Quantum Ising model on the frustrated square lattice

Effects of third-neighbor interactions on the frustrated quantum Ising model

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Metastable states in the J_{1}-J_{2} Ising model

We study the J_{1}-J_{2} Ising model on the square lattice using the random local field approximation (RLFA) and Monte Carlo (MC) simulations for various values of the ratio p=J_{2}/|J_{1}| with antiferromagnetic coupling J_{2}, ensuring spin frustration. RLFA predicts metastable states with zero order parameter (polarization) at low temperature for p∈(0,1). This is supported by our MC simulations, in which the system relaxes into metastable states with not only zero, but also with arbitrary polarization, depending on its initial value, external field, and temperature. We support our findings by calculating the energy barriers of these states at the level of individual spin flips relevant to the MC calculation. We discuss experimental conditions and compounds appropriate for experimental verification of our predictions.

Tensor network simulation for the frustrated J_{1}-J_{2} Ising model on the square lattice

By using extensive tensor network calculations, we map out the phase diagram of the frustrated J_{1}-J_{2} Ising model on the square lattice. In particular, we focus on the cases with controversy in the phase diagram, especially the stripe transition in the regime g=|J_{2}/J_{1}|>1/2 (J_{2}>0,J_{1}<0). While recent studies claimed that the phase transition is of first order when 1/2<g<g^{*} (with the smallest g^{*} being 0.67), our simulations suggest that if there is such a first-order region, it is smaller than those found in earlier studies by other methods. Combining with the analysis of critical properties, we provide evidence that the classical J_{1}-J_{2} model evolves continuously from two decoupled Ising models (g→∞ with central charge c=1) to a point belonging to the tricritical Ising universality class (with c=0.7) as g decreases to g^{*}≃0.54.

Thermally driven state in a spin-1 model with competing interactions

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.

Transverse field effects on the competition between antiferromagnetic and cluster spin-glass phases

We investigate a disordered cluster Ising antiferromagnet in the presence of a transverse field. By adopting a replica cluster mean-field framework, we analyze the role of quantum fluctuations in a model with competing short-range antiferromagnetic and intercluster disordered interactions. The model exhibits paramagnetic (PM), antiferromagnetic (AF), and cluster spin-glass (CSG) phases, which are separated by thermal and quantum phase transitions. A scenario of strong competition between AF and CSG unveils a number of interesting phenomena induced by quantum fluctuations, including a quantum PM state and quantum driven criticality. The latter occurs when the thermally driven PM-AF discontinuous phase transition becomes continuous at strong transverse fields. Analogous phenomena have been reported in a number of systems, but a description of underlying mechanisms is still required. Our results indicate that quantum driven criticality can be found in a highly competitive regime of disordered antiferromagnets, which is in consonance with recent findings in spin models with competing interactions.

Frustration-induced supersolid phases of extended Bose-Hubbard model in the hard-core limit

We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize thed-wave superfluid, which shares the same pairing symmetry with high-Tcmaterials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.

Frustration and inhomogeneous environments in relaxation of open chains with Ising-type interactions

Frustration can contribute to very slow relaxation times in large open chains, as in spin glasses and in biopolymers. However, frustration may not be sufficient to produce broken ergodicity in finite systems. Here we employ a system-plus-reservoir approach to investigate how strongly inhomogeneous environments and frustration compete in the relaxation of finite open chains. We find a sufficient condition for our inhomogeneous environments to break ergodicity. We use the microscopic model to derive a Markovian quantum master equation for a generic chain with ultrastrong intrachain couplings. We show that this microscopic model avoids a spurious broken ergodicity we find in the phenomenological model. We work out an explicit example of broken ergodicity due to the inhomogeneous environment of an unfrustrated spin chain as far as simulating a recent experiment on protein denaturation (where environment inhomogeneity is especially relevant). We finally show that an inhomogeneous environment can mitigate the effects of frustration-induced degeneracies.