Criticality around the Spinodal Point of First-Order Quantum Phase Transitions

TL;DR

This paper reveals that quantum criticality can emerge around the spinodal point of first-order quantum phase transitions, linking it to second-order transitions through an effective Hamiltonian.

Contribution

It introduces a microscopic theory showing how quantum criticality arises at the spinodal point of FOQPTs, connecting first- and second-order quantum phase transitions.

Findings

Resonant local excitations decouple a Hilbert subspace at the spinodal point.

Effective Hamiltonian exhibits a second-order quantum phase transition.

Predicted absence of criticality in the staggered-field PXP model.

Abstract

Universality and scaling are hallmarks of second-order phase transitions but are generally unexpected in first-order quantum phase transitions (FOQPTs). We present a microscopic theory showing that quantum criticality can emerge around the quantum spinodal point of FOQPTs where metastability disappears. We demonstrate that, at this instability, resonant local excitations dynamically decouple a Hilbert subspace characterized by an emergent discrete translational symmetry. Projecting the original Hamiltonian onto this subspace yields an effective Hamiltonian that exhibits a genuine second-order quantum phase transition (SOQPT) and the Kibble-Zurek scaling. We validate this framework in the tilted Ising chain which breaks Z_2 symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the FOQPT dynamics is usually governed by an emergent critical point around the quantum spinodal point. Our study establishes a bridge between the dynamics of the FOQPT and SOQPT, and thus sheds new light on the long-standing conundrum of the dynamics of the FOQPT.