arXiv subjects

Antonio M. García-García

Publications and source records attributed to Antonio M. García-García.

At least 37 records · Page 2Linked to original sources

arXiv2023

Tuning Superinductors by Quantum Coherence Effects for Enhancing Quantum Computing

Research on spatially inhomogeneous weakly-coupled superconductors has recently received a boost of interest because of the experimental observation of a dramatic enhancement of the kinetic inductance with relatively low losses. Here, we study the kinetic inductance and the quality factor of a strongly-disordered weakly-coupled superconducting thin film. We employ a gauge-invariant random-phase approximation capable of describing collective excitations and other fluctuations. In line with the experimental findings, we have found that in the range of frequencies of interest, and for sufficiently low temperatures, an exponential increase of the kinetic inductance with disorder coexists with a still large quality factor $\sim 10^4$. More interestingly, on the metallic side of the superconductor-insulator transition, we have identified a range of frequencies and temperatures $T \sim 0.1T_c$ where quantum coherence effects induce a broad statistical distribution of the quality factor with an average value that increases with disorder. We expect these findings to further stimulate experimental research on the design and optimization of superinductors for a better performance and miniaturization of quantum devices such as qubit circuits and microwave detectors.

cond-mat.supr-con↗

arXiv2023

Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model

Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox and establishing the unitarity of black hole evaporation. In this letter, we propose the dissipative Sachdev-Ye-Kitaev model (SYK) as a minimal quantum model that exhibits entanglement dynamics with features qualitatively similar to replica wormholes. As a demonstration, we investigate the entanglement growth of a pair of dissipative SYK models initialized in a thermofield double state (TFD). In the regime of large $N$ with weak dissipation, we observe a first-order entanglement transition characterized by a switch of the dominant saddle point: from replica diagonal solutions for short times to replica wormhole-like off-diagonal solutions for long times. Furthermore, we show that signature of replica wormholes persists even at moderate $N \lesssim 30$ by using the Monte Carlo quantum trajectory method. Our work paves the way for explorations of replica wormhole physics in quantum simulators.

quant-ph↗

arXiv2023

Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to $100\times100$ where the magnetic flux is introduced by the Peierls's substitution. The substantial larger size than in previous approaches ($\leq 36\times 36$) has allowed us to identify a rich phase diagram as a function of the magnetic flux and the disorder strength. For sufficiently weak disorder, and not too strong magnetic flux, we observe a slightly distorted Abrikosov triangular vortex lattice. An increase in the magnetic flux leads to an unexpected rectangular vortex lattice. A further increase in disorder, or flux gradually destroy the lattice symmetry though strong vortex repulsion persists. An even stronger disorder leads to deformed single vortices with an inhomogeneous core. As number of vortices increases, vortices overlap becomes more frequent. Finally, we show that global phase coherence is a feature of all these phases and that disorder enhances substantially the critical magnetic flux with respect to the clean limit with a maximum on the metallic side of the insulating transition.

cond-mat.supr-con↗

arXiv2023

Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model

Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at timescales that can be much shorter than the Heisenberg time. We study the analog of this timescale in many-body non-Hermitian quantum chaos by a detailed analysis of long-range spectral correlators. For that purpose, we investigate the number variance and the spectral form factor of a non-Hermitian $q$-body Sachdev-Ye-Kitaev (nHSYK) model, which describes $N$ fermions in zero spatial dimensions. After an analytical and numerical analysis of these spectral observables for non-Hermitian random matrices, and a careful unfolding, we find good agreement with the nHSYK model for $q > 2$ starting at a timescale that decreases sharply with $q$. The source of deviation from universality, identified analytically, is ensemble fluctuations not related to the quantum dynamics. For fixed $q$ and large enough $N$, these fluctuations become dominant up until after the Heisenberg time, so that the spectral form factor is no longer useful for the study of quantum chaos. In all cases, our results point to a weakened or vanishing spectral rigidity that effectively delays the observation of full quantum ergodicity. We also show that the number variance displays nonstationary spectral correlations for both the nHSYK model and random matrices. This nonstationarity, also not related to the quantum dynamics, points to intrinsic limitations of these observables to describe the quantum chaotic motion. On the other hand, we introduce the local spectral form factor, which is shown to be stationary and not affected by collective fluctuations, and propose it as an effective diagnostic of non-Hermitian quantum chaos. For $q = 2$, we find saturation to Poisson statistics at a timescale of $\log D$, compared to a scale of $\sqrt D$ for $ q>2$, with $D $ the total number of states.

