Observation of anyonic thermodynamics and generalized Pauli principle
Fansu Wei, Chi Zhang, Zimeng Ye, Dengbo Wang, Botao Wang, Xiaoji Zhou, Hepeng Yao
Abstract
Anyons are quasiparticles with quantum statistics interpolating between those of bosons and fermions. Two distinct manifestations of anyonic behaviour have been theoretically established: fractional exchange statistics where particle exchange can produce any phase, and generalized exclusion statistics which extends the Pauli exclusion principle. While anyons exhibiting fractional exchange statistics have been observed in diverse platforms, experimental realizations of generalized exclusion statistics and direct measurements of its thermodynamic signatures have remained elusive. Here, we realize an anyonic thermodynamic ensemble obeying generalized exclusion statistics and detect its anyonic thermodynamics in a one-dimensional strongly interacting quantum gas. To achieve this, we exploit the bijective mapping between dynamical and statistical interactions in one dimension. By tuning interaction strength and temperature over a wide range, we measure the equation of state and identify clear departures from Bose-Einstein and Fermi-Dirac statistics. These deviations are quantitatively captured by generalized exclusion statistics, providing direct evidence for the generalized Pauli principle. Independent probes of other thermodynamic quantities including pressure and the Tan contact further validate this framework. Our results establish a versatile platform for engineering anyonic exclusion statistics and open the door to thermodynamic applications of anyons in quantum technologies.
AI Impact Assessments
(1 models)Scientific Impact Assessment
1. Core Contribution
This paper reports the first direct experimental realization and thermodynamic characterization of a quantum gas obeying Haldane's generalized exclusion statistics (GES) — a framework that extends the Pauli exclusion principle to allow fractional maximum occupation of quantum states. While fractional exchange statistics (FES) of anyons have been observed in 2D systems (quantum Hall states, superconducting circuits, trapped ions), the complementary concept of generalized exclusion statistics had remained experimentally unverified at the thermodynamic level.
The key insight exploited is the bijective mapping between dynamical interactions and statistical interactions in one dimension: in the Lieb-Liniger model of 1D interacting bosons, tuning the ratio of interaction strength to temperature continuously interpolates between fermionic (Tonks-Girardeau) and bosonic statistics, passing through intermediate anyonic regimes characterized by a statistical parameter 0 < α < 1. By measuring the equation of state — specifically the energy-particle number relation ε(N₁D) — the authors extract the statistical parameter α and demonstrate states with maximum occupation 1/α exceeding unity but remaining finite, directly evidencing the generalized Pauli principle.
2. Methodological Rigor
The experimental approach is well-designed and technically sound. The system consists of ⁶Li₂ Feshbach molecules loaded into 1D tubes formed by a 2D triangular optical lattice, with interaction parameter γ ≥ 20 placing the system firmly in the strongly interacting regime. Several aspects strengthen the methodology:
A notable limitation is the treatment of the tube array as an equivalent single tube via the weighted average N₁D = ΣNⱼ²/ΣNⱼ, though this is validated by QMC simulations. The transverse excitation correction (˜α = α/D⊥²) at high temperatures is admittedly approximate, and the discrepancy at low temperatures attributed to tube distributions could benefit from more rigorous treatment.
3. Potential Impact
Fundamental physics: This work provides the first thermodynamic evidence for GES, connecting a 30-year-old theoretical framework (Haldane 1991, Wu 1994) to measurable observables. It demonstrates that the statistical parameter α is a physically meaningful quantity that can be continuously tuned and experimentally determined.
Platform versatility: The cold-atom platform offers significant advantages over solid-state systems for studying anyonic physics — controllable interactions, tunable temperature, and clean model Hamiltonians. This establishes a new experimental paradigm for engineering fractional statistics.
Quantum technology applications: The authors point toward quantum heat engines with anyonic working media (potentially outperforming bosonic/fermionic counterparts), and base-N quantum computing exploiting the finite occupation number 1/α. While speculative, these directions are grounded in recent theoretical proposals.
Cross-disciplinary relevance: The connection between GES and FES, though the two frameworks describe fundamentally different aspects of anyonic physics, suggests that thermodynamic insights gained here could inform understanding of topological anyons in 2D materials where direct thermodynamic probing is extremely challenging.
4. Timeliness & Relevance
This paper is highly timely. It follows closely on several landmark experiments: the realization of 1D anyons via quantum walks (Kwan et al., Science 2024), observation of anyonization via impurity correlations (Dhar et al., Nature 2025), and non-Abelian braiding demonstrations. However, all prior work focused on exchange statistics or dynamical signatures. The thermodynamic manifestation of anyonic behavior — arguably the most natural prediction of GES — had not been directly observed. This fills a significant gap in the experimental landscape of quantum statistics.
The work also builds naturally on the theoretical framework of Yao et al. (PRL 2018), which predicted the Fermi-Bose thermodynamic crossover in 1D gases and identified the relevant dimensionless parameters. The experimental realization validates and extends this theoretical program.
5. Strengths & Limitations
Key Strengths:
Limitations:
Overall Assessment
This is a significant experimental achievement that provides the first thermodynamic evidence for Haldane's generalized exclusion statistics. The methodology is rigorous, the results are convincing, and the implications span fundamental physics and potential quantum technology applications. The work represents a natural culmination of theoretical predictions spanning three decades and positions cold-atom platforms as a premier setting for exploring fractional statistics.
