Related papers: Topologically shadowed quantum criticality: A non-…
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…
In standard studies of quantum critical points (QCPs), the dynamic critical exponent $z$ is introduced as a fundamental parameter along with global symmetries to identify universality classes. Often, the dynamic critical exponent $z$ is set…
Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave…
We first propose a topological term that captures the "intertwinement" between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" valence solid bond…
We analyze and overview several different unconventional quantum criticalities. One origin of the unconventionality is the proximity to first-order transitions. The border between the first-order and continuous transitions is described by a…
Deconfined quantum criticality of two-dimensional $SU(2)$ quantum antiferromagnets featuring a transition from an antiferromagnetically ordered ground state to a so-called valence-bond solid state, is governed by a non-compact CP$^1$ model…
In symmetry protected topological (SPT) phases, the combination of symmetries and a bulk gap stabilizes protected modes at surfaces or at topological defects. Understanding the fate of these modes at a quantum critical point, when the…
Topological field theories (TFTs) play an important role in characterizing the deep infrared (IR) of many quantum systems with a mass gap, as well as the global symmetries of quantum field theories (QFTs) decoupled from gravity. In…
We study the nonequilibrium driven dynamics at topologically nontrivial quantum critical points (QCPs), and find that topological edge modes at criticality give rise to anomalous dynamical scaling behavior. By analyzing the driven dynamics…
Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond…
Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work however, we show that signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest…
We study the boundary states of the archetypal three-dimensional topological order, i.e. the three-dimensional $\mathbb{Z}_2$ toric code. There are three distinct elementary types of boundary states that we will consider in this work. In…
Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model…
In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $\theta$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($\eta^\prime$…
Quantum phase transitions out of a symmetry-protected topological (SPT) phase in (1+1) dimensions into an adjacent, topologically distinct SPT phase protected by the same symmetry or a trivial gapped phase, are typically described by a…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
The spontaneous breaking of non-invertible symmetries can lead to exotic phenomena such as coexistence of order and disorder. Here we explore second-order phase transitions in 1d spin chains between two phases that correspond to distinct…
Partition functions of quantum critical systems, expressed as conformal thermal tensor networks, are defined on various manifolds which can give rise to universal entropy corrections. Through high-precision tensor network simulations of…
The dissipative XY model in two spatial dimensions belongs to a new universality class of quantum critical phenomena with the remarkable property of the decoupling of the critical fluctuations in space and time. We have shown earlier that…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…