Abstract
In this paper, based on the basic principles of thermodynamics, we explore the hydrodynamic regime of interacting Lifshitz field theories in the presence of broken rotational invariance. We compute the entropy current and discover new dissipative effects which are consistent with the principle of local entropy production in the fluid. In our analysis, we consider both the parity even and the parity odd sector upto first order in the derivative expansion. Finally, we argue that the present construction of the paper could be systematically identified as that of the hydrodynamic description associated with spin waves (away from the domain of quantum criticality) under certain limiting conditions.
Highlights
Low temperature phases of various strange metal systems have been a mysterious issue since their discovery
Spin waves could be thought of as being the gapless(this renders that the underlying theory is scale invariant) excitation (Goldstone modes) associated with the broken O(3) symmetry
The most significant outcome of our analysis is the establishment of the hydrodynamic description away from the quantum criticality
Summary
Low temperature phases of various strange metal systems have been a mysterious issue since their discovery. We consider both the parity even and the parity odd sector of the hydrodynamic constitutive relations and in particular explore how the parity odd transports are affected due to the presence of anisotropy in the system In this sense, the present analysis is valid for all of those fluid systems whose underlying isometry group comprises that of the broken generators of the Lifshitz algebra. Spin waves could be thought of as being the gapless(this renders that the underlying theory is scale invariant) excitation (Goldstone modes) associated with the broken O(3) symmetry (at the level of hydrodynamics such symmetry breaking effects should be manifested in terms of the emergence of the pressure anisotropy in the constitutive relations of the conserved quantities) These excitations clearly break the underlying rotational invariance of the system and they vanish as one approaches the domain of quantum crticality [27,28,29,30]. The entropy production in Lifshitz fluids might have direct or indirect consequences on gravitational particle production through the remarkable identification of gravitational dynamics as an entropic force [31] whose relativistic generalization leads to Einstein’s general theory of relativity
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