Dimensional crossover and phase transitions in coupled chains: DMRG results

Quasi-one-dimensional (Q1D) systems are often studied across various areas of condensed matter and ultracold atomic lattice-gas physics and are often marked by dimensional crossover (DC) as the coupling between one-dimensional systems is increased or temperature decreased. Understanding these crossovers can be challenging due to the very different elementary excitations of 1D systems compared to higher-dimensional ones. In the present work, we combine numerical matrix product state (MPS) methods with mean-field (MF) theory to study paradigmatic cases of DC in systems of hard- and soft-core lattice bosons, with relevance to both condensed matter physics and ultracold atomic gases. We show that the superfluid-to-insulator transition is a first order one, as opposed to the isotropic cases and calculate transition temperatures for the superfluid states, finding excellent agreement with analytical theory while still functioning well where the current analytical framework does not apply. We further confirm the reliability of our approach by comparison to exact Quantum Monte Carlo calculations for the full 3D arrays.