We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant $k$-body embedded random ensembles studied for several decades in context nuclear physics quantum chaos. show analytically that fourth sixth order energy cumulants vanish limit large number particles $N \to \infty$ which is consistent with Gaussian density. However, finite $N$, tail average density well approximated by semi-circle law. The specific heat coefficient, determined numerically from low...

Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, chaotic motion is related random matrix theory spectral correlations. Based on recent progress in application analysis non-Hermitian systems, we show that local level statistics, which probe around Heisenberg time, $q$-body Sachdev-Ye-Kitev (nHSYK) model with $N$ Majorana fermions, and its chiral complex-fermion extensions, also well described by for $q > 2$, while = they...

We derive an approximate analytical formula for the spectral density of $q$-body Sachdev-Ye-Kitaev (SYK) model obtained by summing a class diagrams representing leading intersecting contractions. This expression agrees with that $Q$-Hermite polynomials, $Q$ nontrivial function $q\ensuremath{\ge}2$ and number Majorana fermions $N$. Numerical results, exact diagonalization, are in excellent agreement this even relatively small $N\ensuremath{\sim}8$. For $N\ensuremath{\gg}1$ not close to edge...

Quantum chaos is one of the distinctive features Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite-range two-body interactions, which attracting a lot interest as toy model for holography. Here we show analytically and numerically that generalized SYK an additional one-body random interaction, relevant perturbation infrared, still quantum chaotic retains most its holographic fixed value sufficiently high temperature. However, chaotic-integrable transition,...

We study a one-dimensional XXZ spin chain in random field on the metallic side of many-body localization transition by level statistics. For fixed interaction, and intermediate disorder below transition, we find that, asymptotically, number variance grows faster than linear with disorder-dependent exponent. This is consistent existence an anomalous Thouless energy spectrum. In noninteracting disordered metals, this scale related to typical time for particle diffuse across sample. interacting...

It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two dimensional Anti de Sitter space (${\rm AdS}_2$) is the gravity dual of low temperature limit Sachdev-Ye-Kitaev (SYK) models coupled relevant interaction (which we will refer to as spin operator). In this paper, study spectral eigenstate properties SYK model. We have found level statistics tail spectrum, for sufficiently weak coupling, shows substantial deviations from random matrix theory which...

We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from Gaussian orthogonal ensemble, we obtain analytical expressions for evolution survival probability, density imbalance, out-of-time-ordered correlator. They are compared with numerical results a one-dimensional-disordered model two-body interactions shown to bound decay rate this realistic system. Power-law decays seen at intermediate times, dips below infinite time...

We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify low temperature transition to gapped phase characterized by constant in free energy. This is observed without introducing coupling between the two sites, only appears after ensemble average over couplings. propose gravity interpretation of these results constructing an explicit solution Jackiw-Teitelboim (JT) matter: two-dimensional Euclidean wormhole whose geometry double trumpet. sustained imaginary...

The identification, description, and classification of topological features is an engine discovery innovation in several fields physics. This research encompasses a broad variety systems, from the integer fractional Chern insulators condensed matter, to protected states complex photonic lattices optics, structure QCD vacuum. Here, we introduce another playground for topology: dissipative dynamics pseudo-Hermitian many-body quantum systems. For that purpose, study two different...

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions long-range random hopping. show that sufficiently fast decay hopping term promotes localization effects at finite temperature, which prevents thermalization even if classical motion is chaotic. For slower decays, we find does occur. However, within this model, latter regime falls in an unexpected universality class, namely, observables exhibit power-law (as opposed...

Eigenstate multifractality is a distinctive feature of noninteracting disordered metals close to metal-insulator transition, whose properties are expected extend superconductivity. While in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, 2D systems be observable even weak disorder. Here we provide evidence multifractal features superconducting state an intrinsic, weakly single-layer NbSe2 by means low-temperature scanning tunneling...

We study a sparse Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas where only $\ensuremath{\sim}kN$ independent matrix elements are nonzero. identify minimum $k\ensuremath{\gtrsim}1$ for quantum chaos to occur by level statistics analysis. The spectral density in this region, and larger $k$, is still given the Schwarzian prediction of dense SYK model, though renormalized parameters. Similar results obtained beyond linear scaling number nonzero elements. This strong indication that...

