Investigated Models

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Kazuhiro Sano, Yoshiaki Ōno

We examine effective interactions of the 1D d-p model mapped to a typical one-dimensional(1D) model such as the Hubbard model or the t-J model by the numerical diagonalization method combined with the Luttinger liquid theory. Analysis of the effective coupling constants of the mapped model gives the relationship between these models without ambiguity. We find that the renormalized interaction is relatively weak, though the repulsion of the d-p model at Cu-sites is very strong. We also find that the d-p model corresponds to not the t-J model but the Hubbard model for wide range of the parameters. It suggests that the Hubbard model is more favorable than the t-J model as a effective model of the d-p model in the low energy limit.

Leon Hostetler, Jin Zhang, Ryo Sakai +3 more

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma=0$ and to the extended $q$-state clock model when $\gamma\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

Leon Hostetler, Jin Zhang, Ryo Sakai +3 more

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $γ$) that reduces to the $XY$ model when $γ=0$ and to the extended $q$-state clock model when $γ\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

Cecilia Flori