SciPost Phys. 6, 078 (2019) ·
published 27 June 2019

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We study the robustness of 3D intrinsic topogical 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 groundstate phase diagram with first and secondorder
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.
SciPost Phys. 4, 001 (2018) ·
published 17 January 2018

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The Heisenberg model for S=1/2 describes the interacting spins of electrons
localized on lattice sites due to strong repulsion. It is the simplest
strongcoupling model in condensed matter physics with widespread
applications. Its relevance has been boosted further by the discovery of curate
hightemperature superconductors. In leading order, their undoped parent
compounds realize the Heisenberg model on squarelattices. Much is known about
the model, but mostly at small wave vectors, i.e., for longrange processes,
where the physics is governed by spin waves (magnons), the Goldstone bosons of
the longrange ordered antiferromagnetic phase. Much less, however, is known
for shortrange processes, i.e., at large wave vectors. Yet these processes are
decisive for understanding hightemperature superconductivity. Recent reports
suggest that one has to resort to qualitatively different fractional
excitations, spinons. By contrast, we present a comprehensive picture in terms
of dressed magnons with strong mutual attraction on short length scales. The
resulting spectral signatures agree strikingly with experimental data.
Prof. Schmidt: "Dear Irénée Frerot, we than..."
in Report on Quantum robustness and phase transitions of the 3D Toric Code in a field