First-Order Excited-State Quantum Phase Transition in the Transverse Ising Model with a Longitudinal Field

TL;DR

This paper uncovers a first-order excited-state quantum phase transition in the transverse Ising model with a longitudinal field, contrasting it with the well-known second-order ground-state transition, revealing new fundamental insights.

Contribution

It demonstrates the existence of a first-order QPT in the first excited state of the transverse Ising model with a longitudinal field, a novel finding in quantum phase transition studies.

Findings

First excited state exhibits a first-order QPT with increasing longitudinal field.

Pattern analysis distinguishes between continuous and first-order QPTs.

Ground state shows a second-order QPT, while the first excited state shows a first-order QPT.

Abstract

The investigation of the first-order quantum phase transition (QPT) is far from clarity in comparison to that of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and at the same time the concepts of universality class and critical scaling can be characterized by critical exponents. Here we present a compared study of these two kinds of QPT in the transverse Ising model. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from paramagnetic phase to ferromagnetic one, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in literature. Within the framework of a pattern picture we clearly identify the difference between these two kinds of QPT: for the continuous QPT only the pattern flavoring ferromagnetic phase is always dominant over the others, and on the contrary, there exist at least two competitive patterns in the first-order QPT, which is further indicated by patterns' occupancies calculated by pattern projections on the ground and first excited states wavefunctions. Our result has not only a fundamental significance in the understandings of the nature of QPTs, but also a practical interest in quantum simulations used to test the present finding.