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Register a new userCharged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity
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We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present t
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In this paper we use Euclidean gravity methods to show that charged black holes which are sufficiently close to extremality must be able to decay. The argument proceeds by showing that Euclidean gravity would otherwise imply a violation of charge quantization. As this is the assumption which leads to the weak gravity conjecture, our argument gives a derivation of that conjecture. We use a small negative cosmological constant as an infrared regulator, but our argument applies to near-extremal black holes which are arbitrarily small compared to the $AdS$ curvature scale. We also give a universal formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero fraction, this gives a new proof of the completeness hypothesis for finite gauge fields. Based on these observations we make two conjectures about many-body quantum physics: we propose a lower bound on the critical temperature for the instability of a semi-local quantum liquid, and we propose that our formula for the density of black hole microstates in each representation of a finite gauge group also applies at high energy to any quantum field theory with a finite group global symmetry.
In classical thermodynamics, heat cannot spontaneously pass from a colder system to a hotter system, which is called the thermodynamic arrow of time. However, if the initial states are entangled, the direction of the thermodynamic arrow of time may not be guaranteed. Here we take the thermofield double state at $0+1$ dimension as the initial state and assume its gravity duality to be the eternal black hole in AdS$_2$ space. We make the temperature difference between the two sides by changing the Hamiltonian. We turn on proper interaction between the two sides and calculate the changes in energy and entropy. The energy transfer, as well as the thermodynamic arrow of time, are mainly determined by the competition between two channels: thermal diffusion and anomalous heat flow. The former is not related to the wormhole and obeys the thermodynamic arrow of time; the latter is related to the wormhole and reverses the thermodynamic arrow of time, i.e. transferring energy from the colder side to the hotter side at the cost of entanglement consumption. Finally, we find that the thermal diffusion wins the competition, and the whole thermodynamic arrow of time has not been reversed.
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input. This leaves many of the general assumptions of ETH untested. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH. We discuss and propose protocols to independently measure fluctuations and dissipations as well as higher-order time ordered correlation functions. We first show how the emergence of fluctuation dissipation relations from a nonequilibrium initial state can be observed for the 2D Bose-Hubbard model in superconducting qubits or quantum gas microscopes. Then we focus on the long-range transverse field Ising model (LTFI), which can be realized with trapped ions. The LTFI exhibits rich thermalization phenomena: For strong transverse fields, we observe prethermalization to an effective magnetization-conserving Hamiltonian in the fluctuation dissipation relations. For weak transverse fields, confined excitations lead to non-thermal features resulting in a violation of the fluctuation-dissipation relations up to long times. Moreover, in an integrable region of the LTFI, thermalization to a generalized Gibbs ensemble occurs and the fluctuation-dissipation relations enable an experimental diagonalization of the Hamiltonian. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the butterfly effect implies structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additional correlations.
All global symmetries are expected to be explicitly broken by quantum gravitational effects, and yet may play an important role in Particle Physics and Cosmology. As such, any evidence for a well-preserved global symmetry would give insight into an important feature of gravity. We argue that a recently reported $2.4sigma$ detection of cosmic birefringence in the Cosmic Microwave Background could be the first observational indication of a well-preserved (although spontaneously broken) global symmetry in nature. A compelling solution to explain this measurement is a very light pseudoscalar field that interacts with electromagnetism. In order for gravitational effects not to lead to large corrections to the mass of this scalar field, we show that the breaking of global symmetries by gravity should be bounded above. Finally, we highlight that any bound of this type would have clear implications for the construction of theories of quantum gravity, as well as for many particle physics scenarios.
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