Non local parity order in the two-dimensional Mott insulator

Abstract

The Mott insulator is characterized by having small deviations around the (integer) average particle density n, with pairs with n-1 and n+1 particles forming bound states. In one dimension, the effect is captured by a non-zero value of a non-local "string" of parities, which instead vanishes in the superfluid phase where density fluctuations are large. Here, we investigate the interaction induced transition from the superfluid to the Mott insulator, in the paradigmatic Bose Hubbard model at n=1. By means of quantum Monte Carlo simulations and finite size scaling analysis on LxM ladders, we explore the behavior of "brane" parity operators for L going to infinity from one dimension (i.e., M=1) to two dimensions (i.e., M going to infinity). We confirm the conjecture that, adopting a standard definition, their average value decays to zero in two dimensions also in the insulating phase, evaluating the scaling factor of the "perimeter law" [S.P. Rath et al., Ann. Phys. (N.Y.) 334, 256 (2013)]. Upon introducing a further phase in the brane parity, we show that its expectation value becomes non-zero in the insulator, while still vanishing at the transition to the superfluid phase. These quantities are directly accessible to experimental measures, thus providing an insightful signature of the Mott insulator.

5 pages, 6 figures, updated version

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• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders
• Topological phases in two-legged Heisenberg ladders with alternating interactions
• Brane order and quantum magnetism in modulated anisotropic ladders
• Measuring Non-local Brane Order with Error-corrected Parity Snapshots
• Nonlocal order parameter of pair superfluids
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study
• Fundamental role of nonlocal orders in 1D Extended Bose-Hubbard Model