hep-th↗

arXiv2023

Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model

We study the out-of-equilibrium dynamics of a Sachdev-Ye-Kitaev (SYK) model, $N$ fermions with a $q$-body interaction of infinite range, coupled to a Markovian environment. Close to the infinite-temperature steady state, the real-time Lindbladian dynamics of this system is identical to the near-zero-temperature dynamics in Euclidean time of a two-site non-Hermitian SYK with intersite coupling whose gravity dual has been recently related to wormhole configurations. We show that the saddle-point equations in the real-time formulation are identical to those in Euclidean time. Indeed, an explicit calculation of Green's functions at low temperature, numerical for $q = 4$ and analytical for $q = 2$ and large $q$, illustrates this equivalence. Only for very strong coupling does the decay rate approach the linear dependence on the coupling characteristic of a dissipation-driven approach to the steady state. For $q > 2$, we identify a potential gravity dual of the real-time dissipative SYK model: a double-trumpet configuration in a near-de Sitter space in two dimensions with matter. This configuration, which we term a Keldysh wormhole, is responsible for a finite decay rate even in the absence of coupling to the environment.

hep-th↗

arXiv2022

Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model

We study a two-site Sachdev-Ye-Kitaev model with complex couplings and a weak inter-site interaction. At low temperatures, the system is dual to a Euclidean wormhole in Jackiw-Teitelboim gravity plus matter. Interestingly, the energy spectrum becomes real for sufficiently strong inter-site coupling despite the Hamiltonian being non-Hermitian. In gravity, this complex-to-real transition corresponds to a Euclidean-to-Lorentzian transition: a dynamical restoration of the gravitational SL(2,R) symmetry of the Lorentzian wormhole, broken to U(1) in the Euclidean wormhole. We show this by identifying an order parameter for the symmetry breaking and by matching the oscillating patterns of the Green's functions. Above the transition, the system can be continued to Lorentzian signature and is dual to an eternal traversable wormhole. Additionally, we observe a thermal phase transition from the wormhole to two black holes and provide a detailed matching of the associated physical quantities. The analysis of level statistics reveals that in a broad range of parameters the dynamics is quantum chaotic in the universality class of systems with time reversal invariance.

hep-th↗

arXiv2022

Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

Spectral correlations are a powerful tool to study the dynamics of quantum many-body systems. For Hermitian Hamiltonians, quantum chaotic motion is related to random matrix theory spectral correlations. Based on recent progress in the application of spectral analysis to non-Hermitian quantum systems, we show that local level statistics, which probe the dynamics around the Heisenberg time, of a non-Hermitian $q$-body Sachdev-Ye-Kitev (nHSYK) model with $N$ Majorana fermions, and its chiral and complex-fermion extensions, are also well described by random matrix theory for $q > 2$, while for $q = 2$, they are given by the equivalent of Poisson statistics. For that comparison, we combine exact diagonalization numerical techniques with analytical results obtained for some of the random matrix spectral observables. Moreover, depending on $q$ and $N$, we identify $19$ out of the $38$ non-Hermitian universality classes in the nHSYK model, including those corresponding to the tenfold way. In particular, we realize explicitly $14$ out of the $15$ universality classes corresponding to non-pseudo-Hermitian Hamiltonians that involve universal bulk correlations of classes ${\rm AI}^\dagger$ and ${\rm AII}^\dagger$, beyond the Ginibre ensembles. These results provide strong evidence of striking universal features in non-unitary many-body quantum chaos, which in all cases can be captured by nHSYK models with $q > 2$.

