Quantum criticality and emergent many-body excitations in quasi-one-dimensional quantum magnetic systems

Investigation of quantum criticality in condensed matter systems not only reveals universal behaviors of quantum phase transitions but also deepens our understanding of emergent physics in quantum many-body systems. With accurate descriptions of the ground states and low-energy excitations of (quasi-)one-dimensional (1D) quantum spin models, significant progress has been made in studying quantum criticality and related emergent physics. In this review, we provide a short survey on some recent developments in this field. We start by discussing critical thermodynamics and dynamics of transverse-field Ising chain, highlighting novel quantum integrability and many-body excitations upon relevant perturbations. Dynamical properties of the excitations are further discussed, along with their experimental verification. Along the line of integrability, we further discuss the Heisenberg-Ising chain, introducing the string magnetic state. Among them, non-trivial string solutions which go beyond conventional field theory, have also been observed in experiments. Apart from the critical phenomena associated with the standard Ginzburg-Landau paradigm, we introduce the deconfined quantum criticality, which arises as a consequence of a continuous phase transition between two ordered states. Such a transition goes beyond the description of the Ginzburg-Landau paradigm and is characterized by the emergence of fractionalized spin excitations and enhanced continuous symmetry at the quantum critical point. Finally, we conclude by highlighting potential novel critical phenomena and emergent physics and their realizations in quasi-1D quantum magnetic systems.