# Freiburg 2019 – wissenschaftliches Programm

## Sitzungen | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# FM: Fall Meeting

## FM 59: Enabling Technologies: Quantum Dots and Superconductivity-based Systems

### FM 59.6: Talk

### Mittwoch, 25. September 2019, 15:15–15:30, 3043

Quantum phases and quantum phase transitions in frustrated networks of Josephson junctions — •Mikhail Fistul^{1,2} and Alexei Andreanov^{1} — ^{1}Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon, Republic of Korea — ^{2}National University of Science and Technology MISiS, Russian Quantum Center, Moscow, Russia

We present a theoretical study of spatial correlations of Josephson phases in frustrated quantum networks of Josephson junctions. We focus on one-dimensional sawtooth chains where frustration arises due to the Josephson couplings having alternating signs in a single lattice cell of our model. The classical nonlinear dynamics of such system [1] shows the crossover from non-frustrated to frustrated regimes at the critical value of frustration, f_{c}. Such crossover is characterized by the thermodynamic spatial correlation functions of phases on vertices, ϕ_{n}, i.e. C(n−m)=⟨ cos(ϕ_{n}−ϕ_{m}) ⟩ displaying the transition from long- to short-range spatial correlations.

In the quantum regime using a direct mapping to the classical one- or two-dimensional lattices of spins with alternating sign long-range interactions, we obtain the zero temperature phase diagram (√E_{c}/E_{J})-f, where E_{c} and E_{J} are the charge and Josephson coupling energies, respectively. The various macroscopic quantum phases, e.g. quantum vortices/antivortices, quantum vortex-antivortex pairs,
quantum superposition states, quantum strip phases, are discussed.

[1] A. Andreanov and M. V. Fistul, J. Phys. A: Math. Theor. 52, 105101 (2019).