arXiv subjects

A. V. Lunkin

Publications and source records attributed to A. V. Lunkin.

8 recordsLinked to original sources

arXiv2024

Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble

We present an analytical calculation of the local density of states correlation function $ β(ω) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $Γ_0$. We show that $β(ω\ll Γ_0) \sim W/Γ_0$ (here $W$ is width of the band) whereas $β(ω\gg Γ_0) \sim (W/Γ_0) (ω/Γ_0)^{-μ} $ where $μ$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\ggΓ_0^{-1})] \sim -(Γ_0 t)^{μ/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory.

cond-mat.dis-nn↗

arXiv2022

High-frequency transport and zero-sound in an array of SYK quantum dots

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $σ(ω,p)$ and thermal $κ(ω,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $ω\ll T$ we find the Lorenz ratio $L = κ(0,0)/Tσ(0,0)$ to be non-universal and temperature-dependent. At $ω\gg T$ the conductivity $σ(ω,p)$ contains a pole with nearly linear dispersion $ω\approx sp\sqrt{\ln\fracω{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.

cond-mat.str-el↗

arXiv2022

The butterfly effect in a Sachdev-Ye-Kitaev quantum dot system

We study the out-of-time-order correlation function (OTOC) in a lattice extension of the Sachdev-Ye-Kitaev (SYK) model with quadratic perturbations. The results obtained are valid for arbitrary time scales, both shorter and longer than the Ehrenfest time. We demonstrate that the region of well-developed chaos is separated from the weakly chaotic region by the "front region", which moves ballistically across the lattice. Front velocity is calculated for various system's parameters, for the first time for SYK-like models.

cond-mat.str-el↗

arXiv2021

Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(ω)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $ω$. We find that $W(ω)$ possesses a peak at $ω$ close to the polaron energy splitting $ω_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $ω_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.

cond-mat.str-el↗

arXiv2020

Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane

We study the SYK$_4$ model with a weak SYK$_2$ term of magnitude $Γ$ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, $J/N \ll Γ\ll J/\sqrt{N}$, fluctuations of the Schwarzian mode are suppressed, and the SYK$_4$ mean-field solution remains valid beyond the timescale $t_0 \sim N/J$ up to $t_* \sim J/Γ^2$. Out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent $2πT$, but its prefactor scales as $T$ at low temperatures $T \leq Γ$.

cond-mat.str-el↗

arXiv2018

SYK model with quadratic perturbations: the route to a non-Fermi-liquid

We study the stability of the SYK$_4$ model with a large but finite number of fermions $N$ with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK$_2$ perturbation and demonstrate the stability of the SYK$_4$ infra-red asymptotic behavior characterized by a Green function $G(τ) \propto 1/τ^{3/2} $, with respect to weak perturbation. This result is supported by exact numerical diagonalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.

cond-mat.str-el↗

arXiv2017

Perturbed Kitaev model: excitation spectrum and long-ranged spin correlations

We developed general approach to the calculation of power-law infrared asymptotics of spin-spin correlation functions in the Kitaev honeycomb model with different types of perturbations. We have shown that in order to find these correlation functions, one can perform averaging of some bilinear forms composed out of free Majorana fermions, and we presented the method for explicit calculation of these fermionic densities. We demonstrated how to derive an effective Hamiltonian for the Majorana fermions, including the effects of perturbations. For specific application of the general theory, we have studied the effect of the Dzyaloshinskii-Moriya anisotropic spin-spin interaction; we demonstrated that it leads, already in the second order over its relative magnitude $D/K$, to a power-law spin correlation functions, and calculated dynamical spin structure factor of the system. We have shown that an external magnetic field $h$ in presence of the DM interaction, opens a gap in the excitation spectrum of magnitude $Δ\propto D h$.

cond-mat.str-el↗

arXiv2016

Long-range spin correlations in a honeycomb spin model with magnetic field

We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of weak magnetic field $h\ll J$. Such a perturbation treated in the second order over $h$ leads to the power-law decay of irreducible spin correlation function $S(\mathbf{r},t)=\left\langle \left\langle s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max (t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength equal to 3 lattice constants. In the present Letter we sum main terms in all orders of the perturbation theory for the correlation function $S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in terms of the effective low-energy Hamiltonian written in terms of Majorana fermions, which in the presence of magnetic field acquire vector potential $A_x \propto h_z^2$. Correspondingly, the wave vector of the oscillations in $S(\mathbf{r},t)$ changes according to $δk \propto h_z^2$. We also compute the dynamic structure factor $S(\mathbf{p},ω)$; in the vicinity of $\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads as $S(\mathbf{p},ω)-S(\mathbf{p}_K,ω)\propto\sqrt{ω^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.

cond-mat.str-el↗