# Intrinsic Jump Character of the First-Order Quantum Phase Transitions

## TL;DR

This paper introduces a bond reversal method using the difference of bond strength to distinguish first-order quantum phase transitions from continuous ones, validated on various spin chain models.

## Contribution

The paper proposes a novel bond reversal method based on the difference of bond strength to identify the order of quantum phase transitions, applicable to diverse models.

## Key findings

- First-order QPTs show intrinsic jumps in relevant operators.
- The method successfully distinguishes between first-order and continuous QPTs.
- The transition in the spin ladder switches from continuous to first-order at a specific coupling.

## Abstract

We find that the first-order quantum phase transitions~(QPTs) are characterized by intrinsic jumps of relevant operators while the continuous ones are not. Based on such an observation, we propose a bond reversal method where a quantity $\mathcal{D}$, the difference of bond strength~(DBS), is introduced to judge whether a QPT is of first order or not. This method is firstly applied to an exactly solvable spin-$1/2$ \textit{XXZ} Heisenberg chain and a quantum Ising chain with longitudinal field where distinct jumps of $\mathcal{D}$ appear at the first-order transition points for both cases. We then use it to study the topological QPT of a cross-coupled~($J_{\times}$) spin ladder where the Haldane--rung-singlet transition switches from being continuous to exhibiting a first-order character at $J_{\times, I} \simeq$ 0.30(2). Finally, we study a recently proposed one-dimensional analogy of deconfined quantum critical point connecting two ordered phases in a spin-$1/2$ chain. We rule out the possibility of weakly first-order QPT because the DBS is smooth when crossing the transition point. Moreover, we affirm that such transition belongs to the Gaussian universality class with the central charge $c$ = 1.