In low-dimensional systems, indistinguishable particles can display statistics that interpolate between bosons and fermions. Signatures of these "anyons" have been detected in two-dimensional quasiparticle excitations of the fractional quantum Hall effect, however experimental access to these quasiparticles remains limited. As an alternative to these "topological anyons," we propose "statistical anyons" realized through a statistical mixture of particles with bosonic and fermionic symmetry. We show that the framework of statistical anyons is equivalent to the generalized exclusion statistics (GES) pioneered by Haldane, significantly broadening the range of systems to which GES apply. We develop the full thermodynamic characterizations of these statistical anyons, including both equilibrium and nonequilibrium behavior. To develop a complete picture, we compare the performance of quantum heat engines with working mediums of statistical anyons and traditional topological anyons, demonstrating the effects of the anyonic phase in both local equilibrium and fully nonequilibrium regimes. In addition, methods of optimizing engine performance through shortcuts to adiabaticity are investigated, using both linear response and fast forward techniques.
Following our earlier work on the Ruppeiner geometry of an anyon gas [B. Mirza and H. Mohammadzadeh, Phys. Rev. E {\bf 78,} 021127 (2008)], we will derive nonperturbative thermodynamic curvature of a two-dimensional ideal anyon gas. At different values of the thermodynamic parameter space, some unique and interesting behaviors of the anyon gas are explored. A complete picture of attractive and repulsive phases of the anyon gas is given.
We derive the thermodynamic curvature of a two dimensional ideal anyon gas of particles obeying fractional statistics. The statistical interactions of anyon gas can be attractive or repulsive. For attractive statistical interactions, thermodynamic curvature is positive and for repulsive statistical interactions, it is negative, which indicates a more stable anyon gas. There is a special case between the two where the thermodynamic curvature is zero. Small deviations from the classical limit will also be explored.
The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic quantities, $Q(α)$, of the free anyon gas may be factorized in the terms characteristic of the ideal Bose ($α=0$) and fermion ($α=1$) gases, i.e., $Q(α) = αQ(1) + (1-α) Q(0)$. It is shown that the factorizable property of the thermodynamic quantities, to all orders, can be established from the property of the equivalence between the anyon statistics and statistic…
Thermodynamics of Hamiltonian anyons with applications to quantum heat engines
University of Exeter（埃克塞特大学）；Universidad de Granada（格拉纳达大学）；Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada（格拉纳达大学卡洛斯一世理论与计算物理研究所）
Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum Monte Carlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. While changing the exchange constants, the phase transition changes from continuous to discontinuous one, apparently correlated with the change in the excitations from Abelian to non-Abelian anyons. We show this coincidence by computing the…
One-dimensional anyon models are renewedly constructed by using path integral formalism. A statistical interaction term is introduced to realize the anyonic exchange statistics. The quantum mechanics formulation of statistical transmutation is presented.
We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting …
Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence
California Institute of Technology（加州理工学院）；Ghent university（根特大学）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；University of California, Berkeley（加利福尼亚大学伯克利分校）
The density matrix of a two-anyon system is evaluated and used to investigate the "statistical interparticle potential" following the theory of Uhlenbeck. The main purpose is to see how the statistical potential will depend on the fractional statistical parameter $α$. The result shows that the statistical potential for a two-anyon system with $α\ge {1\over2}$ is always repulsive. For the system with $0<α< {1\over2}$, the potential is repulsive at short distances and becomes attractive at long distances. It remains only in the boson system ($α=0$) that the repulsive potential arising from the e…
The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We establish that a q-deformed algebra can be used to describe the statistics of particles (anyons) interpolating continuously between Bose and Fermi statistics, i.e., fractional statistics. We show that the generalized intermediate statistics splits into the Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The B-anyon thermostat…
We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find that the two-particle interference is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wavepacket can get completely reflected or split into a superposition of a reflected wave and an anti…
Using a proposed generalization of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of vanishing or low temperature. While Friedel-like oscillations are present in nearly all non-bosonic cases at T=0, they are characterized by exponential damping at low temperature. We discuss the dependence of these features on dimensionality and on the value of the statistical parameter alpha.
We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical …
It is shown that, by allowing a transmutation between a boson and a fermion, the system with both bosons and fermions will have the statistical distribution function of an anyon.