hep-th↗

arXiv2022

Half-wormholes in nearly AdS$_2$ holography

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 a Euclidean wormhole which leads to a factorization problem. We propose that half-wormholes provide a gravitational picture for how factorization is restored and show that the Euclidean wormhole emerges from averaging over the boundary conditions. The wormhole is known to be dual to a Sachdev-Ye-Kitaev (SYK) model with random complex couplings. We find that the free energy of the half-wormhole is strikingly similar to that of a single realization of this SYK model. These results suggest that the gravitational path integral computes an average over spacetime D-brane boundary conditions.

hep-th↗

arXiv2022

Replica Symmetry Breaking in Random Non-Hermitian Systems

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a $PT$-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature-independent in the low-temperature phase. The SYK model has a similar behavior for sufficiently low temperature, then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling Left and Right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit.

hep-th↗

arXiv2021

$Q$-Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model

We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two $\hat{q}$-body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the Hermitian conjugate of the other, living in off-diagonal blocks of a larger WSYK Hamiltonian. The spectrum is positive with a hard edge at zero energy. We employ diagrammatic and combinatorial techniques to compute analytically the low-order moments of the Hamiltonian. In the limit of large number $N$ of Majoranas, we have found striking similarities with the moments of the weight function of the Al-Salam-Chihara $Q$-Laguerre polynomials. For $\hat{q} = 3, 4$, the $Q$-Laguerre prediction, with $Q=Q(\hat{q},N)$ also computed analytically, agrees well with exact diagonalization results for $30 < N \leq 34$ while we observe some deviations for $\hat q = 2$. The most salient feature of the spectral density is that, for odd $\hat{q}$, low-energy excitations grow as a stretched exponential, with a functional form different from that of the supersymmetric SYK model. For $\hat q = 4$, a detailed analysis of level statistics reveals quantum chaotic dynamics even for time scales substantially shorter than the Heisenberg time. More specifically, the spacing ratios in the bulk of the spectrum and the microscopic spectral density and the number variance close to the hard edge are very well approximated by that of an ensemble of random matrices that, depending on $N$, belong to the chiral or superconducting universality classes. In particular, we report the first realization of level statistics belonging to the chGUE universality class, which completes the tenfold-way classification in the SYK model.

hep-th↗

arXiv2021

Characterization of collective excitations in weakly-coupled disordered superconductors

Isolated islands in two-dimensional strongly-disordered and strongly-coupled superconductors become optically active inducing sub-gap collective excitations in the ac conductivity. Here, we investigate the fate of these excitations as a function of the disorder strength in the experimentally relevant case of weak electron-phonon coupling. An explicit calculation of the ac conductivity, that includes vertex corrections to restore gauge symmetry, reveals the existence of collective sub-gap excitations, related to phase fluctuations and therefore identified as the Goldstone modes, for intermediate to strong disorder. As disorder increases, the shape of the sub-gap excitation transits from peaked close to the spectral gap to a broader distribution reaching much smaller frequencies. Phase-coherence still holds in part of this disorder regime. The requirement to observe sub-gap excitations is not the existence of isolated islands acting as nano-antennas but rather the combination of a sufficiently inhomogeneous order parameter with a phase fluctuation correlation length smaller than the system size. Our results indicate that, by tuning disorder, the Goldstone mode may be observed experimentally in metallic superconductors based for instance on Al, Sn, Pb or Nb.

cond-mat.supr-con↗

arXiv2021

Reply to Comment on "Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model"

In a recent comment to the paper Chaotic Integrable transition in the SYK model, it was claimed that, in a certain region of parameters, the Lyapunov exponent of the N Majoranas Sachdev-Ye-Kitaev model with a quadratic perturbation, is always positive. This implies that the model is quantum chaotic. In this reply, we show that the employed perturbative formalism breaks down precisely in the range of parameters investigated in the comment due to a lack of separation of time scales. Moreover, based on recent analytical results, we show that for any large and fixed N, the model has indeed a chaotic-integrable transition that invalidate the results of the comment.

cond-mat.str-el↗

arXiv2021

Replica Symmetry Breaking and Phase Transitions in a PT Symmetric Sachdev-Ye-Kitaev Model

We show that the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, nonhermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices are dominated by replica symmetry breaking configurations with a nearly flat free energy that terminates in a first order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relation between both configurations. For a non-chaotic SYK, the results are qualitatively different: the spectrum is gapless in the low temperature phase and there is an infinite number of second order phase transitions unrelated to the restoration of replica symmetry.

hep-th↗

arXiv2021

Euclidean wormhole in the SYK model

We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify a low temperature transition to a gapped phase characterized by a constant in temperature free energy. This transition is observed without introducing a coupling between the two sites, and only appears after ensemble average over the complex couplings. We propose a gravity interpretation of these results by constructing an explicit solution of Jackiw-Teitelboim (JT) gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the double trumpet. This solution is sustained by imaginary sources for a marginal operator, without the need of a coupling between the two boundaries. As the temperature is decreased, there is a transition from a disconnected phase with two black holes to the connected wormhole phase, in qualitative agreement with the SYK observation. The expectation value of the marginal operator is an order parameter for this transition. This illustrates in a concrete setup how a Euclidean wormhole can arise from an average over field theory couplings.

hep-th↗

arXiv2020

Superconductivity at the three-dimensional Anderson metal-insulator transition

We study a disordered weakly-coupled superconductor around the Anderson transition by solving numerically the Bogoliubov-de Gennes (BdG) equations in a three dimensional lattice of size up to $20\times20\times20$ in the presence of a random potential. The spatial average of the order parameter is moderately enhanced as disorder approaches the transition but decreases sharply in the insulating region. The spatial distribution of the order parameter is sensitive to the disorder strength: for intermediate disorders below the transition, we already observe a highly asymmetric distribution with an exponential tail. Around the transition, it is well described by a log-normal distribution and a parabolic singularity spectrum. These features are typical of a multifractal measure. We determine quantitatively the critical disorder at which the insulator transition occurs by an analysis of level statistics in the spectral region that contributes to the formation of the order parameter. Interestingly, spectral correlations at the transition are similar to those found in non-interacting disordered systems at the Anderson transition. A percolation analysis suggests that the loss of phase coherence may occur around the critical disorder.

cond-mat.supr-con↗

arXiv2020

Phase diagram of a two-site coupled complex Sachdev-Ye-Kitaev model

We study the thermodynamic properties of a two-site coupled complex Sachdev-Ye-Kitaev (SYK) model in the large $N$ limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential, and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped and, for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is good indicator to study the phase diagram of the model: it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with $SL(2,R)\times U(1)$ symmetry with an additional potential and a extra degree of freedom related to the charge. In the large $N$ limit, results from this low energy action are consistent with those from the solution of the SD equations. Our findings are a preliminary step towards the characterization of traversable wormholes by its field theory dual, a strongly interacting fermionic system with charger, that is easier to model experimentally.

hep-th↗

arXiv2020

Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals

We study a sparse Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas where only $\sim k N$ independent matrix elements are non-zero. We identify a minimum $k \gtrsim 1$ for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger $k$, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with $N$ of the number of non-zero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading $1/d$ correction of Parisi's U(1) lattice gauge theory in a $d$ dimensional hypercube. In the $k \to 1$ limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed $N$ can be in any universality class of the ten-fold way. The agreement with random matrix statistics is restricted to short range correlations, no more than a few level spacings, in particular in the tail of the spectrum. In addition, emergent discrete global symmetries in most of the disorder realizations for $k$ slightly below one give rise to $2^m$-fold degenerate spectra, with $m$ being a positive integer. For $k =3/4$, we observe a large number of such emergent global symmetries with a maximum $2^8$-fold degenerate spectra for $N = 26$.

hep-th↗

arXiv2020

Visualization of multifractal superconductivity in a two-dimensional transition metal dichalcogenide in the weak-disorder regime

Eigenstate multifractality is a distinctive feature of non-interacting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic weakly disordered single-layer NbSe$_2$ by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. Spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f($α$) shows anomalous scaling behavior typical from 2D weakly disordered systems.

cond-mat.supr-con↗