The concept of a quantum fluctuation phase transition (QFPT) proposes that the collective behavior of quantum fluctuations can itself undergo a non‑analytic change as a control parameter is varied, independently of any underlying order parameter associated with a conventional symmetry breaking. In this work we formulate a minimal theoretical framework that captures fluctuation‑driven criticality, derive mean‑field equations for the free energy as a function of a generalized fluctuation field, and employ a renormalization group (RG) analysis to identify the universality class of the transition. The resulting critical exponents differ from those of standard quantum phase transitions, reflecting the dominance of higher‑order fluctuation terms. We discuss possible experimental signatures in ultracold atomic gases, spin‑oriented systems, and superconducting qubits operating at nanokelvin temperatures, and argue that the observation of a QFPT would provide a new route to discovering exotic quantum phases and could attract Nobel‑prize level attention.
The concept of a quantum fluctuation phase transition (QFPT) proposes that the collective behavior of quantum fluctuations can itself undergo a non‑analytic change as a control parameter is varied, independently of any underlying order parameter associated with a conventional symmetry breaking. In this work we formulate a minimal theoretical framework that captures fluctuation‑driven criticality, derive mean‑field equations for the free energy as a function of a generalized fluctuation field, and employ a renormalization group (RG) analysis to identify the universality class of the transition. The resulting critical exponents differ from those of standard quantum phase transitions, reflecting the dominance of higher‑order fluctuation terms. We discuss possible experimental signatures in ultracold atomic gases, spin‑oriented systems, and superconducting qubits operating at nanokelvin temperatures, and argue that the observation of a QFPT would provide a new route to discovering exotic quantum phases and could attract Nobel‑prize level attention.
Quantum fluctuations are usually regarded as a background effect that perturbs classical order. In this work we propose that quantum fluctuations themselves can undergo a phase transition, a phenomenon we term the Quantum Fluctuation Phase Transition (QFPT). We develop a theoretical framework that treats the amplitude of quantum fluctuations as an order parameter, allowing a direct mapping between the fluctuation strength and the free‑energy landscape. Using a transverse‑field Ising model with tunable long‑range couplings, we derive a mean‑field free energy that exhibits a discontinuity in the fluctuation amplitude at a critical field strength. We further analyze the critical scaling, demonstrating that the QFPT belongs to a new universality class distinct from conventional quantum critical points. The theory predicts observable signatures in the low‑temperature heat capacity, dynamic structure factor, and entanglement entropy, and suggests that extreme‑cold atom or solid‑state systems with controllable interaction ranges could realize QFPTs. This novel mechanism for quantum phase change offers a route to discovering new quantum phases and could have implications for quantum technologies that rely on fluctuation‑driven properties.
Quantum materials exhibit rich phenomenology when driven across quantum critical points. Conventional quantum phase transitions are characterized by the change of an order parameter and the emergence of a divergent correlation length. In this work we propose a new class of quantum phase transitions, termed Quantum Matter Causal Phase Transitions (QMCPT), where the underlying causal structure of the many‑body wavefunction reorganizes itself rather than merely the order parameter. We develop a theoretical framework that describes how a causal graph, built from the entanglement structure of the ground state, can undergo a topological change. The transition is marked by a discontinuity or singularity in the causal depth, a quantity that counts the minimal number of layers of local operations required to prepare the state from a product state. We derive scaling relations for the causal depth near criticality, establish its universal behaviour, and discuss possible experimental signatures in strongly correlated systems such as heavy‑fermion compounds and twisted bilayer graphene. The QMCPT framework offers a new classification of quantum phases and provides a bridge between quantum information theory and condensed matter physics, opening pathways for identifying new materials with quantum critical behaviour and potential Nobel‑level discoveries.
Continuous phase transitions in equilibrium statistical mechanics were successfully described 50 years ago with the development of the renormalization group framework. This framework was initially developed in the context of phase transitions whose universal properties are captured by the long wavelength (and long time) fluctuations of a Landau order parameter field. Subsequent developments include a straightforward generalization to a class of T=0 phase transitions driven by quantum fluctuations. In the last 2 decades it has become clear that there is a vast landscape of quantum phase transitions where the physics is not always usefully (or sometimes cannot be) formulated in terms of fluctuations of a Landau order parameter field. A wide class of such phase transitions - dubbed deconfined quantum critical points - involve the emergence of fractionalized degrees of freedom coupled to emergent gauge fields. Here I review some salient aspects of these deconfined critical points.
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined through the non-analytic behavior of thermodynamic potentials in the thermodynamic limit. This limit is obtained when the number of available configurations of the system approaches infinity, which is conventionally associated to spatially-extended systems formed by an infinite number of degrees of freedom (infinite number of particles or modes). Taking previous ideas to the extreme, we argue that such a limit can be defined even in non-extended systems, providing a specific example in the simplest form of a single-mode bosonic Hamiltonian. In contrast to previous non-extended models, the simplicity of our model allows us to find approximate analytical expressions that can be confronted with precise numerical simulations in all the parameter space, particularly as close to the thermodynamic limit as we want. We are thus able to show that the system undergoes a change displaying all the characteristics of a second-order phase transition as a function of a control parameter. We derive critical exponents and scaling laws revealing the universality class of the model, which coincide with that of more elaborate non-extended models such as the quantum Rabi or Lipkin-Meshkov-Glick models. Analyzing our model, we are also able to offer insights into the features of this type of phase transitions, by showing that the thermodynamic and classical limits coincide. In other words, quantum fluctuations must be tamed in order for the system to undergo a true phase transition.
Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.
In the vicinity of continuous quantum phase transitions (QPTs), quantum systems become scale-invariant and can be grouped into universality classes characterized by sets of critical exponents. We have found that despite scale-invariance and universality, the experimental data still contain information related to the microscopic processes and scales governing QPTs. We have found that for many systems, the scaled data near QPTs can be approximated by the generic exponential dependence introduced in the scaling theory of localization; this dependence includes as a parameter a microscopic seeding scale of the renormalization group, L0. We have also conjectured that for interacting systems, the temperature cuts the renormalization group flow at the length travelled by a system-specific elementary excitation over the life-time set by the Planckian time, τP=ℏ/kBT. We have adapted this approach for QPTs in several systems and showed that L0 extracted from experiment is comparable to physically-expected minimal length scales, namely (i) the mean free path for metal-insulator transition in doped semiconductor Si:B, (ii) the distance between spins in Heisenberg and Ising chains, (iii) the period of an optical lattice for cold atom boson gases, and (iv) the period of a moiré superlattice for the Mott QPT in dichalcogenide bilayers. The metal-insulator transition in Si:P has been explained using a non-interacting version of the model. In two companion papers, we show that in superconducting systems, L0 is comparable to superconducting coherence length, and in quantum Hall systems, to the magnetic length. The developed new method of data analysis identifies microscopic processes leading to QPTs and quantitatively explains and unifies a large body of experimental data.