Phase Diagram of Triangular Lattice Quantum Ising Model under External Field

TL;DR

This paper maps out the phase diagram of the triangular lattice quantum Ising model under external fields using quantum Monte Carlo and DMRG, revealing various phase boundaries and transitions, with implications for experiments and quantum simulations.

Contribution

It provides a systematic, controlled study of the phase diagram of the triangular quantum Ising model, including BKT, UUD, and other phases, using advanced numerical methods.

Findings

Identified phase boundary between UUD and paramagnetic phases with 2D q=3 Potts universality.

Mapped the low-temperature phase boundary between clock and UUD phases.

Analyzed the quantum phase transition between UUD and fully polarized phases.

Abstract

Quantum Ising model on a triangular lattice hosts a finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry, and it will transit into an up-up-down (UUD) phase with $C_3$ symmetry breaking upon an infinitesimal external field along the longitudinal direction, but the overall phase diagram spanned by the axes of external field and temperature remains opaque due to the lack of systematic invesitgations with controlled methodologies. By means of quantum Monte Carlo at finite temperature and ground state density matrix renormalization group simulations, we map out the phase diagram of triangular quantum Ising model. Stemming from the upper BKT temperature at zero field, we obtain the phase boundary between the UUD and paramagnetic phases with its 2D $q=3$ Potts universality at weak field and weakly first order transition at strong field. Originated from the lower BKT temperature at zero field, we analyze the low temperature phase boundary between the clock phase and the UUD phase with Ising symmetry breaking at weak fields and the quantum phase transition between the UUD and fully polarized phases at strong fields. The accurate many-body numerical results are consistent with our field theoretical analysis. The experimental relevance towards the BKT magnet TmMgGaO$_4$ and programmable quantum simulators are also discussed.