A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

Chen, Yang; Muttalib, K. A.

doi:10.1088/0953-8984/6/21/002

Cited by 8 publications

(3 citation statements)

References 19 publications

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“…Thus, it is the Coulomb potential in one-dimension, but modified at small separations with essentially a constant term (instead of going to 0, as the Coulomb potential does). This result makes precise the observation in [34], where it is argued that the temperature effect can be described by additional interaction terms. Note also that this last result leads to an equivalent interpretation in terms of N fermions in one dimension with harmonic confinement, and two-body interactions described by (3.17) .…”

Section: D Exactly Solvable Modelsupporting

confidence: 83%

Chern–simons Theory, Exactly Solvable Models and Free Fermions at Finite Temperature

Tierz

2009

Mod. Phys. Lett. A

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We show that matrix models in Chern-Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wavefunctions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern-Simons theory on S 3 and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular we show that the Chern-Simons partition function can be described by the density matrix of the free fermions in a very particular, crystalline, configuration. For this, we both use the Brownian motion and the matrix model description of Chern-Simons theory and find several common features with c=1 theory at finite temperature. Finally, using the exactly solvable model result, we show that the finite temperature effect can be described with a specific two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at large separations.

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Section: D Exactly Solvable Modelsupporting

confidence: 83%

Chern–simons Theory, Exactly Solvable Models and Free Fermions at Finite Temperature

Tierz

2009

Mod. Phys. Lett. A

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“…For our q-ensemble, V is given by (6). Although the coefficient of the inverse square term still vanishes for β = 2, clearly the long-range (E k −E l ) −1 term does not vanish in this case for any β, and the corresponding Hamiltonian H remains that of a very complicated interacting set of particles [13]. Nevertheless, the important point is that the many-body wavefunction for this Hamiltonian is known from (11) to be 0 , which has the form of a Vandermonde determinant as seen from (8) and (3).…”

Section: Brownian Motion Model Of Q-hermite Ensemblementioning

confidence: 96%

Brownian motion model of aq-deformed random matrix ensemble

Blecken

Muttalib

1998

J. Phys. A: Math. Gen.

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The effect of an external perturbation on the energy spectrum of a mesoscopic quantum conductor can be described by a Brownian motion model developed by Dyson who wrote a Fokker-Planck equation for the evolution of the joint probability distribution of the energy levels. For weakly disordered conductors, which can be described by a Gaussian random matrix ensemble, the solution of the Fokker-Planck equation has recently been obtained to give the correlation of level densities at different energies and different parameter values. In this paper we generalize this calculation to the case of a q-random matrix ensemble which should be relevant for conductors at stronger disorder.

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“…Chen and Muttalib [24] have interpreted a particular unitary ensemble with V (x) ∼ (log x) 2 as a fermionic system at finite temperature. This link is made more concrete by Moshe, Shapiro, and Neuberger [25] who have introduced a random matrix ensemble…”

mentioning

confidence: 99%

Level spacing distribution of critical random matrix ensembles

Nishigaki

1998

Phys. Rev. E

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We consider unitary invariant random matrix ensembles which obey spectral statistics different from the Wigner-Dyson, including unitary ensembles with slowly (∼ log 2 x) growing potentials and the finite-temperature fermi gas model. If the deformation parameters in these matrix ensembles are small, the asymptotically translational-invariant region in the spectral bulk is universally governed by a one-parameter generalization of the sine kernel. We provide an analytic expression for the distribution of the eigenvalue spacings of this universal asymptotic kernel, which is a hybrid of the Wigner-Dyson and the Poisson distributions, by determining the Fredholm determinant of the universal kernel in terms of a Painlevé VI transcendental function. [4]. A characteristic observable in such studies, used analytically or numerically to measure the deviation from integrability, is the probability E(s) of having no energy levels in an interval of width s, or the distribution of spacings between adjacent levels P (s) = E ′′ (s). These observables capture the behavior of local correlations of large number of energy levels, as the former consists of an infinite sum of integrals of regulated † spectral correlators,

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A cross-over from Fermi-liquid to non-Fermi-liquid behaviour in a solvable one-dimensional model

Cited by 8 publications

References 19 publications

Chern–simons Theory, Exactly Solvable Models and Free Fermions at Finite Temperature

Chern–simons Theory, Exactly Solvable Models and Free Fermions at Finite Temperature

Brownian motion model of aq-deformed random matrix ensemble

Level spacing distribution of critical random matrix ensembles

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