# Erlangen 2022 – wissenschaftliches Programm

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# SYQC: Symposium Quantum Cooperativity of Light and Matter

## SYQC 2: Quantum Cooperativity of Light and Matter - Session 2

### SYQC 2.2: Vortrag

### Donnerstag, 17. März 2022, 14:30–14:45, Audimax

**Quantum Criticality of the long-range antiferromagnetic Heisenberg ladder** — •Patrick Adelhardt and Kai Phillip Schmidt — FAU Erlangen-Nürnberg, Germany

The Mermin-Wagner theorem excludes the breaking of a continuous symmetry in one-dimensional spin systems at zero temperature for sufficiently short-ranged interactions. Introducing algebraically decaying long-range couplings on the antiferromagnetic Heisenberg two-leg ladder, we show that a direct second-order quantum phase transition between the topologically ordered rung-singlet phase in the short-range limit and a conventionally Néel-ordered antiferromagnet can be realized in a one-dimensional system. We study the quantum-critical breakdown in the rung-singlet phase using the method of perturbative continuous unitary transformations (pCUT) on white graphs in combination with classical Monte Carlo simulations for the graph embedding in the thermodynamic limit supplemented with linear spin-wave calculations and exact diagonalization to extract the critical point. Exploiting (hyper-)scaling relations, the pCUT method is used to determine the entire set of canonical critical exponents as a function of the decay exponent. We find that the critical behavior can be divided into a long-range mean-field regime and a regime of continuously-varying exponents similar to the long-range transverse-field Ising model despite the presence of distinct orders on different sides of the critical point and the absence of criticality in the short-range limit.