# Finite-Scale Emergence of 2+1D Supersymmetry at First-Order Quantum Phase Transition

## TL;DR

This paper demonstrates that 2+1D supersymmetry can emerge at a first-order quantum phase transition in an Ising magnet, with potential experimental realization using topological superconductor surfaces, revealing finite-scale supersymmetry phenomena.

## Contribution

It shows for the first time that supersymmetry can emerge at a first-order quantum phase transition in 2+1D systems, expanding the understanding of SUSY in condensed matter.

## Key findings

- Supersymmetry emerges at the first-order transition of the Ising magnet.
- Emergence of SUSY is linked to a topological phase transition of Majorana fields.
- The scale of SUSY emergence can be large with small initial masses.

## Abstract

Supersymmetry, a symmetry between fermions and bosons, provides a promising extension of the standard model but is still lack of experimental evidence. Recently, the interest in supersymmetry arises in the condensed matter community owing to its potential emergence at the continuous quantum phase transition. In this work, we demonstrate that 2+1D supersymmetry, relating massive Majorana and Ising fields, might emerge at the first-order quantum phase transition of the Ising magnetization by tuning a single parameter. Although the emergence of the SUSY is only allowed in a finite range of scales due to the existence of relevant masses, the scale range can be large when the masses before scaling are small. We show that the emergence of supersymmetry is accompanied by a topological phase transition for the Majorana field, where its non-zero mass changes the sign but keeps the magnitude. An experimental realization of this scenario is proposed using the surface state of a 3+1D time-reversal invariant topological superconductor with surface magnetic doping.