2023/11/02 by Shackleton, Leyna, Sachdev, Subir
#FOS: Physical sciences #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2311.01572
The triangular lattice antiferromagnet with S=1/2 spins and nearest neighbor interactions is known to have long-range antiferromagnetic order, with nearest-neighbor spins at an angle of 120 degrees. Numerical studies of quantum phases proximate to this state have been limited to small systems because the of the sign-problem in Monte Carlo simulations in imaginary time. We propose an effective lattice model for quantum fluctuations of the antiferromagnetic order, and a sign-problem free Monte Carlo algorithm, enabling studies in large systems sizes. The model is a ℤ2 gauge theory coupled to gauge-charged scalars which have a relativistic dispersion in the continuum limit. Crucially, the gauge theory is odd, i.e. there is a static, background ℤ2 gauge charge on each site, accounting for the Berry phases of the half-odd-integer spins on each site. We present results of simulations on lattices of sizes up to 36 × 36 × 36. Along with the antiferromagnetically ordered phase, our phase diagram has a valence bond solid state with a √(12) × √(12) unit cell, and a gapped ℤ2 spin liquid. Deconfined critical points or phases in intermediate regions are not ruled out by our present simulations.