We explore the critical properties of the recently discovered finite-time dynamical phase transition in the nonequilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the relaxation dynamics and it occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the critical time, we analyze the critical fluctuations at the phase transition in the nearest-neighbor Ising model on a square lattice using Monte Carlo simulations. By means of a finite-size scaling analysis, we extract the critical exponents for the transition. In two spatial dimensions, we find that the exponents are consistent with those of the two-dimensional Ising universality class when the system is initially in the vicinity of the critical point. For initial temperatures below the critical one, however, the critical exponents differ from the Ising-exponents, indicating a distinct dynamical critical phenomenon.
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.
What defines the operational boundary between quantum information and classical magnetism? We present a model-independent methodology for detecting characteristic scales in quantum systems through generalized susceptibility analysis χ(σ)=|d〈O〉/dσ|, where σ represents observation scales across spatial, temporal, and decoherence dimensions. Through comprehensive experiments on a Rigetti Ankaa-3 quantum processor, we identify an operational threshold at γc=0.6737±0.036 under tested noise profiles, exhibiting exceptional peak clarity κ=8.58—the sharpest signal observed across all phenomena. This pronounced transition, validated through bootstrap analysis and multiple susceptibility metrics, suggests critical-like behavior in the quantum-to-classical crossover, though we carefully refrain from claiming a thermodynamic phase transition. The framework successfully extracts characteristic scales without prior theoretical knowledge: correlation length ξ=8.00 qubits, distinct ordering timescales for ferromagnetic (tc=0.36) versus antiferromagnetic (tc=0.91) systems, and the quantum critical field hc=1.821 in the transverse-field Ising model. Robustness analysis confirms stability across smoothing parameters, methods, and metric definitions. Beyond providing actionable guidance for noisy intermediate-scale quantum-era quantum computing, our findings suggest that magnetic correlations exhibit characteristic transitions at specific decoherence scales—an operational perspective connecting quantum information theory and condensed matter physics. While framing this as methodological advance rather than fundamental physics, the identification of critical-like information-to-physics transitions provides practical diagnostics for quantum device characterization and optimization.
Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. They encompass cosmological phase transitions in the early universe and the transition into a quark-gluon plasma in high-energy collisions. Quantum phase transitions, particularly intriguing, occur at temperatures near absolute zero and are driven by quantum fluctuations rather than thermal ones. The strength of the fluctuations is very sensitive to the dimensionality of the physical systems, which determines the existence and nature of phase transitions. Low-dimensional systems often exhibit suppression of phase transitions, while high-dimensional systems tend to exhibit mean-field-like behavior. The localization-delocalization Anderson transition stands out among quantum phase transitions, as it is thought to retain its non-mean-field character across all dimensions. This work marks the first observation and characterization of the Anderson transition in four dimensions using ultracold atoms as a quantum simulator with synthetic dimensions. We characterize the universal dynamics in the vicinity of the phase transition. We measure the critical exponents describing the scale-invariant properties of the critical dynamics, which are shown to obey Wegner's scaling law. Our work is the first experimental demonstration that the Anderson transition is not mean-field in dimension four.
We propose that the temperature dependence of a single quantity $R={\ensuremath{\kappa}}_{i}/\ensuremath{\delta}{n}_{i}^{2}$, the ratio of the local compressibility to the local number fluctuations, can be used to map out the finite temperature phase diagram, diagnose the critical region around a quantum phase transition, and identify critical points belonging to different universality classes. We test our proposal using state-of-the-art large-scale quantum Monte Carlo simulations of the two-dimensional Bose Hubbard model. Our results have implications for recently developed single-site imaging experiments.
Characterizing the low-energy dynamics of quantum materials is crucial for understanding strongly correlated electronic states, yet remains experimentally challenging, particularly in two-dimensional systems. Here, we leverage nitrogen-vacancy (NV) centers in diamond as a non-invasive quantum sensor to study thin-film Bi
2Sr
2CaCu
2O
8+δ (BSCCO), revealing several distinct dynamical phenomena across the superconducting phase diagram. At zero magnetic field and low temperatures, NV depolarization (
T1) spectroscopy captures GHz-scale noise from nodal quasiparticle excitations, consistent with Bardeen--Cooper--Schrieffer (BCS) mean-field theory. Near the critical temperature
Tc≈90 K, supercurrent-fluctuation-induced noise sharply reduces
T1. By analyzing the temperature scaling of
T1, we observe clear deviations from mean-field prediction, reflecting the importance of order parameter fluctuations and enabling the determination of critical exponents. Under a small magnetic field, a broad and asymmetric reduction of
T1 unveils a liquid-like phase of mobile vortices. NV decoherence (
T2) spectroscopy further probes MHz-scale noise and reveals complex vortex-solid fluctuations well below
Tc. Our results establish quantum noise spectroscopy as a non-invasive probe of superconducting dynamics over frequency and length scales complementary to existing techniques.