We study an optical Raman square lattice with $\mathrm{U}(1)$ synthetic gauge flux to show a chiral spin liquid (CSL) phase for cold atoms based on slave-rotor and spinon mean-field theories, respectively. An effective U(1) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find the CSL phase at a strong on-site Fermi Hubbard interacting regime. For large value of Hubbard interaction, we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that the CSL phase is stabilized in the case of strong magnetic frustration. Two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.We study an optical Raman square lattice with $\mathrm{U}(1)$ synthetic gauge flux to show a chiral spin liquid (CSL) phase for cold atoms based on slave-rotor and spinon mean-field theories, respectively. An effective U(1) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find the CSL phase at a strong on-site Fermi Hubbard interacting regime. For large value of Hubbard interaction, we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that the CSL phase is stabilized in the case of strong magnetic frustration. Two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.

arXiv:2306.16466Physical review. B./Physical review. BApr 2, 20243 citations

Mean-field expansion for spin models with medium-range interactions

Andrea Pelissetto C, Paolo Rossi, Ettore Vicari

arXiv:cond-mat/9903410Nuclear Physics BAug 1, 199918 citations

Pre-relaxation in weakly interacting models

Bruno Bertini, Maurizio Fagotti

We consider time evolution in models close to integrable points with hidden symmetries that generate infinitely many local conservation laws that do not commute with one another. The system is expected to (locally) relax to a thermal ensemble if integrability is broken, or to a so-called generalised Gibbs ensemble if unbroken. In some circumstances expectation values exhibit quasi-stationary behaviour long before their typical relaxation time. For integrability-breaking perturbations, these are also called pre-thermalisation plateaux, and emerge e.g. in the strong coupling limit of the Bose–Hubbard model. As a result of the hidden symmetries, quasi-stationarity appears also in integrable models, for example in the Ising limit of the XXZ model. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin- chain with additional perturbations that break integrability. One of the most intriguing results of the analysis is the appearance of persistent oscillatory behaviour. To unravel its origin, we study in detail a toy model: the transverse-field Ising chain with an additional nonlocal interaction proportional to the square of the transverse spin per unit length (2013 Phys. Rev. Lett . 111 197203). Despite being nonlocal, this belongs to a class of models that emerge as intermediate steps of the mean-field mapping and shares many dynamical properties with the weakly interacting models under consideration.We consider time evolution in models close to integrable points with hidden symmetries that generate infinitely many local conservation laws that do not commute with one another. The system is expected to (locally) relax to a thermal ensemble if integrability is broken, or to a so-called generalised Gibbs ensemble if unbroken. In some circumstances expectation values exhibit quasi-stationary behaviour long before their typical relaxation time. For integrability-breaking perturbations, these are also called pre-thermalisation plateaux, and emerge e.g. in the strong coupling limit of the Bose–Hubbard model. As a result of the hidden symmetries, quasi-stationarity appears also in integrable models, for example in the Ising limit of the XXZ model. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin- chain with additional perturbations that break integrability. One of the most intriguing results of the analysis is the appearance of persistent oscillatory behaviour. To unravel its origin, we study in detail a toy model: the transverse-field Ising chain with an additional nonlocal interaction proportional to the square of the transverse spin per unit length (2013 Phys. Rev. Lett . 111 197203). Despite being nonlocal, this belongs to a class of models that emerge as intermediate steps of the mean-field mapping and shares many dynamical properties with the weakly interacting models under consideration.

arXiv:1501.07260Journal of Statistical Mechanics Theory and ExperimentJul 9, 201575 citations

Mean-field theory and statistical treatment of residual interactions

Sakir Ayik B

The European Physical Journal AJun 1, 198087 citations

Universality and tricritical behavior of three-dimensional Ising models with two- and four-spin interactions

Ole G. Mouritsen, Svend J. Knak Jensen, B. Frank

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- ( ${J}_{2}$ ) and four - ( ${J}_{4}$ ) spin interactions. In the limit ${J}_{2}=0$ the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (${J}_{2}$) and four - (${J}_{4}$) spin interactions. In the limit ${J}_{2}=0$ the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.

Physical review. B, Condensed matterJul 1, 198127 citations

Mean field solution of the general spin Blume-Capel model

J. A. Plascak, J. G. Moreira, F.C. SāBarreto

Physics Letters AFeb 1, 1993123 citations

We study an optical Raman square lattice with

\mathrm{U}(1)

synthetic gauge flux to show a chiral spin liquid (CSL) phase for cold atoms based on slave-rotor and spinon mean-field theories, respectively. An effective U(1) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find the CSL phase at a strong on-site Fermi Hubbard interacting regime. For large value of Hubbard interaction, we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that the CSL phase is stabilized in the case of strong magnetic frustration. Two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (

{J}_{2}

) and four - (

{J}_{4}

) spin interactions. In the limit

{J}_{2}=0

the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.