Nonlocal 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 nonzero value of a nonlocal "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 L×M ladders, we explore the behavior of "brane" parity operators from one dimension (i.e., M=1 and L→∞) to two dimensions (i.e., M→∞ and L→∞). 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. (Berlin) 334, 256 (2013)ANPYA20003-380410.1016/j.aop.2013.04.006]. Upon introducing a further phase in the brane parity, we show that its expectation value becomes nonzero 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.

Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders

“…In this respect, recent studies [17] confirm that the insulating state at half filling, which is the counterpart of the LE phase in the charge sector, has the same microscopic structure passing from the one to the two dimensional case by increasing the number of legs M of a ladder. A similar behavior has been also observed within the bosonic Hubbard model [18]. The appearance of the insulating phase is signaled by the hidden ordering of a charge-parity operator, which has to be properly normalized to M in order to remain finite up to the 2D limit [18].…”

“…A similar behavior has been also observed within the bosonic Hubbard model [18]. The appearance of the insulating phase is signaled by the hidden ordering of a charge-parity operator, which has to be properly normalized to M in order to remain finite up to the 2D limit [18].…”

“…The natural extension to a ladder would be a brane of parities, that includes a further summation over the sites of the rung. Similarly to what has been proposed for describing the Mott phase on ladders in the charge channel [17,18], we can define:…”

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ 2 lattice gauge theories

“…Similarly to the analysis in Refs. [48][49][50], this transition can be captured by the parity operator…”

Hidden magnetism in periodically modulated one dimensional dipolar fermions

“…Haldane-like antiferromagnetic orders [1,41] of holon-doublon ( c n = ) or up-down spins ( s n = ). Generalization to higher dimension has also been considered recently [53].…”