Generated Jun 18, 2026
Comparison History (18)
Paper 1 provides the first experimental realization of generalized exclusion statistics (anyonic thermodynamics), a long-sought theoretical prediction. This fills a fundamental gap in quantum statistical mechanics, demonstrating a new form of quantum statistics beyond Bose-Einstein and Fermi-Dirac. Its breadth of impact spans condensed matter, quantum information, and fundamental physics. Paper 2, while revealing an intriguing resistance paradox in the 1D-to-2D crossover, addresses a more specialized question in superfluid transport. Both are rigorous, but Paper 1's novelty in confirming a foundational quantum principle gives it broader and deeper impact.
Paper 1 represents a landmark experimental breakthrough by observing generalized anyonic exclusion statistics, fundamentally extending the Pauli principle. While Paper 2 elegantly unifies quantum thermalization and linear response frameworks, Paper 1's discovery of new quasiparticle thermodynamic behavior has broader paradigm-shifting implications. By successfully engineering anyonic thermodynamics in 1D quantum gases, Paper 1 opens direct, highly relevant pathways for novel quantum computing technologies and advanced materials, giving it the edge in fundamental novelty, breadth of impact, and long-term technological application.
Paper 1 reports the first experimental observation of generalized exclusion statistics (anyonic thermodynamics) in a 1D quantum gas, filling a long-standing gap between theory and experiment. This is a landmark result with broad implications across quantum physics, condensed matter, and quantum technologies. Paper 2 presents a thorough but incremental theoretical study of phase diagrams in a specific Rydberg atom geometry using DMRG, contributing primarily to the specialized community studying Rydberg quantum simulators. Paper 1's novelty, experimental nature, and fundamental significance give it substantially higher impact potential.
Both papers represent significant advances in topological quantum physics. Paper 1 realizes a Pfaffian state with non-Abelian anyonic properties in ultracold atoms—a long-sought milestone directly relevant to topological quantum computing. The demonstration of non-Abelian topological order in a controllable synthetic platform opens pathways to anyonic braiding experiments, which is arguably the central challenge in topological quantum information science. Paper 2 beautifully demonstrates generalized exclusion statistics thermodynamics, but this is conceptually more incremental as it leverages known 1D mappings rather than constructing genuinely new topological states. The non-Abelian aspect of Paper 1 gives it broader impact potential.
Paper 2 likely has higher impact because it reports an experimental observation of generalized exclusion statistics (“generalized Pauli principle”) and its thermodynamic signatures—an outstanding, broadly relevant goal in quantum many-body physics. Direct equation-of-state measurements, validation via pressure and Tan contact, and a tunable 1D platform strengthen methodological rigor and reproducibility. The result is timely and connects to anyons, thermodynamics, statistical mechanics, and quantum technologies, giving wider cross-field reach than Paper 1, which is primarily a numerically exact but more specialized study of quench dynamics in dipolar lattice bosons.
Paper 1 reports the first experimental observation of generalized exclusion statistics (anyonic thermodynamics) in a physical system—a long-sought milestone in quantum physics. It provides direct evidence for the generalized Pauli principle through multiple independent thermodynamic measurements. This represents a fundamental experimental breakthrough with broad implications across condensed matter, statistical mechanics, and quantum technologies. Paper 2 presents a valuable theoretical/computational framework for hybrid quantum simulation but is more incremental, proposing methods that extend existing variational quantum simulation approaches. Experimental firsts demonstrating new physics generally carry higher impact than computational frameworks.
Paper 2 likely has higher impact: it reports the first direct experimental realization and thermodynamic measurement of generalized exclusion statistics (generalized Pauli principle), addressing a long-standing elusive signature of anyons. This is highly novel, timely, and broadly relevant across condensed matter, statistical mechanics, quantum information, and cold-atom quantum simulation, with clearer cross-field conceptual and potential technological implications (thermodynamic anyonic ensembles). Paper 1 is rigorous and important for Floquet many-body localization/transport, but sits in a more specialized subfield with fewer immediate cross-disciplinary applications.
Paper 1 reports the first experimental observation of generalized exclusion statistics (anyonic thermodynamics) in a physical system, addressing a longstanding theoretical prediction that had never been directly verified. This represents a fundamental advance in quantum statistical mechanics with broad implications across condensed matter physics, quantum gases, and quantum technologies. Paper 2 provides valuable ab initio simulations reproducing recent experiments on few-body elliptic flow, but is more incremental—confirming existing observations computationally rather than revealing fundamentally new physics. Paper 1's novelty, breadth of impact, and foundational significance give it higher potential impact.
Paper 1 likely has higher impact: it reports an experimental realization and direct thermodynamic measurements of generalized exclusion statistics (generalized Pauli principle), addressing a long-standing elusive goal and enabling a tunable platform with clear links to quantum simulation and potential quantum-technology applications. Its novelty is both conceptual and experimental, and the results can influence multiple areas (anyon physics, strongly correlated 1D gases, quantum thermodynamics). Paper 2 is elegant and timely but primarily theoretical/proposal-level and narrower in immediate applicability until experimentally demonstrated.
Paper 1 provides the first experimental observation of generalized exclusion statistics (anyonic thermodynamics), a fundamental concept proposed decades ago but never directly measured. This addresses a long-standing open question in quantum physics about the generalized Pauli principle, with broad implications for condensed matter, quantum statistics, and potentially quantum technologies. Paper 2 presents impressive technical advances in creating synthetic microgravity for cold atoms, but is more incremental—offering a convenient laboratory alternative to existing microgravity platforms. Paper 1's fundamental discovery nature gives it higher impact potential across multiple fields.