arXiv:2004.03617 · Physical Review Research

Strongly coupled quantum phonon fluid in a solvable model

Evyatar Tulipman, Erez Berg

Published Sep 17, 2020• 19 citations

Abstract

This work studies a solvable model of strongly coupled phonons that can be viewed as a bosonic variant of the Sachdev-Ye-Kitaev model. In addition to the high-temperature classical and low-temperature semiclassical regimes, the authors show that the model have an intermediate-temperature `Planckian' regime where the quasiparticle picture fails as the phonon lifetime is of the order of the Planckian time scale.

DOI: 10.1103/physrevresearch.2.033431

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arXiv:2004.03617 · Physical Review Research

Strongly coupled quantum phonon fluid in a solvable model

Evyatar Tulipman, Erez Berg

Published Sep 17, 2020• 19 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.033431

Related papers

Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model

Hossein Hosseinabadi, Shane P. Kelly, Jörg Schmalian +1 more

We study thermalization dynamics in a fermion-phonon variant of the Sachdev-Ye-Kitaev model coupled to an external cold thermal bath of harmonic oscillators. We find that quantum critical fermions thermalize more efficiently than phonons, in sharp contrast to the behavior in the Fermi liquid regime. In addition, after a short prethermal stage, the system acquires a quasithermal distribution given by a time-dependent effective temperature, reminiscent of ``hydrodynamic'' relaxation. All physical observables relax at the same rate which scales with the final temperature through an exponent that depends universally on the low-energy spectrum of the system and the bath. Such relaxation rate is derived using a hydrodynamic approximation in full agreement with the numerical solution of a set quantum kinetic equations derived from the Keldysh formalism for nonequilibrium Green's functions. Our results hint toward further research on the applicability of the hydrodynamic picture in the description of the late time dynamics of open quantum systems despite the absence of conserved quantities in regimes dominated by conserving collisions.We study thermalization dynamics in a fermion-phonon variant of the Sachdev-Ye-Kitaev model coupled to an external cold thermal bath of harmonic oscillators. We find that quantum critical fermions thermalize more efficiently than phonons, in sharp contrast to the behavior in the Fermi liquid regime. In addition, after a short prethermal stage, the system acquires a quasithermal distribution given by a time-dependent effective temperature, reminiscent of ``hydrodynamic'' relaxation. All physical observables relax at the same rate which scales with the final temperature through an exponent that depends universally on the low-energy spectrum of the system and the bath. Such relaxation rate is derived using a hydrodynamic approximation in full agreement with the numerical solution of a set quantum kinetic equations derived from the Keldysh formalism for nonequilibrium Green's functions. Our results hint toward further research on the applicability of the hydrodynamic picture in the description of the late time dynamics of open quantum systems despite the absence of conserved quantities in regimes dominated by conserving collisions.

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We study properties of thermal transport and quantum many-body chaos in a lattice model with

N\to\infty

oscillators per site, coupled by strong nonlinear terms. We first consider a model with only optical phonons. We find that the thermal diffusivity

D_{\rm th}

and chaos diffusivity

D_L

(defined as

D_L = v_B^2/ \lambda_L

, where

v_B

and

\lambda_L

are the butterfly velocity and the scrambling rate, respectively) satisfy

D_{\rm th} \approx \gamma D_L

with

\gamma\gtrsim 1

. At intermediate temperatures, the model exhibits a ``quantum phonon fluid'' regime, where both diffusivities satisfy

D^{-1} \propto T

, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale

\hbar/k_B T

. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstone's theorem. As a result, for

d=1,2

, we find that

D_{\rm th}/D_L\to \infty

, while for

d=3

D_{\rm th}

and

D_{L}

remain comparable.

{D}_{\mathrm{th}}

and chaos diffusivity

{D}_{L}

(defined as ${D}_{L}={v}_{B}^{2}/{\ensuremath{\lambda}}_{L}$, where

{v}_{B}

and ${\ensuremath{\lambda}}_{L}$ are the butterfly velocity and the scrambling rate, respectively) satisfy ${D}_{\mathrm{th}}\ensuremath{\approx}\ensuremath{\gamma}{D}_{L}$ with $\ensuremath{\gamma}\ensuremath{\gtrsim}1$. At intermediate temperatures, the model exhibits a quantum ``phonon fluid'' regime, where both diffusivities satisfy ${D}^{\ensuremath{-}1}\ensuremath{\propto}T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $\ensuremath{\hbar}/{k}_{B}T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The long-wavelength acoustic modes remain long-lived even when the system is strongly coupled, due to Goldstone's theorem. As a result, for

d=1,2

, we find that ${D}_{\mathrm{th}}/{D}_{L}\ensuremath{\rightarrow}\ensuremath{\infty}$, while for

d=3, {D}_{\mathrm{th}}

and

{D}_{L}

remain comparable.

\\mathcal{N}=2

theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable

t

J

model of electrons with an SYK-like form. We find a

\\mathbb{Z}_2

fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.