## Presentation

The LPT is based at the University of Toulouse. It has been founded in 1991 and its administrative structure was established in 2003. Before 2003, researchers where rassembled in the Group of Theoretical Physics. This group was hosted by the Laboratoire de Physique Quantique (now LCPQ).

The LPT is member of IRSAMC (The Institute of Research on Complex Atomic and Molecular Systems).

=> There publications before 2003: HAL-LPQ_GPT

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## Last submission

### [hal-02946167] Anomalous U(1) to Z$_q$ cross-over in quantum and classical $q$-state clock models

(23/09/2020)
We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with all-to-all clock transitions with different matrix elements, including the case of transitions restricted to only the nearest clock states. We study the quantum phase transitions in these models with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for $q \ge 4$) to $Z_q$ symmetry of the ordered state. As in classical three-dimensional clock models, the cross-over is governed by a dangerously irrelevant operator with scaling dimension $\Delta_q>3$. We specifically study $q=5,6$ models with different forms of the quantum fluctuations and different anisotropies in the classical models. In all cases studied, we find consistency with the expected classical XY critical exponents related to the conventional order parameter as well as the scaling dimensions $\Delta_q$. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by an angular $Z_q$ symmetric order parameter $\phi_q$, scales with the system size in an unexpected way. As a function of the system size (length) $L$ in the close neighborhood of the critical temperature, $\phi_q \propto L^p$, where the known value of the exponent is $p=2$ in the classical isotropic XY model. In contrast, for strongly anisotropic XY models and all the quantum models studied, we observe $p=3$. For weakly anisotropic models we observe a cross-over from $p=2$ to $p=3$ scaling. The exponent $p$ also directly impacts the exponent $\nu'$ characterizing the divergence of the U(1)length scale $\xi'$ in the thermodynamic limit, according to the general relationship $\nu'=\nu(1+|y_q|/p)$, where $y_q=3-\Delta_q$ is the scaling dimension of the clock field. We present a phenomenological argument for the $p=3$.

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(13/09/2020)