Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVigorousness of effective hydrodynamics from Anderson localization in two dimensional nematic quantum criticality
90
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The $1994$ first discovery of a metal-insulator transition in two dimensions and series of $1997-1998$ experiments on two dimensional metal-insulator transitions in various samples of MOSFETs changed the paradigm of Anderson localization that metals cannot exist in two dimensions. Unfortunately, this delocalization physics of the diffusive regime does not apply to the effective hydrodynamic regime of quantum criticality. In the present study, we investigate effects of mutual correlations between hydrodynamic fluctuations and weak-localization corrections on Anderson localization, based on the renormalization group analysis up to the two-loop order. As a result, we find that the absence of quantum coherence in two-particle composite excitations gives rise to a novel disordered non-Fermi liquid metallic state near two dimensional nematic quantum criticality with nonmagnetic disorders. This research would be the first step in understanding the $T-$linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality.
rate research
Read More
We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $epsilon=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.
We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.
Quasi-two dimensional itinerant fermions in the Anti-Ferro-Magnetic (AFM) quantum-critical region of their phase diagram, such as in the Fe-based superconductors or in some of the heavy-fermion compounds, exhibit a resistivity varying linearly with temperature and a contribution to specific heat or thermopower proportional to $T ln T$. It is shown here that a generic model of itinerant AFM can be canonically transformed such that its critical fluctuations around the AFM-vector $Q$ can be obtained from the fluctuations in the long wave-length limit of a dissipative quantum XY model. The fluctuations of the dissipative quantum XY model in 2D have been evaluated recently and in a large regime of parameters, they are determined, not by renormalized spin-fluctuations but by topological excitations. In this regime, the fluctuations are separable in their spatial and temporal dependence and have a dynamical critical exponent $z =infty.$ The time dependence gives $omega/T$-scaling at criticality. The observed resistivity and entropy then follow directly. Several predictions to test the theory are also given.
Theoretically, it is commonly held that in metals near a nematic quantum critical point the electronic excitations become incoherent on the entire `hot Fermi surface, triggering non Fermi liquid behavior. However, such conclusions are based on electron-only theories, ignoring a symmetry-allowed coupling between the electronic nematic variable and a suitable crystalline lattice strain. Here we show that including this coupling leads to entirely different conclusions because the critical fluctuations are mostly cutoff by the non-critical lattice shear modes. At sufficiently low temperatures the thermodynamics remain Fermi liquid type, while, depending on the Fermi surface geometry, either the entire Fermi surface stays cold, or at most there are hot spots. In particular, our predictions are relevant for the iron-based superconductors.
Earlier Monte-Carlo calculations on the dissipative two-dimensional XY model are extended in several directions. We study the phase diagram and the correlation functions when dissipation is very small, where it has properties of the classical 3D-XY transition, i.e. one with a dynamical critical exponent $z=1$. The transition changes from $z=1$ to the class of criticality with $z to infty$ driven by topological defects, discovered earlier, beyond a critical dissipation. We also find that the critical correlations have power-law singularities as a function of tuning the ratio of the kinetic energy to the potential energy for fixed large dissipation, as opposed to essential singularities on tuning dissipation keeping the former fixed. A phase with temporal disorder but spatial order of the Kosterlitz-Thouless form is also further investigated. We also present results for the transition when the allowed Caldeira-Leggett form of dissipation and the allowed form of dissipation coupling to the compact rotor variables are both included. The nature of the transition is then determined by the Caldeira-Leggett form.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
