Loyola University Maryland

Department of Physics

Hydrodynamics of Quantum Critical Point

Phase Diagram of the high temperature superconductivity with quantum critical point

Hydrodynamics is an effective theory describing the dynamics of a system in a local thermal equilibrium based on symmetries at large distance and time scales, incorporating dissipative effects. Quantum critical point (QCP) at zero temperature is believed to be responsible for the so-called “strange metal region” in high Tc cuprates phase diagrams where, for example, resistivity has an unusual linear temperature dependence upon removing the superconducting dome with a high magnetic field. To describe the hydrodynamics of QCP, the correlation length of the quantum fluctuation should be larger than the system size (so that the system is under the influence of QCP, and the quantum critical scaling properties apply), which has to be larger than the length scale of the thermal fluctuation (so that one can assume local thermal equilibrium, and we don’t need to take into account the details of thermal fluctuations).

Interesting QCPs are realized with the general dynamical exponents z that is not equal to 1 or 2, and thus do not possess the Lorentz or Galilean boost symmetry. The corresponding stress energy tensors are no longer symmetric. I have formulated universal hydrodynamics by utilizing the off-diagonal parts of stress energy tensors. I have uncovered three new transport coefficients, one in neutral and two in charged fluids and provided verifiable experimental consequences. By applying hydrodynamics to systems with QCP, I have determined their temperature dependence using the quantum critical scaling in the articles listed below. This has been done for the first time in literature and is an important and non-trivial extension of Landau-Lifshitz. For Quantum critical region, temperature dependences were determined from the scaling properties of Quantum critical point. Verifiable experimental consequences were also provided.

We also provide another study (also listed below) that reveals an interesting physical consequence on bulk viscosity, which might be useful to determine the dynamical exponent associated with a Quantum critical point. More generally, the formulation can be applied to physical systems when the boost symmetry is broken by any means, e.g., static impurities. The resulting effects can be measured through the new transport coefficients.

Universal temperature dependences of magneto-transports in optimal and over doped phases of high Tc cuprates, like resistivity, inverse Hall angle and Hall coefficients, are in good agreement with a holographic model with Schroedinger symmetry, a promising starting point for understanding the full high Tc cuprates phase diagram. This has been done in collaboration with a high Tc experimentalist and a senior string theorist, and gave me experiences with an experimental lab and related literature. This paper is also listed at the end of this page. The corresponding research web page can be found in this link to Holographic model of Quantum Critical Point.


  1.  C. Hoyos, B. S. Kim and Y. Oz, “Lifshitz Hydrodynamics,” JHEP 1311, 145 (2013). [arXiv:1304.7481 [hep-th]]
  2.  C. Hoyos, B. S. Kim and Y. Oz, “Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity,” JHEP 1403, 029 (2014). [arXiv:1309.6794 [hep-th]]
  3.  C. Hoyos, B. S. Kim and Y. Oz, “Bulk Viscosity in Holographic Lifshitz Hydrodynamics,” JHEP 1403, 050 (2014). [arXiv:1312.6380 [hep-th]]
  4.  B. S. Kim, E. Kiritsis and C. Panagopoulos, “Holographic quantum criticality and strange metal transport,” New J. Phys. 14:043045 (2012). [arXiv:1012.3464 [cond-mat.str-el]]