Exact diagonalization for spin-1/2 chains and the first order quantum phase transitions of the XXX chain in a uniformtransverse field

Abstract

A simple Mathematica code based on the differential realizationof hard-core boson operators for finding exact solutions of theperiodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed; it can easily be used to study generalspin-1/2 interaction systems. As an example, the code is applied to study XXXspin-1/2 chains with nearest neighbor interaction in a uniform transverse field. It shows that there are[N/2] level-crossing points in the ground state, whereN is the periodic number of the system and[x] stands for theinteger part of x, when the interaction strength and magnitude of the magnetic field satisfy certainconditions. The quantum phase transitional behavior in the ground state of the system inthe thermodynamic limit is also studied.