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Dissecting Quantum Phase Transition in the Transverse Ising Model

Yun-Tong YangHong-Gang Luo
Dec 2022
摘要
Irrespective of the fact that a complete theoretical description of criticalphenomena in connection with phase transition has been well-established throughthe renormalization group formalism, the understanding of the phase transitionitself remains incomplete. For example, the questions like why and how thephase transition happens are still unclear. Here we provide a pattern pictureto dissect the quantum phase transition occurring in the transverse Ising modelfor a finite lattice. After the validity of the pattern formulation obtained isconfirmed, the energy contributions of different patterns to the ground stateenergy provide a sufficient detail to show why and how the phase transitiontakes place. Furthermore, a histogram of patterns' occupancy calculated by theprojections of ground state wavefunction on the patterns also shows thedetailed process of the phase transition. Our results are not only fundamentalin understanding the mechanism of phase transition, but also of practicalinterest in quantum simulation platforms.
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