An Exact Diagonalization Study of the Anisotropic Triangular Lattice Heisenberg Model Using Twisted Boundary Conditions

Abstract

The anisotropic triangular model, which is believed to describe the materials Cs${}_2$CuCl${}_4$ and Cs${}_2$CuBr${}_4$, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper we use twisted boundary conditions and exact diagonalization techniques to study the phase diagram of this model. With these boundary conditions we are able to extract the inter- and intrachain ordering $q$-vectors for the $\frac{J^{\prime }}{J}<1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the $q$-vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibits an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.

References in corpus (8)

• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Ordering in spatially anisotropic triangular antiferromagnets
• Spin Liquid Phase in Anisotropic Triangular Lattice Heisenberg Model: Exact diagonalization and density-matrix renormalization group calculations
• Dynamics and transport of the Z_2 spin liquid: application to kappa-(ET)2Cu2(CN)3
• Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1{J}_2{J}_3$ model with Heisenberg interactions
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry
• Quantum disorder in the spatially completely anisotropic triangular lattice I: Heisenberg $S=1/2$ antiferromagnet
• Quantum disorder in the spatially completely anisotropic triangular lattice II: frustrated hard-core bosons

Cited by in corpus (5)

• Unusual ordered phases of highly frustrated magnets: a review
• Frustrated two dimensional quantum magnets
• Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean field study in a spin-rotating frame
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model