Spontaneous symmetry breaking in the non-abelian anyon fluid

Cappelli, Andrea; Valtancoli, P.

doi:10.1016/0550-3213(95)00447-z

Cited by 5 publications

(6 citation statements)

References 43 publications

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“…If the same is true with a system of non-Abelian anyonic excitations (see ref. 71 for an argument that it is), then the observation of such an exotic superconducting state may reveal the existence of a nearby topological phase. (Depending on one's perspective, one might argue that one or the other is the more interesting phase.…”

Section: Discussionmentioning

confidence: 99%

A class of P,T-invariant topological phases of interacting electrons

et al. 2004

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Section: Discussionmentioning

confidence: 99%

A class of P,T-invariant topological phases of interacting electrons

et al. 2004

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“…while our corresponding results are The limits l → ∞ in (39) and (40) are taken together with lim l→∞ l 2 /k = a, where a is kept fixed and a < 1 in (39) and a < 1/2 in (40). The derivation from Eq.…”

Section: A Hard-core Casementioning

confidence: 99%

“…For non-Abelian anyons, a study of the thermodynamical properties in the lowest Landau level of a strong magnetic field has been performed [39], showing that the virial coefficients are independent of the statistics. The theory of non-relativistic matter with non-Abelian Chern-Simons gauge interaction in (2 + 1) dimensions was studied adopting a mean field approximation in the current-algebra formulation already applied to the Abelian anyons and finding a superfluid phase [40].…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of an ideal gas of non-Abelian anyons

2013

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We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-core parameters.Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied.

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“…Details on NACS statistical mechanics [39,[63][64][65][66] are given in Appendix B for general soft-core boundary conditions [40,41]. For non-Abelian anyons, the independence on the statistics of the virial coefficients in a strong magnetic field has been established in [67] while the theory of non-relativistic matter with non-Abelian Chern-Simons gauge interaction in (2+1) dimensions was studied in [68]. The N -body Hamiltonian for ideal non-Abelian Chern-Simons quantum particles can be written as [39]…”

Section: Non-abelian Anyonsmentioning

confidence: 99%

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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Spontaneous symmetry breaking in the non-abelian anyon fluid

Cited by 5 publications

References 43 publications

A class of P,T-invariant topological phases of interacting electrons

A class of P,T-invariant topological phases of interacting electrons

Statistical mechanics of an ideal gas of non-Abelian anyons

Energy–pressure relation for low-dimensional gases

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