Scaling of the disorder operator at (2 +1 )d U(1) quantum criticality
Abstract
We study disorder operator, defined as a symmetry transformation applied to a finite region, across a continuous quantum phase transition in (2 +1 )d . We show analytically that, at a conformally invariant critical point with U(1) symmetry, the disorder operator with a small U(1) rotation angle defined on a rectangle region exhibits powerlaw scaling with the perimeter of the rectangle. The exponent is proportional to the current central charge of the critical theory. Such a universal scaling behavior is due to the sharp corners of the region and we further obtain a general formula for the exponent when the corner is nearly smooth. To probe the full parameter regime, we carry out systematic computation of the U(1) disorder parameter in the square lattice BoseHubbard model across the superfluidinsulator transition with largescale quantum Monte Carlo simulations, and confirm the presence of the universal corner correction. The exponent of the corner term determined from numerical simulations agrees well with the analytical predictions.
 Publication:

Physical Review B
 Pub Date:
 August 2021
 DOI:
 10.1103/PhysRevB.104.L081109
 arXiv:
 arXiv:2101.10358
 Bibcode:
 2021PhRvB.104h1109W
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 7 pages, 5 figures