arXiv subjects

Sean A. Hartnoll

Publications and source records attributed to Sean A. Hartnoll.

At least 37 records · Page 2Linked to original sources

arXiv2021

Entanglement in the Quantum Hall Matrix Model

Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged $U(N)$ matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain 'off-diagonal' matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk 'area law' contribution to the entanglement entropy. All of these entropies are regularized by finite $N$.

hep-th↗

arXiv2021

Phonons, electrons and thermal transport in Planckian high T$_c$ materials

The room temperature thermal diffusivity of high T$_c$ materials is dominated by phonons. This allows the scattering of phonons by electrons to be discerned. We argue that the measured strength of this scattering suggests a converse Planckian scattering of electrons by phonons across the room temperature phase diagram of these materials. Consistent with this conclusion, the temperature derivative of the resistivity of strongly overdoped cuprates is noted to show a kink at a little below 200 K that we argue should be understood as the onset of a high temperature Planckian $T$-linear scattering of electrons by classical phonons. This kink continuously disappears towards optimal doping, even while strong scattering of phonons by electrons remains visible in the thermal diffusivity, sharpening the long-standing puzzle of the lack of a feature in the $T$-linear resistivity at optimal doping associated to onset of phonon scattering.

cond-mat.str-el↗

arXiv2021

Diving into a holographic superconductor

Charged black holes in anti-de Sitter space become unstable to forming charged scalar hair at low temperatures $T < T_\text{c}$. This phenomenon is a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior. The spacetime ends at a spacelike Kasner singularity, and there is no Cauchy horizon. Before reaching the singularity, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible 'Kasner inversions' in which after many e-folds of expansion, the Einstein-Rosen bridge contracts towards the singularity. Due to the Josephson oscillations, the number of Kasner inversions depends very sensitively on $T$, and diverges at a discrete set of temperatures $\{T_n\}$ that accumulate at $T_c$. Near these $T_n$, the final Kasner exponent exhibits fractal-like behavior.

hep-th↗

arXiv2020

Gravitational duals to the grand canonical ensemble abhor Cauchy horizons

The gravitational dual to the grand canonical ensemble of a large $N$ holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordström-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.

hep-th↗

arXiv2020

Bootstrapping Matrix Quantum Mechanics

Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap' methodology. In this approach, operator expectation values are related by symmetries -- such as time translation and $SU(N)$ gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large $N$ single matrix quantum mechanics. Finally, we present new results on the ground state of large $N$ two matrix quantum mechanics.

hep-th↗

arXiv2020

Theory of the Strange Metal Sr$_3$Ru$_2$O$_7$

The bilayer perovskite Sr$_3$Ru$_2$O$_7$ has been widely studied as a canonical strange metal. It exhibits $T$-linear resistivity and a $T\log(1/T)$ electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in `hot' Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, `cold' Fermi surfaces scatter into one hot and one cold electron renders the ostensibly non-critical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a two-dimensional van Hove singularity explains the anomalous transport observed in strained Sr$_2$RuO$_4$.

cond-mat.str-el↗

arXiv2020

Holographic flows from CFT to the Kasner universe

The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific non-analytic corrections to the thermal correlation functions of heavy operators in the dual CFT, in the analytically continued `near-singularity' regime.

hep-th↗

arXiv2020

Deep Quantum Geometry of Matrices

We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to search for gauge invariant low energy states. The ground state, and also long-lived metastable states, of an $\mathrm{SU}(N)$ matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric `mini-BMN' extension, are studied as a function of coupling and $N$. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wavefunction. We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large $N$ limit.

