Thomas Barthel

Abstract The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase transitions, where quantum fluctuations manifest across all length scales.

We explain why and numerically confirm that there are no barren plateaus in the energy optimization of isometric tensor network states (TNS) for extensive Hamiltonians with finite-range interactions, which are, for example, typical in condensed matter physics. Specifically, we consider matrix product states (MPS) with open boundary conditions, tree tensor network states (TTNS), and the multiscale entanglement renormalization ansatz (MERA).

Driving and dissipation can stabilize Bose-Einstein condensates. Using Keldysh field theory, we analyze this phenomenon for Markovian systems that can comprise on-site two-particle driving, on-site single-particle and two-particle loss, as well as edge-correlated pumping. Above the upper critical dimension, mean-field theory shows that pumping and two-particle driving induce condensation right at the boundary between the stable and unstable regions of the noninteracting theory.