Elena Lanina

Bio: Elena Lanina is an academic researcher from Moscow Institute of Physics and Technology. The author has contributed to research in topics: Saddle point & Extrapolation. The author has an hindex of 1, co-authored 2 publications receiving 7 citations.

Spectral form factor in the double-scaled SYK model

Abstract: In this note we study the spectral form factor in the SYK model in large q limit at infinite temperature. We construct analytic solutions for the saddle point equations that describe the slope and the ramp regions of the spectral form factor time dependence. These saddle points are obtained by taking different approaches to the large q limit: the slope region is described by a replica-diagonal solution and the ramp region is described by a replica-nondiagonal solution. We find that the onset of the ramp behavior happens at the Thouless time of order q log q. We also evaluate the one-loop corrections to the slope and ramp solutions for late times, and study the transition from the slope to the ramp. We show this transition is accompanied by the breakdown of the perturbative 1/q expansion, and that the Thouless time is defined by the consistency of extrapolation of this expansion to late times.

Spectral form factor in the double-scaled SYK model.

Abstract: In this note we study the spectral form factor in the SYK model in large $q$ limit at infinite temperature. We construct analytic solutions for the saddle point equations that describe the slope and the ramp regions of the spectral form factor time dependence. These saddle points are obtained by taking different approaches to the large $q$ limit: the slope region is described by a replica-diagonal solution and the ramp region is described by a replica-nondiagonal solution. We find that the onset of the ramp behavior happens at the Thouless time of order $q \log q$. We also evaluate the one-loop corrections to the slope and ramp solutions for late times, and study the transition from the slope to the ramp. We show this transition is accompanied by the breakdown of the perturbative $1/q$ expansion, and that the Thouless time is defined by the consistency of extrapolation of this expansion to late times.

Krylov complexity in large-$q$ and double-scaled SYK model

Abstract: Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The Krylov complexity naturally describes the"size"of the distribution, while the higher cumulants encode richer information. We further consider the double-scaled limit of SYK$_q$ at infinite temperature, where $q \sim \sqrt{N}$. In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge. The growth of Krylov complexity appears to be"hyperfast", which is previously conjectured to be associated with scrambling in de Sitter space.

Dynamical quantum phase transitions in SYK Lindbladians

Abstract: We study the open quantum dynamics of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Of particular interest for us is the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of the large number of fermion flavors, which is formally akin to the thermal phase transition in the twocoupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. Furthermore, we numerically show that signatures of the dynamical quantum phase transitions remain to appear even in the finite number of fermion flavors.

Multi-trace correlators in the SYK model and non-geometric wormholes

Abstract: We consider multi-energy level distributions in the SYK model, and in particular, the role of global fluctuations in the density of states of the SYK model. The connected contributions to the moments of the density of states go to zero as N → ∞, however, they are much larger than the standard RMT correlations. We provide a diagrammatic description of the leading behavior of these connected moments, showing that the dominant diagrams are given by 1PI cactus graphs, and derive a vector model of the couplings which reproduces these results. We generalize these results to the first subleading corrections, and to fluctuations of correlation functions. In either case, the new set of correlations between traces (i.e. between boundaries) are not associated with, and are much larger than, the ones given by topological wormholes. The connected contributions that we discuss are the beginning of an infinite series of terms, associated with more and more information about the ensemble of couplings, which hints towards the dual of a single realization. In particular, we suggest that incorporating them in the gravity description requires the introduction of new, lighter and lighter, fields in the bulk with fluctuating boundary couplings.

From operator statistics to wormholes

Abstract: For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper, we analyze the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit, which is controlled by nonuniversal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described by Altland and Sonner [SciPost Phys. 11, 034 (2021)] with added operator sources, whose leading nontrivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behavior of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave functions. Furthermore, we capture analytically the plateau behavior by taking into account the contribution of a second saddle point. Our main interest is quantum many-body systems with holographic duals, and we explicitly establish the validity of the EFT description in the Sachdev-Ye-Kitaev class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector, we get a detailed understanding of how the ergodic EFT phase is approached, and we derive the relevant Thouless timescales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby universes.

Quantum Quench of the Sachdev-Ye-Kitaev Model

Abstract: We describe the non-equilibrium dynamics of the Sachdev-Ye-Kitaev models of fermions with all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that the final state is thermal, and their numerical analysis appears consistent with a thermalization rate proportional to the absolute temperature of the final state. We also obtain an exact analytic solution of the non-equilibrium dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the fermion Green's function is instantaneous.