Many-body localization transition in coupled incommensurate Heisenberg chains.

In this work, we report a quantum many-body localization (MBL) transition in a ladder formed by two coupled incommensurate spin chains with spin 1/2. The two chains are described by an isotropic Heisenberg model and are coupled to each other by quasi-periodic couplings that decay exponentially with the distance between sites. Using matrix product states (MPS), we study the time evolution of the bipartite entanglement entropy after a quantum quench. We show that the entanglement entropy follows a transition from volume law to area law scaling with increasing the incommensurate ratio of lattice parameters and the inter-chain exchange interaction strength. To characterize the MBL phase, we calculate the inverse participation ratio(IPR) using the exact diagonalization at zero net magnetization, which is extrapolated to the thermodynamic limit. We discuss the interpretation of the MBL transition in light of equivalent fermionic models.