Operator content of entanglement spectra in the transverse field Ising chain after global quenches

Abstract

We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows us to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critical point.

Subsystem complexity after a global quantum quench

“…The temporal evolutions of ∆S A in the bottom panel of figure 14 can be explained by employing the quasi-particle picture [41], which provides the different temporal regimes and the corresponding qualitative behaviour of ∆S A (for the subsystems where a boundary occurs, the quasi-particle picture has been described e.g. in [70]). The different regimes identified by this analysis correspond to the vertical dot-dashed lines in the bottom panel of figure 14.…”

“…The entanglement dynamics after global quantum quenches has been largely explored by considering the temporal evolutions of various entanglement quantifiers. The entanglement entropy has been mainly investigated through various methods [40,[63][64][65][66][67], but also other entanglement quantifiers like the entanglement spectra [68][69][70], the entanglement Hamiltonians [68,69,71], the entanglement negativity [72] and the entanglement contours [69,73,74] have been explored.…”

Complexity of mixed Gaussian states from Fisher information geometry

“…The spectrum of the entanglement hamiltonian, that is usually called entanglement spectrum [122], is rich in information. For instance, in conformal field theories the entanglement spectrum provides both the central charge [123] and the conformal spectrum of the underlying model [110,113,114,120,121,[124][125][126].…”

Entanglement View of Dynamical Quantum Phase Transitions

“…Similarly, a number of studies sought to identify a connection between DQPTs and the behavior of the entanglement entropy. Again, a uniform pattern failed to emerge, with DQPTs in different models being in turn associated with rapid entropy growth [31], local maxima in the entanglement entropy [50], entanglement spectrum crossings [36,51,52] or transitions in a suitably defined entanglement echo [53]. Other works have highlighted a relationship between DQPTs and quasi-particle excitations [41,54].…”