Abstract
A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to further expand the toolbox. Here, we propose to use quasiparticle properties to detect quantum phase transitions. The approach is independent from the choice of boundary conditions, and it does not assume a particular lattice structure. The probe is hence suitable for, e.g., fractals and quasicrystals. The method requires that one can reliably create quasiparticles in the considered systems. In the simplest cases, this can be done by a pinning potential, while it is less straightforward in more complicated systems. We apply the method to several rather different examples, including one that cannot be handled by the commonly used probes, and in all the cases we find that the numerical costs are low. This is so, because a simple property, such as the charge of the anyons, is sufficient to detect the phase transition point. For some of the examples, this allows us to study larger systems and/or further parameter values compared to previous studies.
Highlights
Describing physical systems in terms of phases allows us to focus on key properties rather than the full set of microscopic details
We investigate a model with a particular type of lattice Moore-Read ground state, which was shown in Ref. [26], based on computations of the topological entanglement entropy γ, to exhibit a phase transition as a function of the lattice filling with the transition point in the interval [1/8, 1/2]
We find that the anyons are significantly better at predicting the phase transition point than the energy gap closing for the same system size
Summary
Describing physical systems in terms of phases allows us to focus on key properties rather than the full set of microscopic details. A square lattice and on a fractal lattice, in an interacting Hofstadter model in the presence and in the absence of disorder, and in Kitaev’s toric code in a magnetic field Among these models, we include cases for which the phase transition point is already known, since this allows us to compare with other methods and check the reliability of the anyon approach. We include cases for which the phase transition point is already known, since this allows us to compare with other methods and check the reliability of the anyon approach For all these examples, we find that it is sufficient to compute a relatively simple property, such as the charge of the anyons, to determine the phase transition point. For the model on the fractal, we do not know of other methods that could be used for detecting the phase transition
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