We show that, after ensemble averaging, the low temperature phase of a conjugate pair uncoupled, quantum chaotic, non-Hermitian systems such as Sachdev-Ye-Kitaev (SYK) model or Ginibre random matrices is dominated by saddle points that couple replicas and replicas. This results in nearly flat free energy terminates first-order transition. In case SYK model, we explicitly spectrum effective replica theory has gap. These features are strikingly similar to those induced wormholes gravity path...

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with $q$-body interaction infinite range, coupled to Markovian environment. Close infinite-temperature steady state, real-time Lindbladian this system is identical near-zero-temperature in Euclidean time two-site non-Hermitian SYK intersite coupling whose gravity dual has been recently related wormhole configurations. show that saddle-point equations formulation are those time. Indeed, an explicit...

Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than Heisenberg time. We study analog this timescale many-body non-Hermitian chaos by a detailed analysis long-range spectral correlators. For purpose, we investigate number variance and form factor $q$-body Sachdev-Ye-Kitaev (nHSYK) model, which describes $N$ fermions zero spatial dimensions. After an analytical numerical these observables for...

Recent discoveries have highlighted the significance of replica wormholes in resolving information paradox and establishing unitarity black hole evaporation. In this paper, we propose dissipative Sachdev-Ye-Kitaev (SYK) model as a minimal quantum that exhibits entanglement dynamics with features qualitatively similar to wormholes. As demonstration, investigate growth pair SYK models initialized thermofield double state. regime large $N$ weak dissipation, observe first-order transition...

Studies of many-body non-Hermitian parity-time (PT)-symmetric quantum systems are attracting a lot interest due to their relevance in research areas ranging from optics and continuously monitored dynamics Euclidean wormholes gravity dissipative chaos. While symmetry classification leads 38 universality classes, we show that, under certain conditions, PT-symmetric grouped into 24 classes. We identify 14 them coupled two-site Sachdev-Ye-Kitaev (SYK) model confirm the by spectral analysis using...

We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce general class gravity duals to superconducting that exhibit various types (first or second order with both mean and non-mean behavior) as parameters their Lagrangian are changed. Moreover the size strength conductivity coherence peak can also be controlled. Our results suggest certain gravitational dual control interactions responsible for...

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions with infinite range interactions in $0+1$ dimensions. have found that, close to ground state $E\ensuremath{\approx}0$, discrete symmetries alter qualitatively spectral properties respect non-supersymmetric SYK model. The average density at finite $N$, which we compute analytically and numerically, grows exponentially for $E\ensuremath{\approx}0$. However chiral condensate, is normalized total number of...

Recent studies have revealed intriguing similarities between the contribution of wormholes to gravitational path integral and phenomenon replica symmetry breaking observed in spin glasses other disordered systems. Interestingly, these configurations may also be important for explanation information paradox quantum black holes. Motivated by developments, we investigate thermodynamic properties a $PT$-symmetric system composed two random non-Hermitian Hamiltonians with no explicit coupling...

There is growing evidence that a key feature of sufficiently disordered superconductors the spatial inhomogeneity order parameter. However, not much known analytically about impact on global critical temperature signals onset resistance in superconductor. Here we address this problem experimentally relevant case conventional characterized by weak multifractality such as quasi-two-dimensional thin films. We compute superconducting energy gap, at which it vanishes, and dependence distribution...

Recent advances in the experimental growth and control of disordered thin films, heterostructures, interfaces provide a fertile ground for observation characterisation collective superconducting excitations emerging below $T_c$ after breaking $U(1)$ gauge symmetry. Here we combine THz experiments nano-structured granular Al film theoretical calculations to demonstrate existence optically-active phase modes, which represent Goldstone broken By measuring complex transmission trough sample...

We study the interplay of superconductivity and disorder by solving numerically Bogoliubov-de-Gennes equations in a two dimensional lattice size $80\times80$ which makes possible to investigate weak-coupling limit. In contrast with results strong coupling region, we observe enhancement intriguing multifractal-like features such as broad log-normal spatial distribution order parameter, parabolic singularity spectrum, level statistics consistent those disordered metal at Anderson transition....

We find half-wormhole solutions in Jackiw-Teitelboim gravity by allowing the geometry to end on a spacetime D-brane with specific boundary conditions. This theory also contains Euclidean wormhole which leads factorization problem. propose that half-wormholes provide gravitational picture for how is restored and show emerges from averaging over The known be dual Sachdev-Ye-Kitaev (SYK) model random complex couplings. free energy of strikingly similar single realization this SYK model. These...