Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Unbounded Hydrodynamics in Nodal-Line Semimetals

Sanguk Kim, Geo Jose, Bruno Uchoa

Published Sep 2, 2020• 0 citations
OpenAlex

Abstract

The ratio between the shear viscosity and the entropy $\eta/s$ is considered a universal measure of the strength of interactions in quantum systems. In relativistic systems, this quantity was conjectured to have a universal lower bound $(1/4\pi)\hbar/k_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $\eta/s\propto T$ is \emph{unbounded}, scaling towards zero with decreasing temperature $T$ in the perturbative limit. We find that the hydrodynamic scattering time between collisions $\tau\sim\hbar/\alpha^{2}vk_{F}$, with $vk_{F}$ the energy scale set by the radius of the ring and $\alpha$ the fine structure constant. We suggest that the lower bound criteria should be modified to account for unscreened relativistic systems with a Fermi surface.

Related papers

Hydrodynamic transport and violation of the viscosity-to-entropy ratio bound in nodal-line semimetals

Sang Wook Kim, Geo Jose, Bruno Uchoa

The ratio between the shear viscosity and the entropy $\ensuremath{\eta}/s$ is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound $(1/4\ensuremath{\pi})\ensuremath{\hbar}/{k}_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $\ensuremath{\eta}/s\ensuremath{\propto}T$ violates the universal lower bound, scaling toward zero with decreasing temperature $T$ in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly temperature independent, up to logarithmic scaling corrections, and can be extremely short for large nodal lines, near the Mott-Ragel-Ioffe limit. Our finding suggests that nodal-line semimetals can be very strongly correlated quantum systems.

arXiv:2009.01271•Physical Review Research•Jul 2, 2021•2 citations

Shear viscosity in a non-Fermi-liquid phase of a quadratic semimetal

Philipp T. Dumitrescu

We study finite temperature transport in the Luttinger-Abrikosov-Beneslavskii phase---an interacting, scale invariant, non-Fermi-liquid phase found in quadratic semimetals. We develop a kinetic equation formalism to describe the dc transport properties, which are dominated by collisions, and compute the shear viscosity $\ensuremath{\eta}$. The ratio of shear viscosity to entropy density $\ensuremath{\eta}/s$ is a measure of the strength of interaction between the excitations of a quantum fluid. As a consequence of the quantum critical nature of the system, $\ensuremath{\eta}/s$ is a universal number and we find it to be consistent with a bound proposed from gauge-gravity duality.

arXiv:1406.6337•Physical Review B•Sep 2, 2015•12 citations

Shear viscosity of strongly interacting fermionic quantum fluids

Nandan Pakhira, Ross H. McKenzie

Eighty years ago Eyring proposed that the shear viscosity of a liquid, $η$, has a quantum limit $η\gtrsim n\hbar$ where $n$ is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound $\fracη{s}\geq \frac{\hbar}{4πk_{B}}$ for the ratio between the shear viscosity and the entropy density, $s$. Using Dynamical Mean-Field Theory (DMFT) 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 quasi-particle 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.

arXiv:1504.07131•Physical Review B•Sep 1, 2015•9 citations

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

Clifford Chafin, Thomas Schäfer

We study hydrodynamic fluctuations in a nonrelativistic fluid. We show that in three dimensions, fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ as a function of the temperature. The minimum provides a bound on $\ensuremath{\eta}/s$ which is independent of the conjectured bound in string theory, $\ensuremath{\eta}/s\ensuremath{\ge}\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity, we find $\ensuremath{\eta}/s\ensuremath{\gtrsim}0.2\ensuremath{\hbar}$. This bound is not universal---it depends on the thermodynamic properties of the unitary Fermi gas and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\ensuremath{\omega}$ diverges as $1/\sqrt{\ensuremath{\omega}}$, and that the shear viscosity in two dimensions diverges as $\mathrm{ln}(1/\ensuremath{\omega})$.

arXiv:1209.1006•Physical Review A•Feb 27, 2013•51 citations

Hydrodynamic transport in the Luttinger-Abrikosov-Beneslavskii non-Fermi liquid

Julia M. Link, Igor F. Herbut

We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well known that when the chemical potential is right at the band touching point, the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at $T=0$, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of 4 with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading-order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.

arXiv:1911.06431•Physical review. B./Physical review. B•Mar 26, 2020•12 citations

