Quantum Critical Dynamics of the Random Transverse Field Ising Spin Chain

TL;DR

This paper investigates the critical dynamics of the random transverse-field Ising chain, revealing logarithmic decay in spin correlations and novel power-law decay in energy correlations through numerical simulations.

Contribution

It provides the first detailed numerical analysis of dynamical correlations in the critical region of the disordered quantum Ising chain, confirming scaling theory predictions.

Findings

Logarithmic decay of spin autocorrelations with exponents related to magnetization.

Power-law decay of energy autocorrelations with new critical exponents.

Comparison of numerical results with scaling theory predictions.

Abstract

Dynamical correlations of the spin and the energy density are investigated in the critical region of the random transverse-field Ising chain by numerically exact calculations in large finite systems (L<=128). The spin-spin autocorrelation function is found to decay proportional to (log t)^{-2x_m} and (log t)^{-2x_m^s} in the bulk and on the surface, respectively, with x_m and x_m^s the bulk and surface magnetization exponents, respectively. On the other hand the critical energy-energy autocorrelation functions have a power law decay, which are characterized by novel critical exponents eta_e~2.2 in the bulk and eta_e^s~2.5 at the surface, respectively. The numerical results are compared with the predictions of a scaling theory.