Lattice vibration as a knob for novel quantum criticality: Emergence of supersymmetry from spin-lattice coupling

TL;DR

This paper reveals that lattice vibrations can induce a novel supersymmetric quantum criticality in spin chains, challenging the traditional view of vibrations as sources of decoherence in quantum systems.

Contribution

It demonstrates, through theoretical models and numerical methods, that strong spin-lattice coupling can lead to stable supersymmetric quantum criticality, a novel state not previously observed.

Findings

Discovery of supersymmetric quantum criticality with central charge c=3/2

Proposal of a spin-lattice coupled Ising chain as a candidate system

Generalized conditions for quantum criticality involving lattice vibrations

Abstract

Control of quantum coherence in many-body system is one of the key issues in modern condensed matter. Conventional wisdom is that lattice vibration is an innate source of decoherence, and amounts of research have been conducted to eliminate lattice effects. Challenging this wisdom, here we show that lattice vibration may not be a decoherence source but an impetus of a novel coherent quantum many-body state. We demonstrate the possibility by studying the transverse-field Ising model on a chain with renormalization group and density-matrix renormalization group method, and theoretically discover a stable $\mathcal{N}=1$ supersymmetric quantum criticality with central charge $c=3/2$. Thus, we propose an Ising spin chain with strong spin-lattice coupling as a candidate to observe supersymmetry. Generic precursor conditions of novel quantum criticality are obtained by generalizing the Larkin-Pikin criterion of thermal transitions. Our work provides a new perspective that lattice vibration may be a knob for exotic quantum many-body states.