# FisMat2017 - Submission - View

**Abstract's title**: Nonlocal Parity Order in the Two-Dimensional Mott Insulator

**Affiliation**: Politecnico di Torino

**Affiliation Address**: Corso Duca degli Abruzzi, 24 - 10129 Torino

**Country**: Italy

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'' parity operator, which by contrast 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, we explore the behavior of brane parity operators from the one-dimensional to the two-dimensional limit. 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 {\it et al.}, Ann. Phys. (N.Y.) {\bf 334}, 256 (2013)]. Upon introducing a further phase in the brane parity, we show that its expectation value is instead finite in the insulator, while vanishing at the transition to the superfluid phase. These quantities are directly accessible to experimental measures, providing an insightful signature of the Mott insulator.