Quantum effects can stabilize wormhole solutions in general relativity, allowing information and matter to be transported between two connected spacetimes. Here we study the revival dynamics of signals sent between two weakly coupled quantum chaotic systems, represented as identical Sachdev-Ye-Kitaev models, that realize holographically a traversable wormhole in anti-de Sitter spacetime AdS_{2} for large number N of particles. In this limit we find clear signatures of wormhole behavior: an excitation created in one system is quickly scrambled under its unitary dynamics, and is reassembled in the other system after a characteristic time consistent with holography predictions. This leads to revival oscillations that at low but finite temperature decay as a power law in time. For small N we also observe revivals and show that they arise from a different, nongravitational mechanism.
Quantum effects can stabilize wormhole solutions in general relativity, allowing information and matter to be transported between two connected spacetimes. Here we study the revival dynamics of signals sent between two weakly coupled quantum chaotic systems, represented as identical Sachdev-Ye-Kitaev models, that realize holographically a traversable wormhole in anti-de Sitter spacetime AdS_{2} for large number N of particles. In this limit we find clear signatures of wormhole behavior: an excitation created in one system is quickly scrambled under its unitary dynamics, and is reassembled in the other system after a characteristic time consistent with holography predictions. This leads to revival oscillations that at low but finite temperature decay as a power law in time. For small N we also observe revivals and show that they arise from a different, nongravitational mechanism.
Recent work has shown that coupling two identical Sachdev-Ye-Kitaev (SYK) models can realize a phase of matter that is holographically dual to an eternal traversable wormhole.This phase supports revival oscillations between two quantum chaotic systems that can be interpreted as information traversing the wormhole.Here we generalize these ideas to a pair of coupled SYK models with complex fermions that respect a global U(1) charge symmetry.Such models show richer behavior than conventional SYK models with Majorana fermions and may be easier to realize experimentally.We consider two different couplings, namely, tunneling and charge-conserving two-body interactions, and obtain the corresponding phase diagram using a combination of numerical and analytical techniques.At low temperature, we find a charge-neutral gapped phase that supports revival oscillations, with a ground state close to the thermofield double, which we argue is dual to a traversable wormhole.We also find two different gapless non-Fermi liquid phases with tunable charge density which we interpret as dual to a "large" and "small" charged black hole.The gapped and gapless phases are separated by a first-order phase transition of the Hawking-Page type.Finally, we discuss an SU(2)-symmetric limit of our model that is closely related to proposed realizations of SYK physics with spinful fermions in graphene, and explain its relevance for future experiments on this system.
Abstract We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of N Majorana fermions coupled by random q-body interactions. The degree of sparseness is captured by a regular hypergraph in such a way that the Hamiltonian contains exactly k N independent terms. We improve on the theoretical understanding of the sparseness property by using known measures of hypergraph expansion. We show that the sparse version of the two coupled SYK model is gapped with a ground state close to a thermofield double state. Using Krylov subspace and parallelization techniques, we simulate the system for q = 4 and q = 8. The sparsity of the model allows us to explore larger values of N than the ones existing in the literature for the all-to-all SYK. We analyze in detail the two-point functions and the transmission amplitude of signals between the two systems. We identify a range of parameters where revivals obey the scaling predicted by holography and signals can be interpreted as traversing the wormhole.
In recent years a new paradigm has emerged to investigate non-Fermi liquids without quasiparticles, based on the exactly-solvable Sachdev-Ye-Kitaev model which consists of a large number of fermions with all-to-all, random Gaussian interactions. This model exhibits a rich phenomenology at low energy, including power-law decaying spectral functions, maximal chaos and connections to black hole horizons in anti-de Sitter spacetime. These intriguing properties have inspired a broad research program at the intersection of condensed matter physics, quantum information and quantum gravity. In this thesis we explore the phases and phase transitions occurring in Sachdev-Ye-Kitaev models that are coupled in various ways, with an eye on physical platforms that could enable their realization in condensed matter systems. This journey takes us from the investigation of quantum chaos in many-body systems and revival dynamics in traversable wormholes, all the way to the physics of disordered graphene flakes and unconventional superconductivity.
