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We study various thermodynamic and transport properties of a holographicmodel of a nodal line semimetal (NLSM) at finite temperature, including thequantum phase transition to a topologically trivial phase, with Diracsemimetal-like conductivity. At zero temperature, composite fermion spectralfunctions obtained from holography are known to exhibit multiple Fermisurfaces. Similarly, for the holographic NLSM we observe multiple nodal linesinstead of just one. We show, however, that as the temperature is raised thesenodal lines broaden and disappear into the continuum one by one, so there is afinite range of temperatures for which there is only a single nodal linevisible in the spectrum. We compute several transport coefficients in theholographic NLSM as a function of temperature, namely the charge and thermalconductivities, and the shear viscosities. By adding a new non-linear couplingto the model we are able to control the low frequency limit of the electricalconductivity in the direction orthogonal to the plane of the nodal line,allowing us to better match the conductivity of real NLSMs. The boundaryquantum field theory is anisotropic and therefore has explicitly broken Lorentzinvariance, which leads to a stress tensor that is not symmetric. This hasimportant consequences for the energy and momentum transport: the thermalconductivity at vanishing charge density is not simply fixed by a Wardidentity, and there are a much larger number of independent shear viscositiesthan in a Lorentz-invariant system.

Thermodynamics and transport of holographic nodal line semimetals