A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model

TL;DR

This study uses quantum fidelity measures from exact diagonalizations to map the phase diagram of an anisotropic triangular Heisenberg model, revealing connections between known phases and identifying potential new disordered states.

Contribution

It introduces a combined use of ground- and excited-state quantum fidelities to explore phase boundaries and transitions in the anisotropic triangular lattice Heisenberg model.

Findings

Identification of BKT-type transition and Majumdar-Ghosh point extensions

Detection of bounded regions in the phase diagram with distinct order parameters

Suggestion of a gapless disordered phase connected to the J1-J2 chain

Abstract

Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the $J'-J_2$ plane of this model, which connects the $J_1-J_2$ chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the $J_1-J_2$ chain ($J'=0$) are found to extend into the $J'-J_2$ plane and connect with points on the $J_2=0$ axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities $\chi_{\rho}$, $\chi_{120^{\circ}}$, $\chi_D$ and $\chi_{CAF}$ which are associated with the spin stiffness, $120^{\circ}$ spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the $J',J_2 \ll J$ phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the $J_1-J_2$ chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.