Time Evolution of the Magnetic Chains with Uniaxial Anisotropy

Abstract

In the framework of the matrix product states representation the eect of the single-ion anisotropy on the time evolution of the initial state after a sudden quench of the local magnetic eld has been investigated. The overlap of the initial and time-evolved states, so called the Loschmidt echo, magnetization proles and correlation functions are presented.

Pulsed Nonlinear Coupler as an Effective Tool for the Bell-Like States Generation

“…where |ψ cut is derived from the analytical formulae, whereas |ψ was found with application of the "exact" numerical methods. At this point, it should be mentioned that in the papers devoted to the solid state physics the fidelity is called the Loschmidt echo [8,9]. Thus, in Fig.…”

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

“…Based on them the ground state (the so-called valencebond-state) can be built [10,11]. However, when we are dealing with an open chain, both S = 1 spins at the ends can be replaced by the S = 1/2 spins to keep unchanged a nonzero energy gap between the singlet ground state |ψ 0 and the first excited state [10,12,13]. The groundstate energy per spin is E ≈ −1.40 J and the excitation spectrum has a gap ∆ ≈ 0.41 J [14].…”

“…Thus, the time of calculations is significantly reduced for d = 1 strongly correlated systems. When the variational principle is applied, the ground state can be found by the minimization procedure ψ|H|ψ under the constraint ψ|ψ = 1 [31]. Moreover, it is one of the most attractive features of the MPS representation that the time evolution can also be performed very efficiently.…”