Statistical mechanics of an ideal gas of non-Abelian anyons

Mancarella, Francesco; Trombettoni, Andrea; Mussardo, Giuseppe

doi:10.1016/j.nuclphysb.2012.10.020

Cited by 16 publications

(25 citation statements)

References 64 publications

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“…Therefore, the equations derived here also apply in the case of inverse square potentials in arbitrary spatial dimension and other SO(2, 1) invariant systems such as anyons [37][38][39][40][41][42].…”

Section: Comments and Conclusionmentioning

confidence: 99%

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Ordóñez

2016

Physica A: Statistical Mechanics and its Applications

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We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical SO(2, 1) Schrödinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state -pressure relationship -may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.

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Section: Comments and Conclusionmentioning

confidence: 99%

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Ordóñez

2016

Physica A: Statistical Mechanics and its Applications

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“…In Section VI the 2D anyonic gas is studied, and shown to have vanishing internal energy shift in the high-temperature limit. This is in agreement with (21) because, referring as α to the statistical parameter, B h.c. [34,38], where c 1 , c 1 , c 2 are suitable functions, hence both are subleading w.r.t. β log β in the β → 0 limit.…”

Section: Energy-pressure Relation For Imperfect Gases At High Tementioning

confidence: 99%

“…Different approaches have been subsequently used in order to approximate the values of a few higher virial coefficients, including the semiclassical approximation [28] and Monte Carlo computations [29] (for more references see [25,30]). The thermodynamics of a system of free non-Abelian anyons appears as a harder task and, so far, only results about the second virial coefficient are available [31][32][33][34]. In Section VI we also study the shift of the internal energy of soft-core anyonic gases: a family of models for "colliding" anyons (featuring generalized soft-core boundary conditions) can be introduced as the set of well-defined self-adjoint extensions of the Schrödinger anyonic Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Energy–pressure relation for low-dimensional gases

Mancarella¹,

Mussardo²,

Trombettoni³

2014

Nuclear Physics B

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A particularly simple relation of proportionality between internal energy and pressure holds for scale-invariant thermodynamic systems (with Hamiltonians homogeneous functions of the coordinates), including classical and quantum -Bose and Fermi -ideal gases. One can quantify the deviation from such a relation by introducing the internal energy shift as the difference between the internal energy of the system and the corresponding value for scale-invariant (including ideal) gases.After discussing some general thermodynamic properties associated with the scaleinvariance, we provide criteria for which the internal energy shift density of an imperfect (classical or quantum) gas is a bounded function of temperature. We then study the internal energy shift and deviations from the energy-pressure proportionality in low-dimensional models of gases interpolating between the ideal Bose and the ideal Fermi gases, focusing on the Lieb-Liniger model in 1d and on the anyonic gas in 2d.In 1d the internal energy shift is determined from the thermodynamic Bethe ansatz integral equations and an explicit relation for it is given at high temperature. Our results show that the internal energy shift is positive, it vanishes in the two limits of zero and infinite coupling (respectively the ideal Bose and the Tonks-Girardeau gas) and it has a maximum at a finite, temperature-depending, value of the coupling.Remarkably, at fixed coupling the energy shift density saturates to a finite value for arXiv:1407.0028v2 [quant-ph] 28 Aug 2014 infinite temperature. In 2d we consider systems of Abelian anyons and non-Abelian Chern-Simons particles: as it can be seen also directly from a study of the virial coefficients, in the usually considered hard-core limit the internal energy shift vanishes and the energy is just proportional to the pressure, with the proportionality constant being simply the area of the system. Soft-core boundary conditions at coincident points for the two-body wavefunction introduce a length scale, and induce a non-vanishing internal energy shift: the soft-core thermodynamics is considered in the dilute regime for both the families of anyonic models and in that limit we can show that the energy-pressure ratio does not match the area of the system, opposed to what happens for hard-core (and in particular 2d Bose and Fermi) ideal anyonic gases.

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“…Also anyons can potentially be used in quantum computing. For example, Freedman et al [16] proved that for certain types of non-Abelian anyons [17,18,19] braiding enables one to perform universal quantum computation [20,21].…”

Section: Introductionmentioning

confidence: 99%

Modeling free anyons at the bosonic and fermionic ends

Vasiuta

Rovenchak

2018

Physica A: Statistical Mechanics and its Applications

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The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is suggested as a modification of the Gibbs factor in the Bose and Fermi statistics. The proposed expressions are studied in the bosonic and fermionic limits. The obtained virial coefficients coincide with those of free anyons up to the fourth and fifth virial coefficients (the proposed approach can be extended for higher ones as well) and up to the second order in the anyonic parameter. The effective excitation spectrum corresponding to anyons is calculated.Comment: 17 pages, 6 figure

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Statistical mechanics of an ideal gas of non-Abelian anyons

Cited by 16 publications

References 64 publications

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Energy–pressure relation for low-dimensional gases

Modeling free anyons at the bosonic and fermionic ends

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