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 $\mathbb{Z}_2$ symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the dynamics of FOQPTs is usually governed by an emergent critical point around the quantum spinodal point. Our results uncover a hidden criticality in FOQPTs, reshaping the conventional understanding of FOQPTs beyond the mean-field theory.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 $\mathbb{Z}_2$ symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the dynamics of FOQPTs is usually governed by an emergent critical point around the quantum spinodal point. Our results uncover a hidden criticality in FOQPTs, reshaping the conventional understanding of FOQPTs beyond the mean-field theory.

cond-mat.stat-mechCross-listedarXiv:2605.06436May 8, 20260 citations

Observation of generalized Kibble-Zurek mechanism across a first-order quantum phase transition in a spinor condensate

L.-Y. Qiu, Hongyu Liang, Yan-Bin Yang +4 more

The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.The Kibble-Zurek mechanism provides a unified theory to describe the universal scaling laws in the dynamics when a system is driven through a second-order quantum phase transition. However, for first-order quantum phase transitions, the Kibble-Zurek mechanism is usually not applicable. Here, we experimentally demonstrate and theoretically analyze a power-law scaling in the dynamics of a spin-1 condensate across a first-order quantum phase transition when a system is slowly driven from a polar phase to an antiferromagnetic phase. We show that this power-law scaling can be described by a generalized Kibble-Zurek mechanism. Furthermore, by experimentally measuring the spin population, we show the power-law scaling of the temporal onset of spin excitations with respect to the quench rate, which agrees well with our numerical simulation results. Our results open the door for further exploring the generalized Kibble-Zurek mechanism to understand the dynamics across first-order quantum phase transitions.

arXiv:2001.10210Science AdvancesMay 22, 202041 citations

Dynamical scaling behavior in non-equilibrium quantum phase transitions

Shusa Deng

Jan 1, 20110 citations

Common Scaling Functions in Dynamical and Quantum Phase Transitions

Takahiro Nemoto

Springer thesesNov 5, 20151 citation

Complete finite-size scaling theory of Renyi thermal entropy for second, first and weak first order quantum phase transitions

Zhe Wang, Zhu, Yanzhang, Ding, Yi-Ming +2 more

Establishing the nature of a quantum phase transition in finite-size simulations -- whether continuous, first-order, or weak first-order -- is a fundamental challenge in quantum many-body computation. Especially, the weak first-order phase transition is affected by a super large correlation length and always displays as a continuous critical point in simulated finite-sizes. The core difficulty lies in the fact that there is no effective finite-size theory to distinguish these phase transitions in the realistic simulations limited by the computational resource. In this work, we have fixed this problem by introducing a unified finite-size framework based on the Renyi thermal entropy (RTE) and its derivative (DRTE) to detect and characterize quantum phase transitions. We derive complete scaling theories for the RTE and DRTE at second-order, first-order, and weak first-order transitions, showing that the DRTE naturally isolates the singular part of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at (2+1)-dimensional O( $N$ ) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the $J$ -- $Q$ models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios.Establishing the nature of a quantum phase transition in finite-size simulations -- whether continuous, first-order, or weak first-order -- is a fundamental challenge in quantum many-body computation. Especially, the weak first-order phase transition is affected by a super large correlation length and always displays as a continuous critical point in simulated finite-sizes. The core difficulty lies in the fact that there is no effective finite-size theory to distinguish these phase transitions in the realistic simulations limited by the computational resource. In this work, we have fixed this problem by introducing a unified finite-size framework based on the Renyi thermal entropy (RTE) and its derivative (DRTE) to detect and characterize quantum phase transitions. We derive complete scaling theories for the RTE and DRTE at second-order, first-order, and weak first-order transitions, showing that the DRTE naturally isolates the singular part of the free energy and strengthens the characteristics of various phase transitions in finite sizes. Using quantum Monte Carlo simulations, we demonstrate accurate data collapse and extraction of critical exponents at (2+1)-dimensional O($N$) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the $J$--$Q$ models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios.

arXiv:2506.16111Jun 19, 20250 citations

\mathbb{Z}_2

symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the dynamics of FOQPTs is usually governed by an emergent critical point around the quantum spinodal point. Our results uncover a hidden criticality in FOQPTs, reshaping the conventional understanding of FOQPTs beyond the mean-field theory.

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) critical points. More importantly, the DRTE provides a smoking-gun signature of weak first-order transitions through a clear double-peak structure and a crossing at zero, which we unambiguously observe in debated deconfined quantum criticality candidates such as the

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models. Our approach offers a general, unbiased, and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing ambiguities between continuous and weak first-order scenarios.