Disorder Line and Incommensurate Floating Phases in the Quantum Ising Model on an Anisotropic Triangular Lattice

TL;DR

This study uses Quantum Monte Carlo simulations to explore the phase diagram of the quantum Ising model on an anisotropic triangular lattice, revealing a disorder line, incommensurate floating phases, and low-entropy phase transitions.

Contribution

It provides the first detailed phase diagram of the anisotropic triangular lattice quantum Ising model, identifying the disorder line and characterizing the floating incommensurate phase.

Findings

Disorder line meets the zero-temperature axis at J'≈0.7J.

Incommensurate phase at larger J' is a floating phase with power-law correlations.

Phase transitions occur at very low entropy in the presence of a transverse field.

Abstract

We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal second-neighbor interaction $J'$, interpolating between square-lattice ($J'=0$) and triangular-lattice ($J'=J$) limits. At a transverse-field of $B_x=J$, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at $J'\approx 0.7 J$. Strong evidence is provided that the incommensurate phase at larger $J'$, at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous Quantum Monte Carlo work by Isakov and Moessner for the isotropic triangular lattice ($J'=J$). For the isotropic triangular-lattice, we also obtain the entropy function and constant entropy contours using a mix of Quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in presence of a transverse field occur at very low entropy.