Probing Criticality in Quantum Spin Chains with Neural Networks
This work addresses the computational bottleneck in simulating quantum systems for physicists, but it is incremental as it builds on existing neural network applications in quantum physics.
The authors tackled the problem of identifying quantum phase transitions in quantum spin chains, such as the transverse field Ising chain and anisotropic XY chain, by showing that simple neural networks with no hidden layers can effectively distinguish between magnetically ordered and disordered phases, with results applicable to a wide class of interacting quantum many-body systems.
The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of macroscopic phases of matter and associated phase transitions as well as efficient quantum state representation. In this work, we address quantum phase transitions in quantum spin chains, namely the transverse field Ising chain and the anisotropic XY chain, and show that even neural networks with no hidden layers can be effectively trained to distinguish between magnetically ordered and disordered phases. Our neural network acts to predict the corresponding crossovers finite-size systems undergo. Our results extend to a wide class of interacting quantum many-body systems and illustrate the wide applicability of neural networks to many-body quantum physics.