# Regensburg 2019 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 21: Statistical Physics (General) II

### DY 21.3: Vortrag

### Dienstag, 2. April 2019, 14:30–14:45, H6

**Solving the quantum dimer and six vertex models one electric field line at a time** — Inti Sodemann^{1}, Jonah Herzog-Arbeitman^{2}, and •Sebastián Felipe Mantilla Serrano^{1} — ^{1}Max Planck Institute for the Physics of Complex Systems Dresden, Germany — ^{2}Princeton University, Princeton, USA

The phase diagram of the quantum dimer model in the square lattice has recently been challenged by Monte Carlo studies that question the existence of a resonant plaquette state neighboring the Rokhsar-Kivelson point (Phys. Rev. B 90, 245143 (2014) and Phys. Rev. B 98, 064302 (2018)). This model can be viewed as a U(1) lattice gauge theory with a finite density of fluctuating electric field lines. Here we take a different line of attack on this model and on the related six-vertex model (6VM), by exploiting the global conservation law of the number of electric field lines, which allows us to study an isolated fluctuating electric field line. In the case of the 6VM we map it onto the spin 1/2 XXZ chain which can be solved exactly. For the QDM the problem maps onto a two-leg spin 1/2 ladder which we solve using numerical exact diagonalization. Our findings are consistent with the existence of three distinct phases including a Luttinger liquid phase which is the 1D precursor to the fully 2Dplaquette phase. The uncanny resemblance of our single electric field line problem and the classic 2Dproblem suggests that much of the behaviour of the latter might be understood by thinking of it as a closely packed array of quasi-1D electric field lines which by themselves are undergoing non-trivial phase transitions