One of the most unconventional features of topological phases of matter is the emergence of quasiparticles with exotic statistics, such as non-Abelian anyons in two-dimensional systems. Recently, a different type of exotic particle statistics that is consistently defined in any dimension, called R parastatistics [Z. Wang , ], is also shown to be possible in a special family of topological phases. However, the physical significance of emergent parastatistics still remains elusive. Here, we demonstrate a distinctive physical consequence of parastatistics by proposing a challenge game that can only be won in a noise-robust way using physical systems hosting paraparticles, as passing the challenge requires the two participating players to secretly communicate in an indirect way by exploiting the nontrivial exchange statistics of the quasiparticles. The winning strategy using emergent paraparticles is robust against noise, as well as the most relevant class of eavesdropping via local measurements. This provides both an operational definition and an experimental identity test for paraparticles, alongside a potential application in secret communication.
Parastatistics is an exotic type of exchange statistics beyond fermions and bosons. Paraparticles transform in higher dimensional representations of the exchange symmetry group, analogous to non-Abelian anyons, yet consistently defined in any dimension. Although paraparticles have long been proposed, they were widely believed to be physically equivalent to fermions or bosons. Nevertheless, a recent paper proposed a different theory, called
R-parastatistics, and demonstrated that nontrivial
R-paraparticles can emerge as quasiparticles in condensed matter systems, and are observably distinct from both fermions and bosons. This paper develops the theoretical foundation and several extensions of
R-parastatistics, with particular emphasis on its observable consequences. Central to this paper is a general theory of local observables extending the basic family introduced before. First, we define local observables that distinguish particle types. Second, we formulate local observables at special point defects that probe the internal indices of
R-paraparticles, crucial for observing
R-parastatistics and for the proposed applications in quantum information. Third, we introduce local observables that create or annihilate particle-antiparticle pairs, important for building a relativistic quantum field theory for
R-paraparticles. We further introduce generalized hidden symmetries that act on internal indices of
R-paraparticles while preserving the local observable algebra, providing a basis for proving local indistinguishability and for connecting to a categorical description of
R-paraparticles. This work sets a solid theoretical foundation for understanding the fundamental physical properties of
R-paraparticles and pave the way for finding them in nature.
Abstract It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimensions 1–5 . In principle, a second exception known as parastatistics, which extends outside two dimensions, has been considered 6 but was believed to be physically equivalent to fermions and bosons 7–9 . Here we show that non-trivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. These new types of identical particle obey generalized exclusion principles, leading to exotic free-particle thermodynamics distinct from any system of free fermions and bosons. We formulate our theory by developing a second quantization of paraparticles that naturally includes exactly solvable non-interacting theories and incorporates physical constraints such as locality. We then construct a family of exactly solvable quantum spin models in one and two dimensions, in which free paraparticles emerge as quasiparticle excitations, and their exchange statistics can be physically observed and are notably distinct from fermions and bosons. This demonstrates the possibility of a new type of quasiparticle in condensed matter systems and—more speculatively—the potential for previously unconsidered types of elementary particle.
Quantum many body physics is an exciting research area, involving novel phases of matter with fundamentally new properties, but is also notoriously hard due to complexity of interacting quantum systems. Some popular approaches involve approximation techniques and numerical simulations, which are known to fail in several important cases. In contrast, rigorous mathematical tools, such as exact solutions and operator inequalities, have a narrower range of applicability, but provide guaranteed results and insights into the underlying physical mechanisms. This research aims to develop new techniques in this direction and use them to explore novel phases of matter. My first direction is to construct toy models where exact solutions are possible. Such models are important as they prove that certain physical phenomena are theoretically possible in nature, and often lead to the discovery of new phases. Such insights are provided by three exactly solvable models I have discovered: (1) a family of 1D quantum spin models hosting free parastatistical quasiparticles (an exotic type of identical particles beyond fermions, bosons, and anyons), proving for the first time that parastatistics is theoretically possible as an emergent phenomenon; (2) a 3D classical Ising model whose phases are characterized by topological features of certain loop observables, suggesting existence of previously unknown classical phases and phase transitions with topological order parameters; and (3) a family of models with exact p-wave superconducting ground states demonstrating the existence of Majorana quasiparticles and non-Abelian statistics in particle number-conserving systems. My second direction is to derive rigorous bounds and exact constraints on physical observables, which are applicable to large families of quantum many-body systems. I present three directions of progress: (1) a method that dramatically improves the upper bounds on the speed of information propagation in locally-interacting systems, which significantly extends the scope of these bounds and enables new applications; (2) bounds on finite-size errors in numerical simulations of lattice systems, including quench dynamics and gapped ground states; and (3) a locality bound on gapped ground states of power-law interacting systems, which leads to a generalization of the aforementioned error bounds to such systems. These error bounds have important theoretical implications such as proving the existence of the thermodynamic limit and stability of phases, and are practically useful in determining the validity of finite-size numerical simulations.
The quest for non-Abelian anyons, exotic quasiparticles fundamental to topological quantum computing, remains a forefront challenge in condensed matter physics. This paper explores the universal topological signatures that characterize non-Abelian anyons when hosted within engineered flat band systems. Flat bands, distinguished by their quenched kinetic energy, dramatically enhance interaction effects, providing a unique platform for stabilizing exotic many-body phases and fostering the emergence of non-Abelian statistics. We theoretically investigate how specific lattice geometries and tuning parameters in various engineered platforms, such as Moiré superlattices, photonic crystals, and ultracold atomic gases, can lead to the formation of topological flat bands conducive to non-Abelian anyonic excitations. Our analysis identifies several universal signatures, including robust ground state degeneracy sensitive to system topology, characteristic patterns in topological entanglement entropy, and distinct braiding statistics manifested through non-Abelian holonomies and fractional quantum numbers. These signatures are shown to be robust against local perturbations and largely independent of microscopic details, providing reliable indicators for experimental detection. We discuss the implications for developing fault-tolerant quantum computation and outline potential experimental methodologies for probing these predicted signatures, emphasizing the transformative potential of engineered flat bands in advancing topological quantum science.