Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations

TL;DR

This paper explores sign-problem-free lattice models for quantum Monte Carlo simulations, enabling detailed study of complex quantum phases and transitions, and connecting lattice physics with continuum quantum field theories.

Contribution

It introduces designer Hamiltonians that are free of sign problems yet host rich quantum states, facilitating detailed analysis of quantum phase transitions and their field theory descriptions.

Findings

Successful simulation of Neel to valence-bond solid transitions

Demonstration of topological Z2 spin liquids in anisotropic models

Advances in quantum Monte Carlo algorithms for entanglement entropy

Abstract

We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo 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 in which competing interactions lead to non-magnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connections with low-energy effective quantum field theories. As specific examples, we discuss the transition from a Neel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids and the XY* transition. We briefly review recent progress on quantum Monte Carlo algorithms, including ground state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.