Debanjan Chowdhury

Slow scrambling in disordered quantum systems

Recent work has studied the growth of commutators as a probe of chaos and information scrambling in quantum many-body systems. In this work we study the effect of static disorder on the growth of commutators in a variety of contexts. We find generically that disorder slows the onset of scrambling, and, in the case of a many-body localized state, partially halts it. We access the many-body localized state using a standard fixed point Hamiltonian, and we show that operators exhibit slow logarithmic growth under time evolution. We compare the result with the expected growth of commutators in both localized and delocalized non-interacting disordered models. Finally, based on a scaling argument, we state a conjecture about the effect of weak interactions on the growth of commutators in an interacting diffusive metal.

Multipoint correlators of conformal field theories: implications for quantum critical transport

We compute three-point correlators between the stress-energy tensor and con- served currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an e↵ective action on 3+1 dimensional anti-de Sitter space (AdS4), and depend upon the co-ecient, , of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of . The CFTs of free fermions and bosons take the values =1 /12,1/12 respectively, and so saturate the bound | | 1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of . The value of also controls the fre- quency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of lead to an appealing physical inter- pretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics. This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

Quantum Butterfly Effect in Weakly Interacting Diffusive Metals

We 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

Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice

z > 1

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

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Density-wave instabilities of fractionalized Fermi liquids

A quantum spin liquid is a spin state with no magnetic order even at the lowest temperatures. To explain neutron scattering data on a ‘kagome lattice’ antiferromagnet, visons (elementary excitations of vortices) must be included, in addition to the usual fractionalized spinons.

Mixed-valence insulators with neutral Fermi surfaces

The nature of the pseudogap regime of cuprate superconductors at low hole density remains unresolved. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low-energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge-density wave order at intermediate temperatures and quantum oscillations at high magnetic fields and low temperatures. Here we show that a model of competing charge-density wave and superconducting orders provides a unified description of the intermediate and low-temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero-field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge-density and superconducting orders. Our results are compatible with experimental trends.

Feedback of superconducting fluctuations on charge order in the underdoped cuprates

Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic correlations, where the electronic excitations are coupled to the fractionalized excitations of a quantum fluctuating antiferromagnet on the square lattice. The resulting charge density wave state emerging out of such a fractionalized Fermi-liquid (FL*) has wavevectors of the form

Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models

(\pm Q_0,0), (0,\pm Q_0)

Singularity of the London penetration depth at quantum critical points in superconductors.

, with a predominantly