Chao Niu

Comparison of holographic and field theoretic complexities for time dependent thermofield double states

A bstractWe compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the “complexity-action” (CA) conjecture and “complexity-volume” (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2E/(πℏ) saturating the Lloyd’s bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.

Diffusion and Butterfly Velocity at Finite Density

A bstractWe study diffusion and butterfly velocity (vB) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (μ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D± describing the coupled diffusion of charge and energy. By computing D± exactly, we find that in the incoherent regime (β/T ≫ 1, β/μ ≫ 1) D+ is identified with the charge diffusion constant (Dc) and D− is identified with the energy diffusion constant (De). In the coherent regime, at very small density, D± are ‘maximally’ mixed in the sense that D+(D−) is identified with De(Dc), which is opposite to the case in the incoherent regime. In the incoherent regime De ∼ C−ℏvB2/kBT where C− = 1/2 or 1 so it is universal independently of β and μ. However, Dc∼C+ℏvB2/kBT

Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models

{D}_c\sim {C}_{+}\hslash {v}_{{}^B}^2/{k}_BT

Universal corner contributions to entanglement negativity

where C+ = 1 or β2/16π2T2 so, in general, C+ may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

Axiomatic complexity in quantum field theory and its applications

A bstractThe holographic complexity is UV divergent. As a finite complexity, we propose a “regularized complexity” by employing a similar method to the holographic renor-malization. We add codimension-two boundary counterterms which do not contain any boundary stress tensor information. It means that we subtract only non-dynamic back-ground and all the dynamic information of holographic complexity is contained in the regularized part. After showing the general counterterms for both CA and CV conjectures in holographic spacetime dimension 5 and less, we give concrete examples: the BTZ black holes and the four and five dimensional Schwarzschild AdS black holes. We propose how to obtain the counterterms in higher spacetime dimensions and show explicit formulas only for some special cases with enough symmetries. We also compute the complexity of formation by using the regularized complexity.

More on complexity of operators in quantum field theory

A bstractWe study a relation between the thermal diffusivity (DT ) and two quantum chaotic properties, Lyapunov time (τL) and butterfly velocity (vB ) in strongly correlated systems by using a holographic method. Recently, it was shown that Ei:=DT,i/vB,i2τLi=x,y

T

{\mathbb{E}}_i:={D}_{T,i}/\left({v}_{{}^{B,i}}^2{\tau}_L\right)\left(i=x,y\right)