hep-th↗

arXiv2019

Theory of diffusive fluctuations

The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of non-linear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point half way to the diffusive pole, at frequency $ω= -\frac{i}{2}Dk^2$. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

hep-th↗

arXiv2019

On the Planckian bound for heat diffusion in insulators

High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $τ\gtrsim τ_\text{Pl} \equiv \hbar/(k_B T)$, despite phonon dynamics being entirely classical at these temperatures. We argue that this Planckian bound is due to a quantum mechanical bound on the sound velocity: $v_s < v_M$. The `melting velocity' $v_M$ is defined in terms of the melting temperature of the crystal, the interatomic spacing and Planck's constant. We show that for several classes of insulating crystals, both simple and complex, $τ/τ_\text{Pl} \approx v_M/v_s$ at high temperatures. The velocity bound therefore implies the Planckian bound.

cond-mat.mtrl-sci↗

arXiv2019

Topological order in matrix Ising models

We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single `spherical' constraint. In this way we generalize the results of [1] to a wide class of Ising Hamiltonians with $O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z})$ symmetry. The models can undergo topological large $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix $S_{aB}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

hep-th↗

arXiv2019

Quantum Scrambling and State Dependence of the Butterfly Velocity

Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.

hep-th↗

arXiv2019

Theory of the collective magnetophonon resonance and melting of the field-induced Wigner solid

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.

cond-mat.mes-hall↗

arXiv2018

Locality Bound for Dissipative Quantum Transport

We prove an upper bound on the diffusivity of a general local and translation invariant quantum Markovian spin system: $D \leq D_0 + \left(α\, v_\text{LR} τ+ β\, ξ\right) v_\text{C}$. Here $v_\text{LR}$ is the Lieb-Robinson velocity, $v_\text{C}$ is a velocity defined by the current operator, $τ$ is the decoherence time, $ξ$ is the range of interactions, $D_0$ is a microscopically determined diffusivity and $α$ and $β$ are precisely defined dimensionless coefficients. The bound constrains quantum transport by quantities that can either be obtained from the microscopic interactions ($D_0, v_\text{LR}, v_\text{C},ξ$) or else determined from independent local non-transport measurements ($τ,α,β$). We illustrate the general result with the case of a spin half XXZ chain with on-site dephasing. Our result generalizes the Lieb-Robinson bound to constrain the sub-ballistic diffusion of conserved densities in a dissipative setting.

quant-ph↗

arXiv2018

Bad metallic transport in a modified Hubbard model

Strongly correlated metals often display anomalous transport, including $T$-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for such bad metals, by supplementing the well-known Hubbard model --- with hopping $t$ and on-site repulsion $U$ --- with a `screened Coulomb' interaction between charge densities that decays exponentially with spatial separation. This interaction entirely lifts the extensive degeneracy in the spectrum of the $t=0$ Hubbard model, allowing us to fully characterize the small $t$ electric, thermal and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe $T$-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Weidemann-Franz law and a large thermopower that can undergo sign change. At intermediate temperatures $t \ll k_B T \lesssim U$, the approximate $T$-linear resistivity arises from a cancellation between the nontrivial temperature dependence of both diffusivities and thermodynamic susceptibilities, as observed in recent transport experiments on cold atomic gases.

cond-mat.str-el↗

arXiv2018

Thermalization, Viscosity and the Averaged Null Energy Condition

We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size `fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.

hep-th↗

arXiv2018

Holographic quantum matter

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

hep-th↗

arXiv2018

Theory of the supercyclotron resonance and Hall response in anomalous 2d metals

Weakly disordered superconducting films can be driven into an anomalous low temperature resistive state upon applying a magnetic field. Recent experiments on weakly disordered amorphous InO$_x$ have established that both the Hall resistivity and the frequency of a cyclotron-like resonance in the anomalous metal are highly suppressed relative to the values expected for a conventional metal. We show that both of these observations can be understood from the flux flow dynamics of vortices in a superconductor with significant vortex pinning. Results for flux flow transport are obtained using a systematic hydrodynamic expansion, controlled by the diluteness of mobile vortices at low temperatures. Hydrodynamic transport coefficients are related to microscopics through Kubo formulae for the longitudinal and Hall vortex conductivities, as well as a `vorto-electric' conductivity.

cond-mat.supr-con↗