Bridging Lattice-Scale Physics and Continuum Field Theory with Quantum Monte Carlo Simulations

摘要

We discuss designer Hamiltonians-lattice models tailored to be free from sign problems (“de-signed”)when simulated with quantumMonte Carlo (QMC) methods but which still host complex many-body states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems inwhich competing interactions lead to nonmagnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connectionswith low-energy effective quantum field theories. As specific examples,we discuss the transition from aNéel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid (VBS) in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z_2 spin liquids and theXY* transition.We briefly review recent progress on QMC algorithms, including ground-state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.