Critical behavior in the presence of an order-parameter pinning field

TL;DR

This study investigates quantum critical phenomena using a pinning-field approach in a 2D quantum Heisenberg model and an improved classical 3D Ising model, revealing complex scaling behaviors and universal critical exponents.

Contribution

It demonstrates the effectiveness of the pinning-field method in locating quantum critical points and uncovers new universal critical exponents at the critical adsorption fixed point.

Findings

Pinning-field approach locates quantum critical points across various strengths.

Strong corrections to scaling complicate critical behavior identification.

Discovery of a new universal critical exponent at the critical adsorption fixed point.

Abstract

We apply a recently advocated simulation scheme that employs a local order-parameter pinning field to study quantum critical phenomena in the two-dimensional square-lattice bilayer quantum Heisenberg model. Using a world-line quantum Monte Carlo approach, we show that for this model, the pinning-field approach allows to locate the quantum critical point over a wide range of pinning-field strengths. However, the identification of the quantum critical scaling behavior is found to be hard since the pinning field introduces strong corrections to scaling. In order to further elucidate the scaling behavior in this situation, we also study an improved classical lattice model in the three-dimensional Ising universality class by means of Monte Carlo simulations on large lattice sizes, which allow us to employ refined finite-size scaling considerations. A renormalization group analysis exhibits the presence of an important crossover effect from the zero pinning-field to a critical adsorption fixed point. In line with field-theoretical results, we find that at the critical adsorption fixed point the short-distance expansion of the order-parameter profile exhibits a new universal critical exponent. This result also implies the presence of slowly decaying scaling corrections, which we analyze in detail.