Critical phenomena are ubiquitous in all of physics, appearing in their distinct and universal forms at every phase transition. Quantum critical phenomena are equally universal but far more enigmatic, causing a system described by a microscopic, quantum Hamiltonian to be governed only by its most macroscopic properties (the dimensions of space and of the order parameter). Experimental studies of quantum critical phenomena are inordinately difficult, due to the need for fine control over both the temperature and a quantum tuning parameter in the region of a quantum critical point. However, recent studies of the pressure-induced magnetic quantum phase transition in dimerized antiferromagnets have rekindled intense interest in a number of long-standing questions, both qualitative and quantitative, about quantum criticality.

These questions include the interplay of independence of quantum and thermal fluctuations in the quantum critical regime, the strength of the multiplicative logarithmic corrections at the upper critical dimension and the (nonuniversal) constants of proportionality affecting the experimental visibility of the phenomena, including the width of the quantum and thermal critical regions. All of these issues are closely related and we provide answers to all of them by performing a systematic numerical investigation of the quantum phase transition in a 3D S = 1/2 dimerized Heisenberg antiferromagnet. This model is a direct analogue of the quantum magnet TlCuCl_3, in which detailed experiments have measured the properties of the critical regime around the pressure-controlled quantum phase transition.

This system is at the upper critical dimension, where the dominant qualitative phenomenon predicted by field-theoretical approaches is logarithmic corrections to the mean-field scaling properties of all physical observables. These corrections reflect the incipient entanglement of quantum and thermal fluctuations. The quantitative study of logarithmic corrections is an inordinately difficult task due to their weak functional forms and strong sensitivity to error bars and exact extrapolations, and so requires extremely high numerical precision. Several studies in the past have failed to find meaningful evidence for their presence, calling into question both the constants of proportionality involved and the overall theoretical framework.

With the specific target of characterising the logarithmic corrections, Prof. Zi Yang Meng's group in IOP (including graduate student Yan Qi Qi and Zi Yang Meng) in collaboration with Prof. Bruce Normand from Renmin University of China and Prof. Anders Sandvik from Boston University in US, have performed very large-scale quantum Monte Carlo simulations with state-of-the-art algorithms and methods, allied with high-precision finite-size extrapolations, to approach points unprecedentedly close to the quantum phase transition. Our results allow us to extract precise multiplicative logarithmic corrections to the leading mean-field critical properties in the 4D O(3) universality class of the model. We provide the first exact numerical verification of the logarithmic corrections predicted for the order parameter (the zero-temperature staggered magnetization). Deriving a scaling ansatzfor the ordering temperature T_N away from the quantum-critical point (which was not previously available with logarithmic correction included), we alsodemonstrate that T_N obeys exactly the same logarithmic form as the sublatticemagnetization at zero temperature. This entirely new result, the exact linearity of a ``quantum'' and a ``thermal'' quantity throughout the phase diagram, wasunexpected and we discuss its implications. The nature of our finite-size data also allow us to demonstrate the predicted logarithmic corrections in the size scaling of the magnetic susceptibility, verifying the field-theoretical connection from partition-function zeros to thermodynamic observables, including notonly the multiplicative log correction but also a subleading correction.

These results are of interest to a broad cross-section of the physicscommunity, spanning theory, numerics and experiment in hard and soft condensed matter, cold atoms, field theory and high-energy physics. They lie beyond the limits of what was previously possible and open new horizons in the quantitative study of quantum criticality.

This study entitled “Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets” was published on Phys. Rev. B 92, 214401（2015）.
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.214401

This work was supported by theNational Natural Science Foundation of China under Grant No. 11174365, and by the National Basic Research Program of China under Grant No. 2012CB921704 (B.N.). The simulations were carried out at the National Supercomputer Center in Tianjin on the platform TianHe-1A.A.W.S.was supported by the NSF under Grant No. DMR-1410126, by the Simons Foundation, and by the Center for International Collaboration at the Institute of Physics of the Chinese Academy of Sciences.