Fluctuations and quantum criticality in the two‐dimensional Bose Hubbard model

Abstract

At a quantum phase transition, one ground state evolves into a different one by passing through a quantum critical region with enhanced spatial and temporal fluctuations. A method to map the quantum critical region using the single, local quantity R, the ratio of compressibility to local number fluctuations is proposed. R can be calculated from in situ experiments and also enables thermometry and phase diagnosis (for example whether superfluid or Mott insulating). The definition of R can be generalized to inhomogeneous systems and provides a powerful tool for experimentally mapping the finite temperature phase diagram demonstrated here for the two-dimensional Bose Hubbard model.

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

“…At the BKT transition in the thermodynamic limit $$\rho _\text{s}$$ has a discontinuous jump, while the compressibility κ exhibits a kink. [ 55,78 ] In CMF theory, because vortex fluctuations are not taken into account, $$\rho _\text{s}$$ vanishes linearly, while compressibility exhibits a jump at the SF–NF boundary even at finite temperature, as shown in Figure 5b. Based on the vanishing of $$\rho _\text{s}$$, or equivalently α SF , we obtain a phase diagram in the $$\mu /U-t/U$$ plane at a finite temperature, shown in Figure 5a.…”

“…[ 15 ] The SF–NF transition and the behavior of other thermodynamic quantities have been investigated in a few theoretical studies. [ 51–58 ] Experimentally, the reduction of $$T_\text{c}$$ near the QCP has been observed across a vacuum‐to‐superfluid transition [ 11,12 ] and across the MI‐SF transition at a constant particle density (particle number per lattice site) $$\bar{n}=1$$. [ 59 ] However, a systematic analysis on the effect of correlation at low temperature is lacking, particularly in 2D systems where simple mean‐field and perturbative methods fail due to enhanced fluctuations, as well as exact solution methods like density matrix renormalization group (DMRG) are not easily available.…”