Quantum criticality of two-dimensional quantum magnets with long-range interactions

TL;DR

This paper investigates how long-range interactions affect quantum phase transitions in two-dimensional quantum magnets, revealing different universality classes depending on frustration and interaction range.

Contribution

It combines perturbative continuous unitary transformations with Monte Carlo simulations to analyze critical behavior in long-range quantum Ising models on square and triangular lattices.

Findings

Unfrustrated systems exhibit a transition from mean-field to nearest-neighbor universality with varying exponents.

Frustrated systems remain in the nearest-neighbor universality class regardless of long-range interactions.

Critical exponents vary continuously in unfrustrated cases as a function of interaction decay.

Abstract

We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents, while the system remains in the universality class of the nearest-neighbor model in the frustrated cases independent of the long-range nature of the interaction.