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Quantum Fluctuation Phase Transition (QFPT)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.21972868

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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.
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 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=0T = 0T=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.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
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.
We study quantum criticality in the infinite range transverse-field Ising model. We find subtle differences with respect to the well-known single-site mean-field theory, especially in terms of gap, entanglement and quantum criticality. The calculations are based on numerical diagonalization of Hamiltonians with up to a few thousand spins. This is made possible by the enhanced symmetries of the model, which divide the Hamiltonian into many block-diagonal sectors. The finite temperature phase diagram and the characteristic jump in heat capacity closely resemble the behavior in mean-field theory. However, unlike mean-field theory where excitations are always gapped, the excitation gap in the infinite range model goes to zero from both the paramagnetic side and from the ferromagnetic side on approach to the quantum critical point. Also, contrary to mean-field theory, at the quantum critical point the quantum Fisher information becomes large, implying long-range multipartite entanglement. We find that the main role of temperature is to shift statistical weights from one conserved sector to another. However, low energy excitations in each sector arise only near the quantum critical point implying that low energy quantum fluctuations can arise only in the vicinity of the quantum critical field where they can persist up to temperatures of order the exchange constant.