Holographic quantum circuits from splitting/joining local quenches

Recently an effective membrane theory valid in a "hydrodynamic limit" was proposed to describe entanglement dynamics of chaotic systems based on results in random quantum circuits and holographic gauge theories. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to hydrodynamics, joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to higher derivative gravity and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.

“…which in the zero temperature limit β → ∞ reproduces the results for ground state joining quenches [26,27]:…”

Section: Field Theory Computationssupporting

confidence: 79%

“…Riemann surface, which can be conformally mapped into the half-plane [26,27,36]. For two-dimensional theories, it is convenient to introduce complex coordinates w,w, with w = x + iτ ; the conformal map is then a biholomorphic transformation w → f (w).…”

Section: Field Theory Computationsmentioning

confidence: 99%

Exploring the membrane theory of entanglement dynamics

Virrueta

2020

“…It is very interesting to compare our result to the dynamics of the reflected entropy in other CFTs, in particular, integrable CFTs. There are many works to study entanglement entropy after a local quench in various setups [4,5,52,53,71,[86][87][88][89][90][91]. Their motivation is to characterize CFT classes by the dynamics of entanglement.…”

Section: Reflected Entropy In Integrable Systemmentioning

confidence: 99%

“…The Renyi entropy is a generalization of the entanglement entropy, which is defined as 2) and the limit n → 1 of the Renyi entropy defines the entanglement entropy S (A). For this measure, a large number of works have been done to characterize the dynamics, for example, after joining quench [1], global quench [2,3], splitting quench [4] and double quench [5][6][7].…”

Section: Introduction and Summary 1introductionmentioning

confidence: 99%

Entanglement wedge cross section from CFT: dynamics of local operator quench

Kusuki

Tamaoka

2020

We derive dynamics of the entanglement wedge cross section from the reflected entropy for local operator quench states in the holographic CFT. By comparing between the reflected entropy and the mutual information in this dynamical setup, we argue that (1) the reflected entropy can diagnose a new perspective of the chaotic nature for given mixed states and (2) it can also characterize classical correlations in the subregion/subregion duality. Moreover, we point out that we must improve the bulk interpretation of a heavy state even in the case of well-studied entanglement entropy. Finally, we show that we can derive the same results from the odd entanglement entropy. The present paper is an extended version of our earlier report arXiv:1907.06646 and includes many new results: non-perturbative quantum correction to the reflected/odd entropy, detailed analysis in both CFT and bulk sides, many technical aspects of replica trick for reflected entropy which turn out to be important for general setup, and explicit forms of multi-point semi-classical conformal blocks under consideration.

“…In a CFT, there are two main families of quantum quenches [13]: in a global quench, the initial state is globally different from the energy eigenstates, as e.g. in [14,15]; in a local quench, the initial state is locally different from an energy eigenstate, as for examples in the joining and splitting quenches [16][17][18] or in the local operator quench [10][11][12]. In this paper, we consider the subsystem trace distance in latter category of quenches: at an initial time t = 0, a local operator is inserted somewhere in the ground state of the theory, and then the system is let evolve without further disturbance.…”

Section: Introductionmentioning

confidence: 99%

Subsystem distance after a local operator quench

Zhang

Calabrese

2020

We investigate the time evolution of the subsystem trace distance and Schatten distances after local operator quenches in two-dimensional conformal field theory (CFT) and in one-dimensional quantum spin chains. We focus on the case of a subsystem being an interval embedded in the infinite line. The initial state is prepared by inserting a local operator in the ground state of the theory. We only consider the cases in which the inserted local operator is a primary field or a sum of several primaries. While a nonchiral primary operator can excite both left-moving and rightmoving quasiparticles, a holomorphic primary operator only excites a right-moving quasiparticle and an anti-holomorphic primary operator only excites a left-moving one. The reduced density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to the RDM of the interval without any quasiparticles. Moreover, the RDMs of two intervals hosting quasiparticles at different positions are also orthogonal to each other. We calculate numerically the entanglement entropy, Rényi entropy, trace distance, and Schatten distances in time-dependent states excited by different local operators in the critical Ising and XX spin chains. These results match the CFT predictions in the proper limit.