Universal Quantum Viscosity in a Unitary Fermi Gas

C. Cao, Ethan Elliott, J. Joseph +4 more

A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, in which the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale ħ n, where n is the density and ħ is Planck's constant h divided by 2π, whereas at high temperatures the natural scale is p(T)(3)/ħ(2), where p(T) is the thermal momentum. We used breathing mode damping to measure the shear viscosity at low temperature. At high temperature T, we used anisotropic expansion of the cloud to find the viscosity, which exhibits precise T(3/2) scaling. In both experiments, universal hydrodynamic equations including friction and heating were used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare it with that of a perfect fluid.

arXiv:1007.2625•Science•Dec 10, 2010•332 citations
The ratio between the shear viscosity and the entropy η/s\eta/sη/s is considered a universal measure of the strength of interactions in quantum systems. In relativistic systems, this quantity was conjectured to have a universal lower bound (1/4π)ℏ/kB(1/4\pi)\hbar/k_{B}(1/4π)ℏ/kB​, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that η/s∝T\eta/s\propto Tη/s∝T is \emph{unbounded}, scaling towards zero with decreasing temperature TTT in the perturbative limit. We find that the hydrodynamic scattering time between collisions τ∼ℏ/α2vkF\tau\sim\hbar/\alpha^{2}vk_{F}τ∼ℏ/α2vkF​, with vkFvk_{F}vkF​ the energy scale set by the radius of the ring and α\alphaα the fine structure constant. We suggest that the lower bound criteria should be modified to account for unscreened relativistic systems with a Fermi surface.
The ratio between the shear viscosity and the entropy $\ensuremath{\eta}/s$ is considered a universal measure of the strength of interactions in quantum systems. This quantity was conjectured to have a universal lower bound $(1/4\ensuremath{\pi})\ensuremath{\hbar}/{k}_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $\ensuremath{\eta}/s\ensuremath{\propto}T$ violates the universal lower bound, scaling toward zero with decreasing temperature TTT in the perturbative limit. We find that the hydrodynamic scattering time between collisions is nearly temperature independent, up to logarithmic scaling corrections, and can be extremely short for large nodal lines, near the Mott-Ragel-Ioffe limit. Our finding suggests that nodal-line semimetals can be very strongly correlated quantum systems.
We study finite temperature transport in the Luttinger-Abrikosov-Beneslavskii phase---an interacting, scale invariant, non-Fermi-liquid phase found in quadratic semimetals. We develop a kinetic equation formalism to describe the dc transport properties, which are dominated by collisions, and compute the shear viscosity $\ensuremath{\eta}$. The ratio of shear viscosity to entropy density $\ensuremath{\eta}/s$ is a measure of the strength of interaction between the excitations of a quantum fluid. As a consequence of the quantum critical nature of the system, $\ensuremath{\eta}/s$ is a universal number and we find it to be consistent with a bound proposed from gauge-gravity duality.
Eighty years ago Eyring proposed that the shear viscosity of a liquid, ηηη, has a quantum limit η≳nℏη\gtrsim n\hbarη≳nℏ where nnn is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound ηs≥ℏ4πkB\fracη{s}\geq \frac{\hbar}{4πk_{B}}sη​≥4πkB​ℏ​ for the ratio between the shear viscosity and the entropy density, sss. Using Dynamical Mean-Field Theory (DMFT) 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^{3}3He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T21/T^{2}1/T2 dependence, where TTT is the temperature. With increasing temperature and interaction strength UUU there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle 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^{3}3He. 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.
We study hydrodynamic fluctuations in a nonrelativistic fluid. We show that in three dimensions, fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ as a function of the temperature. The minimum provides a bound on $\ensuremath{\eta}/s$ which is independent of the conjectured bound in string theory, $\ensuremath{\eta}/s\ensuremath{\ge}\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$, where sss is the entropy density. For the dilute Fermi gas at unitarity, we find $\ensuremath{\eta}/s\ensuremath{\gtrsim}0.2\ensuremath{\hbar}$. This bound is not universal---it depends on the thermodynamic properties of the unitary Fermi gas and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\ensuremath{\omega}$ diverges as $1/\sqrt{\ensuremath{\omega}}$, and that the shear viscosity in two dimensions diverges as $\mathrm{ln}(1/\ensuremath{\omega})$.
We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well known that when the chemical potential is right at the band touching point, the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at T=0T=0T=0, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of 4 with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading-order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.
A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, in which the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale ħ n, where n is the density and ħ is Planck's constant h divided by 2π, whereas at high temperatures the natural scale is p(T)(3)/ħ(2), where p(T) is the thermal momentum. We used breathing mode damping to measure the shear viscosity at low temperature. At high temperature T, we used anisotropic expansion of the cloud to find the viscosity, which exhibits precise T(3/2) scaling. In both experiments, universal hydrodynamic equations including friction and heating were used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare it with that of a perfect fluid.