lattice Fermion Model
• A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices