Nielsen complexity of a TFD of a quantum harmonic oscillator in external magnetic field
Drawing on the growing links between quantum information theory and black hole physics, we explore the circuit complexity of a quantum
harmonic oscillator in the presence of an external magnetic field. By applying the Nielsen approach within the thermofield dynamics (TFD)
framework, we calculate the complexity of thermofield double states. Our analysis uncovers several notable characteristics of this complexity. Lastly, we derive the Lloyd bound for the system and demonstrate that it is upheld.
An equivalence of three butterflies in Lifshitz background
In this work, we investigate two salient chaotic features, namely Lyapunov exponent and butterfly velocity, in the context of an asymptotically Lifshitz black hole background with an arbitrary critical exponent. These features are computed using three methods: entanglement wedge method, out-of-time-ordered correlator computation and pole-skipping. We present a comparative study of the aforementioned features where all of these methods yield exactly similar results for the butterfly velocity and Lyapunov exponent. This establishes an equivalence between all three methods for probing chaos in the chosen gravity background. Furthermore, we evaluate the chaos at the classical level by computing the eikonal phase and Lyapunov exponent from the bulk gravity. These quantities emerge as nontrivial functions of the anisotropy index. By examining the classical eikonal phase, we uncover different scattering scenarios in the near-horizon and near-boundary regimes. We also discuss potential limitations regarding the choice of the turning point of the null geodesic in our approach.
Floquet SYK wormholes
We study the non-equilibrium dynamics of two coupled SYK models, conjectured to be holographically dual to an eternal traversable wormhole in AdS2. We consider different periodic drivings of the parameters of the system. We analyze the energy flows in the wormhole and black hole phases of the model as a function of the driving frequency. Our numerical results show a series of resonant frequencies in which the energy absorption and heating are enhanced significantly and the transmission coefficients drop, signalling a closure of the wormhole. These frequencies correspond to part of the conformal tower of states and to the boundary graviton of the dual gravitational theory. Furthermore, we provide evidence supporting the existence of a hot wormhole phase between the black hole and wormhole phases. When driving the strength of the separate SYK terms we find that the transmission can be enhanced by suitably tuning the driving.
Chern-Simons and Boundaries: The Neverending Story
One concept that needs to be better understood in the holographic duality is the introduction of torsion in gravity theory. Furthermore, first order gravity formalism seems to be computationally simpler but conceptually more challenging to tackle. Chern-Simons gravity is an example of a theory where we can test different implications of the torsion tensor in the AdS/(B)CFT duality set-up. This poster presents some of our recent results in that direction.
Trapping and Chaos in Bubbling AdS Spaces
We study the dynamics of null geodesics in 1/2 BPS bubbling AdS space. Building on prior research that established a connection between certain null geodesics confined to a specific (phase) plane and chaotic billiards, we extend the analysis to geodesics that are not restricted to a plane. We calculate the escape rate and Lyapunov exponent for trapped geodesics in these geometries. Our results show that in systems with large spatial dimensions, the Kolmogorov-Sinai entropy—representing the rate of information growth—is influenced by a non-zero escape rate, leading to a value lower than the Lyapunov exponent. Additionally, our findings validate, within numerical precision, the Gaspard-Nicolis relation, which links Kolmogorov-Sinai entropy, Lyapunov exponent, and escape rate.
Holographic Lattices and Luttinger's Theorem
AdS/CFT correspondence can provide a novel, nonperturbative insight into strongly correlated materials. We solve numerically a system of Einstein-Maxwell-dilaton equations with periodic boundary conditions which describes strongly correlated matter at finite temperature and chemical potential on a square lattice. The metric in the deep interior is hyperscaling-violating, implying an anomalous scaling of thermodynamic quantities. We then compute the charge density of the system and inspect the validity of the Luttinger's theorem. The dependence of the charge density on doping and its profile confirm that the system is in metallic phase. However, the Luttinger's theorem is strongly violated, meaning that the system is a non-Fermi liquid, despite having stable quasiparticle peaks in the spectrum.
Hydrodynamics in 1d spin chains from a Holographic Perspective
Many physical systems admit a simplified description of their dynamics when examined at macroscopic scales. This simplified description—generally referred to as hydrodynamics—is governed by a restricted set of macroscopic observables that includes conserved quantities, Goldstone modes, and order parameters. An outstanding challenge in quantum many-body physics is finding this hydrodynamic description in terms of the microscopic variables. I will present a method inspired by holography for constructing the effective hydrodynamic description in the form of a transfer matrix and a set of hydrodynamically-relevant variables. The method proceeds by constructing an alternative representation of the operator dynamics in the form of a local (1+1)d "bulk" theory. I will show how the properties of the auxiliary bulk encode the existence of an effective local equation of motion of a given model, allowing for the extraction of hydrodynamic parameters like diffusion constants and characteristic thermalization scales. I will show results for various qubit and fermionic systems, and compare to the known literature.
Geometric and phase space (de)localization in a semiclassical Bose-Hubbard chain
Anomalous diffusion is observed in the semiclassical approximation of the Bose-Hubbard model. We present a few crucial criteria for the
development of anomalous transport on long timescales. The criteria encapsulate both the initial geometry of the system (coordinate distribution of the particles) and the initial phase space statistics. We also find cases when diffusion breaks down completely (there is no
transport at all): it turns out that the operators which are sufficiently nonlocal exhibit no diffusion. In particular, this implies that (non-local) quantum corrections eventually destroy anomalous transport as we move away from the semiclassical regime.
Spectral Form Factor and Random Walks
This work examines the relationship between the spectral form factor (SFF) and planar random walks. The SFF is a measure used to identify the onset of quantum chaos and scrambling. We demonstrate that the moments of the SFF in generic quantum chaotic systems exhibit similar behavior to the moments of the distribution describing the positions of random walkers in the Euclidean plane. This similarity holds for the mean, variance, skewness, kurtosis, and all higher-order moments of the underlying probability distribution function. Additionally, we suggest a potential generalization of planar random walks that avoid intersections along the trajectory, and explore potential applications to integrable quantum systems.
Signs for scalar field chaoticity
We study interesting but simple examples of models being integrable but exhibiting some features commonly attributed to chaotic dynamics. In the first case, we consider free massive scalar field dynamics in finite volume following a quench excitation and show that correlation function peak distribution is not necessarily exponential as expected but in some cases close to the level spacing distribution of Gaussian ensembles. In the second case, we generalize the free scalar field model on a curved background with the Dirichlet boundary conditions imposed (normal modes). In the case of BTZ spacetime, the appearance of the RMT profile for the spectral form factor was recently reported in literature. We discuss here massive field and the de Sitter spacetime case.
Hamiltonian Forging of a Thermofield Double
The preparation of Thermofield Double states is of extreme importance due to its connection with wormhole teleportation. Following proposals in the literature we study its variational preparation as the ground state of an interacting Hamiltonian on the doubled Hilbert space. We focus on generic fermionic hamiltonians and find an exact solution for the quadratic case, which provides a warm start for the general case. The problem is naturally suited for the use of the entanglement forging strategy, in which only circuits of size N are required. We comment the case of SYK at the end.