Person: Patel, Aavishkar
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Patel
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Aavishkar
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Patel, Aavishkar
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Publication Quantum Butterfly Effect in Weakly Interacting Diffusive Metals(American Physical Society (APS), 2017-09-14) Patel, Aavishkar; Chowdhury, Debanjan; Sachdev, Subir; Swingle, BrianWe study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron-field operators inherits a light-cone-like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent z>1.Publication Hyperscaling at the spin density wave quantum critical point in two-dimensional metals(American Physical Society (APS), 2015) Patel, Aavishkar; Strack, Philipp; Sachdev, SubirThe hyperscaling property implies that spatially isotropic critical quantum states in d spatial dimensions have a specific heat which scales with temperature as Td/z, and an optical conductivity which scales with frequency as ω(d−2)/z for ω ≫ T, where z is the dynamic critical exponent. We examine the spin-density wave critical fixed point of metals in d = 2 found by Sur and Lee (Phys. Rev. B 91, 125136 (2015)) in an expansion in ϵ = 3 − d. We find that the contributions of the “hot spots” on the Fermi surface to the optical conductivity and specific heat obey hyperscaling (up to logarithms), and agree with the results of the large N analysis of the optical conductivity by Hartnoll et al. (Phys. Rev. 84, 125115 (2011)). With a small bare velocity of the boson associated with the spin density wave order, there is an intermediate energy regime where hyperscaling is violated with d → dt, where dt = 1 is the number of dimensions transverse to the Fermi surface. We also present a Boltzmann equation analysis which indicates that the hot spot contribution to the DC conductivity has the same scaling as the optical conductivity, with T replacing ω.Publication Confinement transition to density wave order in metallic doped spin liquids(American Physical Society (APS), 2016) Patel, Aavishkar; Chowdhury, Debanjan; Allais, Andrea; Sachdev, SubirInsulating quantum spin liquids can undergo a confinement transition to a valence bond solid via the condensation of topological excitations of the associated gauge theory. We extend the theory of such transitions to fractionalized Fermi liquids (FL*): these are metallic doped spin liquids in which the Fermi surfaces only have gauge neutral quasiparticles. Using insights from a duality transform on a doped quantum dimer model for the U(1)-FL* state, we show that projective symmetry group of the theory of the topological excitations remains unmodified, but the Fermi surfaces can lead to additional frustrating interactions. We propose a theory for the confinement transition of Z2-FL* states via the condensation of visons. A variety of confining, incommensurate density wave states are possible, including some that are similar to the incommensurate d-form factor density wave order observed in several recent experiments on the cuprate superconductors.Publication DC resistivity at the onset of spin density wave order in two-dimensional metals(American Physical Society (APS), 2014) Patel, Aavishkar; Sachdev, SubirThe theory for the onset of spin density wave order in a metal in two dimensions flows to strong coupling, with strong interactions not only at the “hot spots,” but on the entire Fermi surface. We advocate the computation of dc transport in a regime where there is rapid relaxation to local equilibrium around the Fermi surface by processes which conserve total momentum. The dc resistivity is then controlled by weaker perturbations which do not conserve momentum. We consider variations in the local position of the quantum-critical point, induced by long-wavelength disorder, and find a contribution to the resistivity which is linear in temperature (up to logarithmic corrections) at low temperature. Scattering of fermions between hot spots, by short-wavelength disorder, leads to a residual resistivity and a correction which is linear in temperature.Publication Quantum Chaos on a Critical Fermi Surface(Proceedings of the National Academy of Sciences, 2017-02-07) Patel, Aavishkar; Sachdev, SubirWe compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of N species of fermions at nonzero density coupled to a U(1) gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of N, the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.Publication Shear Viscosity at the Ising-Nematic Quantum Critical Point in Two-Dimensional Metals(American Physical Society (APS), 2017-02-15) Eberlein, Andreas; Patel, Aavishkar; Sachdev, SubirIn an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio (kB/ℏ)η/s, where η is the shear viscosity and s is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension d=2 by an expansion below d=5/2. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: η scales in the same manner as a chiral conductivity, and the ratio η/s diverges at low temperature (T) as T−2/z, where z is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.