Fig. 4 Characterizing phase transitions of matter coupled to a ℤ2 gauge field in a two-leg ladder. Characterizing phase transitions of matter coupled to.

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Fig. 4 Characterizing phase transitions of matter coupled to a ℤ2 gauge field in a two-leg ladder. Characterizing phase transitions of matter coupled to a ℤ2 gauge field in a two-leg ladder. We consider the Hamiltonian from Eq. 24. (A) In the charge sector, we observe transitions from an SF state, characterized by a vanishing parity correlator Op(Lx/2 → ∞ ) → 0 in the thermodynamic limit, to an insulating rung-Mott state at the commensurate filling Na = Lx, characterized by Op(Lx/2 → ∞ ) > 0 and exponentially decaying correlations. Here, we present exemplary results for t∼ya/t∼xa=3 and t∼yf/t∼xa=0.54. (B) In the gauge sector, we find a transition from a disordered phase, where the ℤ2 electric field dominates, to a phase where the ℤ2 magnetic field dominates. In the second case, the order parameter 〈τ^〈i,j〉yz〉≠0 corresponds to a spontaneously broken global ℤ2 symmetry (23). In the two phases, the corresponding vison excitations of the ℤ2 gauge field (C) have different characteristics. The numerical results in (A) [respectively (B)] are obtained by considering periodic boundary conditions (respectively Lx = 96 rungs with open boundaries). (D) Analogs of Wilson loops W^(d) in the two-leg ladder are string operators of visons. Luca Barbiero et al. Sci Adv 2019;5:eaav7444 Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).