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APS

Ground states in the thermodynamic limit for models with quenched disorder

A. Alan Middleton

Published Mar 1, 2000• 0 citations
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Numerical ground state calculations are used to study four models with quenched disorder in finite samples with free boundary conditions. Extrapolation to the infinite volume limit indicates that the configurations in ``windows'' of fixed size converge to a unique configuration, up to global symmetries. The scaling of this convergence is consistent with calculations based on the fractal dimension of domain walls. These results provide strong evidence for the ``two-state'' picture of the low temperature behavior of these models. Convergence in three-dimensional systems can require relatively large windows.
Our investigation concerns the quenching process in systems with several degenerate ordered ground states. In the process the system is initially in thermal equilibrium at high temperature; then a sudden cooling drives the system towards a new equilibrium state. It comes out that when the number of ground states is large, the system evolves into a state made of many coexisting ordered phases, whose mutual interaction energy is not negligible in comparison with the total system energy. This is obtained provided the thermodynamic limit is taken before the infinite time limit.
A numerical linked-cluster algorithm was recently introduced to study quantum quenches in the thermodynamic limit starting from thermal initial states [M. Rigol, Phys. Rev. Lett. 112, 170601 (2014)]. Here, we tailor that algorithm to quenches starting from ground states. In particular, we study quenches from the ground state of the antiferromagnetic Ising model to the XXZ chain. Our results for spin correlations are shown to be in excellent agreement with recent analytical calculations based on the quench action method. We also show that they are different from the correlations in thermal equilibrium, which confirms the expectation that thermalization does not occur in general in integrable models even if they cannot be mapped to noninteracting ones.