https://d-a-reiss.github.io/tags/quantum-phase-transitions/Recent content in Quantum-Phase-Transitions on David A. ReissHugo -- 0.165.0en-usFri, 29 Nov 2019 00:00:00 +0000https://d-a-reiss.github.io/publications/2020-muhlhauser-fracton-phases/Fri, 29 Nov 2019 00:00:00 +0000https://d-a-reiss.github.io/publications/2020-muhlhauser-fracton-phases/The quantum robustness of fracton phases is investigated by studying the influence of quantum fluctuations on the X-Cube model and Haah’s code, which realize a type-I and type-II fracton phase, respectively. To this end a finite uniform magnetic field is applied to induce quantum fluctuations in the fracton phase resulting in zero-temperature phase transitions between fracton phases and polarized phases. Using high-order series expansions and a variational approach, all phase transitions are classified as strongly first order, which turns out to be a consequence of the (partial) immobility of fracton excitations. Indeed, single fractons as well as few-fracton composites can hardly lower their excitation energy by delocalization due to the intriguing properties of fracton phases, as demonstrated in this work explicitly in terms of fracton quasi-particles.https://d-a-reiss.github.io/publications/2019-reiss-toric-code-field/Mon, 11 Feb 2019 00:00:00 +0000https://d-a-reiss.github.io/publications/2019-reiss-toric-code-field/We study the robustness of 3D intrinsic topological order under external perturbations by investigating the paradigmatic microscopic model, the 3D toric code in an external magnetic field. Exact dualities as well as variational calculations reveal a ground-state phase diagram with first and second-order quantum phase transitions. The variational approach can be applied without further approximations only for certain field directions. In the general field case, an approximative scheme based on an expansion of the variational energy in orders of the variational parameters is developed. For the breakdown of the 3D intrinsic topological order, it is found that the (im-)mobility of the quasiparticle excitations is crucial in contrast to their fractional statistics.https://d-a-reiss.github.io/publications/2017-adelhardt-haldane-phases/Mon, 09 Oct 2017 00:00:00 +0000https://d-a-reiss.github.io/publications/2017-adelhardt-haldane-phases/We use linked-cluster expansions to analyze the quantum phase transitions between symmetry unbroken trivial and topological Haldane phases in two different spin-one chains. The first model is the spin-one Heisenberg chain in the presence of a single-ion anisotropy while the second one is the dimerized spin-one Heisenberg chain. For both models we determine the ground-state energy and the one-particle gap inside the non-topological phase as a high-order series using perturbative continuous unitary transformations. Extrapolations of the gap series are applied to locate the quantum critical point and to extract the associated critical exponent. We find that this approach works unsatisfactory for the anisotropic chain, since the quality of the extrapolation appears insufficient due to the large correlation length exponent. In contrast, extrapolation schemes display very good convergence for the gap closing in the case of the dimerized spin-one Heisenberg chain.