Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model

Abstract

We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

6 pages and 4 figures, URL: http://link.aps.org/doi/10.1103/PhysRevA.87.043606

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• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Producing Coherent Excitations in Pumped Mott Antiferromagnetic Insulators
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• Fidelity Susceptibility in the Quantum Rabi Model
• Characterization of Bose-Hubbard Models with Quantum Non-demolition Measurements
• Phase-induced transport in atomic gases: from superfluid to Mott insulator
• Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions
• Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model