Abstract
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 δt the quantity teqδt−1, where δt and teq are injection time and equilibration time respectively, behaves adiabatically, 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.
Highlights
We study the time evolution of holographic mutual and tripartite information for a zero temperature CF T, derives to a non-relativistic thermal Lifshitz field theory by a quantum quench
In [22, 23], by applying AdS/CF T correspondence, the authors showed that the entanglement entropy of a region A in a CF T is proportional to the area of a surface which has the minimum area among surfaces whose boundaries coincide with the boundary of the region A which is known as Ryu-Takayanagi (RT ) prescription
If one would like to calculate the amount of the correlation between two sub-system A and B, mutual information is the quantity needs to be computed and the tripartite information is a quantity to study the degree of the extensivity of the mutual information
Summary
The gauge/gravity duality [1, 2] provides a wide range of domain to study strongly coupled quantum field theories whose dual are the gravitational theories in one higher dimension. One can extend the standard AdS/CF T dictionary in order to study the dual field theory This special class of Lifshitz spacetime can be considered holographically as a continuous deformation of corresponding CF T by time component of a vector primary operator ζa of conformal dimension ∆ = d, namely. In [29] the authors consider a nice mechanism to study the symmetry breaking of a C√F T towards a non-relativistic Lifshitz scaling with z = 1 + 2 They consider a quantum quench profile j(t) ≡√ 2 J(t), coupled to the vector primary operator ζt(x) in the action (16) which interpolates smoothly between 0 and 2.
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