Machine learning approach to study quantum phase transitions of a frustrated one dimensional spin-1/2 system.

Frustration-driven quantum fluctuation leads to many exotic phases in the ground state (GS) and the study of these quantum phase transitions is one of the most challenging areas of research in condensed matter physics. We study a frustrated HeisenbergJ1-J2model of spin-1/2 chain with nearest exchange interactionand next nearest exchange interactionusing the principal component analysis (PCA) which is an unsupervised machine learning technique. In this method most probable spin configurations (MPSCs) of GS and first excited state (FES) for differentJ2/J1are used as the input in PCA to construct the covariance matrix.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising-Heisenberg rung interactions.

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase.