Phases and phase transitions of a disordered quantum clock model

We investigate the effects of quenched randomness on the phase diagram and the phase transitions of the quantum clock model. To this end, we map the model onto a (1+1)-dimensional classical spin Hamiltonian with correlated disorder which we study by means of large-scale Monte-Carlo simulations. For weak randomness, the model features an emerging quasi-long-range ordered XY phase that separates the symmetry-broken long-range ordered phase from the disordered phase. With increasing randomness, the XY phase shrinks and vanishes in a tricritical point. Along all phase boundaries, we characterize the critical behaviors and relate them to the Harris Criterion, strong-disorder renormalization group predictions [1], as well as the properties of disorderd rotor Hamiltonians [2].

[1] T. Senthil and S. N. Majumdar, Phys. Rev. Lett. 76, 3001 (1996).

[2] F. Hrahsheh and T. Vojta, Phys. Rev. Lett. 109,265303 (2012).