A bstract The rapid development of quantum science and technology is leading us into an era where quantum many-body systems can be comprehended through quantum simulations. Holographic duality, which states gravity and spacetime can emerge from strongly interacting systems, then offers a natural avenue for the experimental study of gravity physics without delving into experimentally infeasible high energies. A prominent example is the simulation of traversable wormholes through the wormhole teleportation protocol, attracting both theoretical and experimental attention. In this work, we develop the theoretical framework for computing the fidelity of wormhole teleportation in N -qubit systems with all-to-all interactions, quantified by mutual information and entanglement negativity. The main technique is the scramblon effective theory, which captures universal out-of-time-order correlations in generic chaotic systems. We clarify that strong couplings between the two systems are essential for simulating the probe limit of semi-classical traversable wormholes using strongly interacting systems with near-maximal chaos. However, the teleportation signal diminishes rapidly when reducing the system size N , requiring a large number of qubits to observe a sharp signature of emergent geometry by simulating the Sachdev-Ye-Kitaev model. This includes both the causal time-order of signals and the asymmetry of the teleportation signal for coupling with different signs. As a comparison, the teleportation signal increases when reducing N in weakly interacting systems. We also analyze the fidelity of the generalized encoding scheme in fermionic string operators.
It has been recently proposed by Maldacena and Qi that an eternal traversable wormhole in a two-dimensional anti--de Sitter space is the gravity dual of the low temperature limit of two Sachdev-Ye-Kitaev (SYK) models coupled by a relevant interaction (which we will refer to as spin operator). We study spectral and eigenstate properties of this coupled SYK model. We find that level statistics in the tail of the spectrum, and for a sufficiently weak coupling, show substantial deviations from random matrix theory, which suggests that traversable wormholes are not quantum chaotic. By contrast, for sufficiently strong coupling, corresponding to the black hole phase, level statistics are well described by random matrix theory. This transition in level statistics coincides approximately with a previously reported Hawking-Page transition for weak coupling. We show explicitly that this thermodynamic transition turns into a sharp crossover as the coupling increases. Likewise, this critical coupling also corresponds to the one at which the overlap between the ground state and the thermofield double state (TFD) is smallest. In the range of sizes we can reach by exact diagonalization, the ground state is well approximated by the TFD only in the strong coupling limit. This is due to the fact that the ground state is close to the eigenstate of the spin operator corresponding to the lowest eigenvalue which is an exact TFD at infinite temperature. In this region, the spectral density is separated into blobs centered around the eigenvalues of the spin operator. For weaker couplings, the exponential decay of coefficients in a tensor product basis, typical of the TFD, becomes power law. Finally, we also find that the total Hamiltonian has an additional discrete symmetry which has not been reported previously.
Traversability dynamics of minimal Sachdev-Ye-Kitaev Wormhole-inspired teleportation protocol with a parity-time (PT)-symmetric non-Hermitian deformation
Holography-inspired teleportation has recently emerged as a significant area of research in quantum many-body systems. In this work, we investigate the effects of PT symmetric non-unitary deformations on the traversability of the wormhole-inspired teleportation protocol modeled by coupled Sachdev-Ye-Kitaev systems prepared in a Thermofield Double state bath. By introducing balanced gain and loss terms to the boundary Hamiltonians, we identify a phase transition driven by spectral exceptional points, where the real energy eigenvalues of the effective Hamiltonian coalesce and bifurcate into complex conjugate pairs. We demonstrate that the PT-broken phase acts as an amplifier, enabling exponential growth in the norm of the teleported signal while preserving the causal time window for the wormhole's traversability. A statistical study of disorder realizations reveals that the critical non-Hermiticity threshold γc follows a log-normal distribution, reflecting the sensitivity of the transition to the microscopic level spacing of the chaotic SYK spectrum. Furthermore, we observe a ``Purification" effect deep in the broken phase, where the teleportation channel acts as an entanglement distiller, yielding near-perfect teleportation fidelity for post-selected states. Our results suggest that the non-Hermitian topology can be harnessed to enhance holographic quantum communication, providing a robust mechanism for signal amplification in noisy, minimal quantum many-body systems.