Abstract
We investigate the evolution of holographic entanglement entropy (HEE) and holographic complexity (HC) under a thermal quench in Einstein-Maxwell-axion theory, which is dual to a field theory with momentum relaxation on the boundary. A strip-shaped boundary geometry is utilized to calculate HEE and HC via ``$\text{entropy}=\text{surface}$'' and ``$\text{complexity}=\text{volume}$'' conjecture, respectively. By fixing other parameters, we claim that either large enough black hole charge or width of the strip will introduce swallow-tail behaviors in HEE and multivalues in HC due to the discontinuity of the minimum Hubeny-Rangamani-Takayanagi surface. Meanwhile, we explore the effects of momentum relaxation on the evolution of HEE and HC. The results present that the momentum relaxation will suppress the discontinuity to occur as it increases. For large enough momentum relaxation, the continuity of HEE and HC will be recovered.
Highlights
Holography [1,2,3] has provided a close connection among the quantum information, condensed matter, and quantum gravity
We investigate the evolution of holographic entanglement entropy (HEE) and holographic complexity (HC) under a thermal quench in Einstein-Maxwell-axion theory, which is dual to a field theory with momentum relaxation on the boundary
We studied the evolution of HEE and HC under a thermal quench in EMA theory
Summary
Holography [1,2,3] has provided a close connection among the quantum information, condensed matter, and quantum gravity. The study of HEE and HC will provide us more indirect but effective information to explore the nature of the spacetime, in particular the physics of the black hole horizon and its thermal and entanglement structures. We will investigate the evolution of HEE and HC under a thermal quench in Einstein-Maxwell gravity coupled with two linear spacial-dependent scalar fields in the bulk, which is called Einstein-Maxwell-axion (EMA) theory. Here we shall focus on the simplest four-dimensional case in this setup which is dual to three-dimensional boundary theory It was addressed in [40] that the scalar fields in the bulk source a spatially dependent field theory with momentum relaxation, while the linear coefficient of the scalar fields describes the strength of the momentum relaxation.
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