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The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is extended to dynamical problems. The auto-correlation functions of the Transverse Ising chain are derived by this method. It is shown that the Trotter-directional correlation function is interpreted as a Matsubaras temperature Green function and that the auto-correlation function is given by analytic continuation of the Green function. We propose the Trotter-directional correlation function is a new measure of the quantum fluctuation and show how it works well as a demonstration.
The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^alpha$, $1<alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite c
We investigate the entanglement dynamics between two distant qubits by analyzing correlations in the quantum Ising model. Starting from the spin system in a paramagnetic regime enforced by the external magnetic field $B$, we then switch on the ferrom
We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probab
Taking one-dimensional random transverse Ising model (RTIM) with the double-Gaussian disorder for example, we investigated the spin autocorrelation function (SAF) and associated spectral density at high temperature by the recursion method. Based on t
I study the universal finite-size scaling function for the lowest gap of the quantum Ising chain with a one-parameter family of ``defect boundary conditions, which includes periodic, open, and antiperiodic boundary conditions as special cases. The un