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Unconventional U(1) to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Z</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:math> crossover in quantum and classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math> -state clock models
We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with all-to-all clock transitions with different choices for the matrix elements. We study the quantum phase transitions in these models using quantum Monte Carlo simulations and finite-size scaling, with the aim of characterizing the crossover from emergent U(1) …