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Register a new userHolographic Mutual and Tripartite Information in a Symmetry Breaking Quench
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We study the time evolution of holographic mutual and tripartite information for a zero temperature $CFT$, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench. We observe that the symmetry breaking does not play any role in the phase space, phase of parameters of sub-systems, and the length of disentangling transition. Nevertheless, mutual and tripartite information indeed depend on the rate of symmetry breaking. We also find that for large enough values of $delta t$ the quantity $t_{eq}delta t^{-1}$, where $delta t$ and $t_{eq}$ are injection time and equilibration time respectively, behaves universally, $i.e.$ its value is independent of length of separation between sub-systems. We also show that tripartite information is always non-positive during the process indicates that mutual information is monogamous.
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Holographic mutual and tripartite information have been studied in a non-conformal background. We have investigated how these observables behave as the energy scale and number of degrees of freedom vary. We have found out that the effect of degrees of freedom and energy scale is opposite. Moreover, it has been observed that the disentangling transition occurs at large distance between sub-systems in non-conformal field theory independent of l. The mutual information in a non-conformal background remains also monogamous.
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual information based on the $2-$Renyi entanglement entropy and using a locality result stemming from quasi-adiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum $XY$ model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.
We use flat-space holography to calculate the mutual information and the 3-partite information of a two-dimensional BMS-invariant field theory (BMSFT$_2$). This theory is the putative holographic dual of the three-dimensional asymptotically flat spacetimes. We find a bound in which entangling transition occurs for zero and finite temperature BMSFTs. We also show that the holographic 3-partite information is always non-positive which indicates that the holographic mutual information is monogamous.
Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Renyi generalizations in holographic duality. We first review the definition of the Renyi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Renyi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Renyi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.
We explore the far from equilibrium response of a holographic superfluid using the AdS/CFT correspondence. We establish the dynamical phase diagram corresponding to quantum quenches of the order parameter source field. We find three distinct regimes of behaviour that are related to the spectrum of black hole quasi-normal modes. These correspond to damped oscillations of the order parameter, and over-damped approaches to the superfluid and normal states. The presence of three regimes, which includes an emergent dynamical temperature scale, is argued to occur more generally in time-reversal invariant systems that display continuous symmetry breaking.
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