Unconventional Quantum Critical Points

TL;DR

This paper reviews the theory of unconventional quantum critical points that go beyond traditional Landau theory, focusing on their field theories, universality classes, and relevance to recent experiments and simulations.

Contribution

It provides a comprehensive overview of three types of unconventional quantum critical points, highlighting their theoretical descriptions and experimental relevance.

Findings

Classifies three types of unconventional quantum critical points.

Connects theoretical models with recent numerical and experimental results.

Discusses universality classes and field theories of these critical points.

Abstract

In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and semiclassical spin ordered phase; (2). The transition between topological order and valence bond solid phase; (3). The direct second order transition between different competing orders. We focus on the field theory and universality class of these unconventional quantum critical points. Relation of these quantum critical points with recent numerical simulations and experiments on quantum frustrated magnets are also discussed.