It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli operators. Here we show that the same entangled states of the same lattice are capable of supporting the non-abelian Ising model, where the concatenated operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code anyons, reproducing the required fusion, braiding and statistical properties. We…
We have obtained an expansion of the reduced density matrices (or, equivalently, correlation functions of the fields) of impenetrable one-dimensional anyons in terms of the reduced density matrices of fermions using the mapping between anyon and fermion wavefunctions. This is the generalization to anyonic statistics of the result obtained by A. Lenard for bosons. In the case of impenetrable but otherwise free anyons with statistical parameter $κ$, the anyonic reduced density matrices in the grand canonical ensemble is expressed as Fredholm minors of the integral operator ($1-γ\hat θ_T$) with c…
The low energy properties of the one-dimensional anyon gas with $δ$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter $α$ is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of $α$ in the dispersion relations.
Universitat de València-CSIC（瓦伦西亚大学-CSIC）；IFIC, Universitat de València-CSIC（IFIC，瓦伦西亚大学-CSIC）；JILA, NIST, and Department of Physics, University of Colorado（JILA，美国国家标准与技术研究院，科罗拉多大学物理系）；University of Colorado（科罗拉多大学）；IUMPA - Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València（IUMPA-纯数学与应用数学大学研究所，巴伦西亚理工大学）；Adam Mickiewicz University（亚当·密茨凯维奇大学）；DIPC - Donostia International Physics Center（DIPC-圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（IKERBASQUE，巴斯克科学基金会）；ICREA（加泰罗尼亚高级研究学院）；ETH Zurich（苏黎世联邦理工学院）
The analytical expressions of the Joule-Thomson coefficient for homogeneous and harmonically trapped three-dimensional ideal anyons which obey Haldane fractional exclusion statistics are derived. For an ideal Fermi gas, the Joule-Thomson coefficient is negative, which means that there is no maximum Joule-Thomson inversion temperature. With careful study, it is found that there exists a Joule-Thomson inversion temperature in the fractional exclusion statistics model. Furthermore, the relations between the Joule-Thomson inversion temperature and the statistical parameter $g$ are investigated.
We discuss the problem of anyonic statistics in one and two spatial dimensions from the point of view of statistical physics. In particular we want to understand how the choice of the Bornvon Karman or the twisted periodic boundary conditions necessary in a Monte Carlo simulation to mimic the thermodynamic limit of the many body system influences the statistical nature of the particles. The particles can either be just bosons, when the configuration space is simply connected as for example for particles on a line. They can be bosons and fermions, when the configuration space is doubly connecte…
We investigate the quantum transport of anyons in one space dimension. After establishing some universal features of non-equilibrium systems in contact with two heat reservoirs in a generalised Gibbs state, we focus on the abelian anyon solution of the Tomonaga-Luttinger model possessing axial-vector duality. In this context a non-equilibrium representation of the physical observables is constructed, which is the basic tool for a systematic study of the anyon particle and heat transport. We determine the associated Lorentz number and describe explicitly the deviation from the standard Wiedeman…
We demonstrate how the generalized Pauli exclusion principle emerges for quasiparticle excitations in 2d topological phases. As an example, we examine the Levin-Wen model with the Fibonacci data (specified in the text), and construct the number operator for fluxons living on plaquettes. By numerically counting the many-body states with fluxon number fixed, the matrix of exclusion statistics parameters is identified and is shown to depend on the spatial topology (sphere or torus) of the system. Our work reveals the structure of the (many-body) Hilbert space and some general features of thermody…
It is mentioned that anyon thermodynamic potential $Q(α, N)$ could not be factorized in terms characteristic of the ideal boson $α=0$ and fermion $α=1$ gases by the relation $Q(α, N) = (1-α) Q(0, N_b)+ αQ(1, N_f)$ in which $N=N_f +N_b$, that claimed in Phys. Rev. Lett. 78, 3233 (1997). Our analyses indicate that the thermodynamic quantities of anyon gas may be factorized as $Q(α) = αQ(1) + (1-α) Q(0)$ only in the two-dimension system.
In this manuscript, we calculate the scalar curvature of a two-dimensional thermodynamic space to study the properties of two thermodynamic systems. In particular, we study the stability and possible anyonic behavior of quantum group invariant systems and systems with fractal distribution functions.
