Emergent Hydrodynamics in Condensed Matter and
High-energy Physics

In this talk I will review recent developments in the construction of hydrodynamic theories in which translations are broken either spontaneously or pseudo-spontaneously, in the presence of a strong, external magnetic field. I will show that Hall transport coefficients become important when the magnetic field is strong. Moreover I will prove that, using the Ward Identities of the theory, the hydrodynamic AC correlators can be expressed in terms of the DC conductivities (which can be measured in real condensed matter systems) and a couple of intrinsic scales (which can be extracted from AC correlators). Finally, I will verify the validity of our hydrodynamic framework in well known holographic Q-lattice like theories. I will then show how the present results can be useful in testing the transport properties of the strange metal phase of cuprates.

Due to its rotation, Earth traps a few equatorial ocean and atmospheric waves, including Kelvin, Yanai, Rossby, and Poincare modes. It has been recently demonstrated that the mathematical origin of equatorial waves is intricately related to the nontrivial topology of hydrodynamic equations describing oceans or the atmosphere. In the present work, we consider plasma oscillations supported by a two-dimensional electron gas confined at the surface of a sphere or a cylinder. We argue that in the presence of a uniform magnetic field, these systems host a set of equatorial magnetoplasma waves that are counterparts to the equatorial waves trapped by Earth. For a spherical geometry, the equatorial modes are well developed only if their penetration length is smaller than the radius of the sphere. For a cylindrical geometry, the spectrum of equatorial modes is weakly dependent on the cylinder radius and overcomes finite-size effects. We argue that this exceptional robustness can be explained by destructive interference effects. We discuss possible experimental setups, including grains and rods composed of topological insulators (e.g., Bi2Se3) or metal-coated dielectrics (e.g., Au2S).

The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to equilibrium states is considered and its monotonicity property with respect to an open quantum system evolution is used to obtain second lawlike inequalities. We discuss this first for generic quantum systems in contact with a thermal bath and subsequently turn to a formulation suitable for the description of local dynamics in a relativistic quantum field theory. A local version of the second law similar to the one used in relativistic fluid dynamics can be formulated with relative entropy or even relative entanglement entropy in a space-time region bounded by two light cones. We also give an outlook toward isolated quantum field theories and discuss the role of entanglement for relativistic fluid dynamics.

We present a general scheme to approach the space - time evolution of deformations, currents, and the electric field in charge density waves related to appearance of intrinsic topological defects: dislocations, their loops or pairs, and solitons. We derive general equations for the multi-fluid hydrodynamics taking into account the collective mode, electric field, normal electrons, and the intrinsic defects. These equations may allow to study the transformation of injected carriers from normal electrons to new periods of the charge density wave, the collective motion in constrained geometry, and the plastic states and flows. As an application, we present analytical and numerical solutions for distributions of fields around an isolated dislocation line in the regime of nonlinear screening by the gas of phase solitons.

We construct the constitutive relations, up to first order in derivatives, of a boost-agnostic charged fluid in the presence of a background electric field. This allows us to describe polarized fluids with a finite-momentum ground state. For this state to be stationary - and for a consistent derivative expansion - it is necessary to include additional energy and momentum relaxation terms in the hydrodynamic equations of motions. We can fix the coefficients of these terms, except two, with respect to the thermodynamic properties of the fluid. In this talk, I will describe the construction and present the resulting constitutive relations.

Clean two-dimensional Dirac systems have received a lot of attention for being a prime candidate to observe hydrodynamical transport behavior in interacting electronic systems. This is mostly due to recent advances in the preparation of ultrapure samples with sufficiently strong interactions. In this paper, we investigate the role of collective modes in the thermo-electric transport properties of those systems. We find that dynamical particle-hole pairs, plasmons, make a sizeable contribution to the thermal conductivity. While the increase at the Dirac point is moderate, it becomes large towards larger doping. We suspect, that this is a generic feature of ultraclean two-dimensional electronic systems, also applicable to degenerate systems.

In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this work, we propose a hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. Starting from the Boltzmann equation, we introduce the effects of the Berry curvature to electron hydrodynamics and formulate a generalized Euler equation for noncentrosymmetric metals. We show that this equation reveals a variety of novel anomalous nonlocal/nonlinear transport phenomena; chiral vortical effect, quantum nonlinear Hall effect, thermal-gradient induced anomalous Hall effect, etc., whose transport coefficients are described by geometrical quantities such as Berry curvature dipole [1]. Furthermore, we give a symmetry classification of these coefficients and compare the results with existing hydrodynamic materials. In the presentation, we would like to discuss what phenomena are predicted to be observed in experiments in noncentrosymmetric materials, including bilayer-graphene and transition metal dichalcogenides. [1] I. Sodemann and L. Fu, PRL 115, 216806 (2015)

Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.