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arXiv:2308.00018 · The European Physical Journal C

Entanglement and Chaos near critical point in strongly coupled Gauge theory

Debanjan Karan, Sanjay Pant

Published Feb 2, 2024• 14 citations
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Abstract

Abstract We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large N strongly coupled thermal field theory with critical point, having a well defined gravity dual known as 1RC black hole. The bulk theory accommodates a dimensionless parameter $$\xi $$ ξ , proportional to the charge of the 1RC black hole. Holographically, $$\xi \rightarrow 2$$ ξ → 2 limit ensures an existence of a critical point in the dual boundary theory. We show that the logarithmic negativity in low and high temperature limits enhances with increasing $$\xi $$ ξ . We analytically compute the EWCS in low and high temperature limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Furthermore, we study the chaotic behaviour of the field theory by analyzing a shock wave in the dual eternal 1 RC black hole and then estimate the degradation of TMI. The rate of such disruption of TMI slows down as the value of critical parameter $$\xi $$ ξ takes higher values.

DOI
10.1140/epjc/s10052-024-12463-9

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Abstract We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large N strongly coupled thermal field theory with critical point, having a well defined gravity dual known as 1RC black hole. The bulk theory accommodates a dimensionless parameter ξ\xi ξ ξ , proportional to the charge of the 1RC black hole. Holographically, ξ→2\xi \rightarrow 2ξ→2 ξ → 2 limit ensures an existence of a critical point in the dual boundary theory. We show that the logarithmic negativity in low and high temperature limits enhances with increasing ξ\xi ξ ξ . We analytically compute the EWCS in low and high temperature limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Furthermore, we study the chaotic behaviour of the field theory by analyzing a shock wave in the dual eternal 1 RC black hole and then estimate the degradation of TMI. The rate of such disruption of TMI slows down as the value of critical parameter ξ\xi ξ ξ takes higher values.
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We consider the minimal area of the entanglement wedge cross section (EWCS) in Einstein gravity. In the context of holography, it is proposed that this quantity is dual to different information measures, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Motivated by these proposals, we examine in detail the low and high temperature corrections to this quantity and show that it obeys the area law even in the finite temperature. We also study EWCS in nonrelativistic field theories with nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is an increasing function of the dynamical exponent due to the enhancement of spatial correlations between subregions for larger values of zzz. We find that EWCS is monotonically decreasing as the hyperscaling violating exponent increases. We also obtain this quantity for an entangling region with singular boundary in a three dimensional field theory and find a universal contribution where the coefficient depends on the central charge. Finally, we verify that for higher dimensional singular regions the corresponding EWCS obeys the area law.