Alladi Ramakrishnan Hall

Machine learning approach to study phase transition in spin systems using principal component analysis

Saniur Rahman

S N BOSE

he quantum effect in insulating magnetic materials and the interaction-driven quantum phase transitions in these systems are the frontiers of research in condensed matter physics. In these systems, only spin degrees of freedom are active and the nature of the spin-exchange interaction determines the magnetic properties. Most of these materials are three-dimensional, but the exchange couplings can be confined to a quasi-one-dimensional nature, effectively forming spin chains and spin ladders. The confinement of the spin exchanges in the low-dimensional enhances the quantum fluctuation resulting in the emergence of the various exotic quantum ground state phases such as ferromagnetic, antiferromagnetic, dimer, spiral, vector chiral, spin liquid, etc. However, the calculation of the ground and excited states is a challenging task due to the exponentially growing Hilbert space with the system size. In this work, our main focus is to study of the quantum phase transitions in spin chains such as spin-1/2 $J_1-J_2$ model and spin-1/2 XXZ model using one of the unsupervised machine learning (ML) technique principal component analysis (PCA). We propose different numerical approaches to find the quantum phases and their phase boundaries for these spin systems.
First we We consider the simplest spin models such as spin-1/2 J1-J2 model and spin-1/2 XXZ model to study the quantum phase transitions using an unsupervised machine learning method called Principal Component Analysis (PCA). By proposing an iterative variational method (IVM), we generate the most probable spin configurations (MPSC) which can be used as input in PCA. We show that the direct use of the MPSCs as input in the PCA is efficient in producing the principal components that determine the phase boundaries for the spin-1/2 J1-J2 model [1]. For the spin-1/2 XXZ model, feature engineering, i.e. the use of the MPSCs and their weights, can successfully characterise the phase boundaries by following a finite-size scaling [2].