Berlin 2024 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 24: Quantum-Critical Phenomena

TT 24.4: Talk

Tuesday, March 19, 2024, 10:15–10:30, H 2053

Quantum criticality of the antiferromagnetic XXZ square lattice bilayer with long-range interactions — •Patrick Adelhardt and Kai Phillip Schmidt — Department of Physics, Staudtstraße 7, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany

The majority of numerical approaches investigating quantum systems with algebraically decaying long-range interactions is restricted to one dimensions or to two-dimensional systems with quickly-decaying long-range interactions.While models with discrete symmetries like the long-range transverse-field Ising model have been studied thoroughly, much less is known about long-range models with continuous symmetries. We study the breakdown of the rung-singlet phase in the two-dimensional XXZ bilayer model with unfrustrated staggered long-range interactions. To this end we use the method of perturbative continuous unitary transformations (pCUT) with classical Monte Carlo simulations yielding high-order series in the thermodynamic limit about the limit of isolated dimers. This allows us to determine the critical point, the dispersion in the rung-singlet phase close to it, as well as critical exponents as a function of the decay exponent. While for quickly-decaying interactions we identify three critical regimes with 3D XY, Heisenberg, and Ising criticality depending on the anisotropy in the XXZ Hamiltonian, for strong interactions we observe a single long-range mean-field regime and continuously varying critical exponents between these regimes.

Keywords: Series expansions; Monte Carlo method; Critical exponents; Upper critical dimension; Goldstone modes