I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings J J , the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude t t . The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J| k B T / | J | , and on the ratio of the spin coupling to the hopping J/t J / t . I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.
I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings J J , the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude t t . The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J| k B T / | J | , and on the ratio of the spin coupling to the hopping J/t J / t . I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.
I unveil an emergent localization phenomenon pertaining to the motion of a dopant in a thermal spin lattice. This is rendered localized by thermal spin fluctuations, whereby it is in stark constrast to the intrinsic origin of Anderson localization for quenched disorder. The system of interest consists of spin- 1 / 2 particles organized in a two-leg ladder with nearest-neighbor Ising interactions J . The motion of a hole—the dopant—is initialized by suddenly removing a spin from the thermal spin ensemble, which then moves along the ladder via nearest-neighbor hopping t . I find that the hole remains for all values of J / t and for nonzero temperatures. The origin is an effective disorder potential seen by the hole and induced by thermal spin fluctuations. Its length scale is found to match with the underlying spin-spin correlation length at low temperatures. For ferromagnetic couplings ( J < 0 ), the associated localization length of the hole increases with decreasing temperature and becomes proportional to the correlation length at low temperatures, asymptotically delocalizing at low temperatures. For antiferromagnetic couplings ( J > 0 ), there is a smooth crossover between thermal localization at high temperatures to localization driven by the antiferromagnetic order at low temperatures. At infinite temperatures, the dynamics becomes independent of the sign of the spin coupling, whereby the localization length is a universal function of | J | / t , diverging as ( t / J ) 2 for | J | ≪ t . Finally, I analyze a setup with Rydberg-dressed atoms, which naturally realizes finite-range Ising interactions, accessible in current experimental setups. I show that the discovered localization phenomenon can be probed on experimentally accessible length- and timescales, providing a strong testing ground for my predictions. Published by the American Physical Society 2024
We consider the thermal phase transition from a paramagnetic to a stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1<0 (nearest neighbor, ferromagnetic) and J2>0 (second neighbor, antiferromagnetic). The striped phase breaks a Z4 symmetry and is stabilized at low temperatures for g=J2/∣J1∣>1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [Phys. Rev. Lett. 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J1-J2 model has a line of very weak first-order phase transitions in the whole region 1/2<g<g∗, where ${g}^{*}=0.67\ifmmode\pm\else\textpm\fi{}0.01$. Thereafter, the transitions from g=g∗ to $g\ensuremath{\rightarrow}\ensuremath{\infty}$ are continuous and can be fully mapped, using universality arguments, to the critical line of the well-known Ashkin-Teller model from its four-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g∗ in the J1-J2 model. The continuous transitions near g∗ can therefore be mistaken for first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g>1/2. Most of our conclusions are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.
The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg t − J ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is for all investigated temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [, ]. In the presence of spin-exchange processes at rate α , the dopant diffuses with a diffusion coefficient, D h , depending nonmonotonically on α . It initially increases linearly as D h ∝ α for α ≪ 1 before dropping off as α − 1 for α > 1 . Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient D h follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.
We investigate, using the density-matrix renormalization group, the evolution of the Nagaoka state with ${t}^{\ensuremath{'}}$ hopping that frustrates the hole kinetic energy in the $U=\ensuremath{\infty}$ Hubbard model on the square and anisotropic triangular lattices. We find that the Nagaoka ferromagnet survives up to a rather small ${t}_{c}^{\ensuremath{'}}/t\ensuremath{\sim}0.2.$ At this critical value, there is a transition to an antiferromagnetic phase that depends on the lattice: a Q=(Q,0) spiral order, which continuously evolves with ${t}^{\ensuremath{'}}$, for the triangular lattice and the usual $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ N\'eel order for the square lattice. Remarkably, the local magnetization takes its classical value for all considered ${t}^{\ensuremath{'}}$ (${t}^{\ensuremath{'}}/t\ensuremath{\le}1$). Our results show that the recently found classical kinetic antiferromagnetism, a perfect counterpart of Nagaoka ferromagnetism, is a generic phenomenon in these kinetically frustrated electronic systems.
The model of localized fermions on the triangular lattice is analyzed in means of the Monte Carlo simulations in the grand canonical ensemble. The Hamiltonian of the system has a form of the extended Hubbard model (at the atomic limit) with nearest-neighbor Ising-like magnetic J interactions and onsite Coulomb U interactions. The model is investigated for both signs of J, arbitrary U interaction, and arbitrary chemical potential μ (or, equivalently, arbitrary particle concentration n). Based on the specific heat capacity and sublattice magnetization analyses, the phase diagrams of the model are determined. For ferromagnetic case (J<0), the transition from the ordered phase (which is a standard ferromagnet and can be stable up to k_{B}T/|J|≈0.61) is found to be second order (for sufficiently large temperatures k_{B}T/|J|≳0.2) or first order (for -1<U/|J|<-0.65 at the half-filling, i.e., n=1). In the case of J>0, the ordered phase occurs in a range of -1/2<U/|J|<0 (for n=1), while for larger U the state with short-range order is also found (also for n≠1). The ordered phase is characterized by an antiferromagnetic arrangement of magnetic moments in two sublattices forming the hexagonal lattice. The transition from this ordered phase, which is found also for μ≠0 (n≠1) and U/|J|>-1/2 is always second order for any model parameters. The ordered phase for J>0 can be stable up to k_{B}T/|J|≈0.06.
Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.