Shear viscosity of strongly interacting fermionic quantum fluids

Abstract

Eighty years ago, Eyring proposed that the shear viscosity of a liquid η has a quantum limit η n where n is the density of the fluid. Using holographic duality and the anti-de Sitter/conformal field theory correspondence in string theory, Kovtun, Son, and Starinets (KSS) conjectured a universal bound η s 4πk B for the ratio between the shear viscosity and the entropy density s. Using dynamical mean-field theory, we calculate the shear viscosity and entropy density for a fermionic fluid described by a single-band Hubbard model at half-filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid 3 He. At low temperature, the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T 2 dependence, where T is the temperature. With increasing temperature and interaction strength U , there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasiparticle-based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid 3 He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge-transfer salts.

Viscosity bound violation in viscoelastic Fermi liquids

“…equation for a sound wave propagating at velocity c 1 which is in agreement with our analysis and interpretation of equation(20).…”

“…To better understand η/s within the context of strongly correlated systems, we develop a simple theoretical model to calculate the quasiparticle scattering rates of a strongly correlated quantum liquid above T c . Such a model differs from past calculations [17][18][19][20] in that we include the effects of superfluid fluctuations as T T c  + .…”

Notes on shear viscosity bound violation in anisotropic models

“…On the other hand, based on the dynamical mean field theory (DMFT), Pakhira and McKenzie have found that both the KSS and Hartnoll bounds are violated in a singleband Hubbard model [7,8]. For the shear viscosity to entropy density ratio for an electron fluid, which is described by a single-band Hubbard model at half filling, the KSS bound was found to be strongly violated in the bad-metal regime for parameters appropriate to lattice electronic systems, such as cuprates and organic charge-transfer salts.…”

“…Basically, an arbitrary violation of the KSS bound would occur if H(u H ) → ∞, so a specific C cannot exist. In turn, D would also break down [7][8][9][10][11].…”

Hydrodynamic approach justified for low-temperature transport in Ioffe-Regel limit metal

“…Here, l ee = 2 kF EF kT 2 is the mean free path of e-e scattering, k F = mV F /h the Fermi vector. At T = 0 the e-e collisions are completely damped, then l η = a while electron viscosity yields a constant value η = 1 5 h m [21]. Then, at finite temperature viscosity length scale is defined mostly by scattering with atomic core while l η ≤ a.…”