Multi-discontinuity algorithm for world-line Monte Carlo simulations

We introduce a novel multi-discontinuity algorithm for efficient global update of world-line configurations in Monte Carlo simulations of interacting quantum systems. This new algorithm is a generalization of the two-discontinuity algorithms introduced in Refs. [N. Prokof'ev, B. Svistunov, and I. Tupitsyn, Phys. Lett. A {\bf 238}, 253 (1998)] and [O. Sylju{\aa}sen and A. Sandvik, Phys. Rev. E {\bf 66}, 046701 (2002)] . This generalization is particularly effective for studying Bose-Einstein condensates (BEC) of composite particles. In particular, we demonstrate the utility of the generalized algorithm by simulating a Hamiltonian for an S=1 anti-ferromagnet with strong uniaxial single-ion anisotropy. The multi-discontinuity algorithm not only solves the freezing problem that arises in this limit, but also allows for efficiently computing the off-diagonal correlator that characterizes a BEC of composite particles.Comment: 5 pages, 5 figure

Efficient Langevin Simulation of Coupled Classical Fields and Fermions

We introduce an efficient Langevin method to study bilinear Fermionic Hamiltonians interacting with classical fields. Our method is suitable for very large systems and offers high accuracy. To demonstrate the method, we study complex non-coplanar chiral spin textures on the triangular Kondo lattice model. We also explore non-equilibrium mesoscale physics such as chiral domain coarsening and Z2 vortex annihilation.Comment: 5 pages, 3 figure

Quantum Tricriticality in Antiferromagnetic Ising Model with Transverse Field: A Quantum Monte-Carlo Study

Quantum tricriticality of a $J_1$-$J_2$ antiferromagnetic Ising model on a square lattice is studied using the mean-field (MF) theory, scaling theory, and the unbiased world-line quantum Monte-Carlo (QMC) method based on the Feynman path integral formula. The critical exponents of the quantum tricritical point (QTCP) and the qualitative phase diagram are obtained from the MF analysis. By performing the unbiased QMC calculations, we provide the numerical evidence for the existence of the QTCP and numerically determine the location of the QTCP in the case of $J_1=J_2$. From the systematic finite-size scaling analysis, we conclude that the QTCP is located at $H_{\rm QTCP}/J_1=3.260(2)$ and $\Gamma_{\rm QTCP}/J_1=4.10(5)$. We also show that the critical exponents of the QTCP are identical to those of the MF theory because the QTCP in this model is in the upper critical dimension. The QMC simulations reveal that unconventional proximity effects of the ferromagnetic susceptibility appear close to the antiferromagnetic QTCP, and the proximity effects survive for the conventional quantum critical point. We suggest that the momentum dependence of the dynamical and static spin structure factors is useful for identifying the QTCP in experiments.Comment: 12 pages, 9 figure

Numerical evidence of quantum melting of spin ice: quantum-classical crossover

Unbiased quantum Monte-Carlo simulations are performed on the nearest-neighbor spin-$\frac{1}{2}$ pyrochlore XXZ model with an antiferromagnetic longitudinal and a weak ferromagnetic transverse exchange couplings, $J$ and $J_\perp$. The specific heat exhibits a broad peak at $T_{\mathrm{CSI}}\sim0.2J$ associated with a crossover to a classical Coulomb liquid regime showing a suppressed spin-ice monopole density, a broadened pinch-point singularity, and the Pauling entropy for $|J_\perp|\ll J$, as in classical spin ice. On further cooling, the entropy restarts decaying for $J_\perp>J_{\perp c}\sim-0.104J$, producing another broad specific heat peak for a crossover to a bosonic quantum Coulomb liquid, where the spin correlation contains both photon and quantum spin-ice monopole contributions. With negatively increasing $J_\perp$ across $J_{\perp c}$, a first-order thermal phase transition occurs from the quantum Coulomb liquid to an XY ferromagnet. Relevance to magnetic rare-earth pyrochlore oxides is discussed.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev. Let

Colossal enhancement of spin-chirality-related Hall effect by thermal fluctuation

The effect of thermal fluctuation on the spin-chirality-induced anomalous Hall effect in itinerant magnets is theoretically studied. Considering a triangular-lattice model as an example, we find that a multiple-spin scattering induced by the fluctuating spins increases the Hall conductivity at a finite temperature. The temperature dependence of anomalous Hall conductivity is evaluated by a combination of an unbiased Monte Carlo simulation and a perturbation theory. Our results show that the Hall conductivity can increase up to $10^3$ times the ground state value; we discuss that this is a consequence of a skew scattering contribution. This enhancement shows the thermal fluctuation significantly affects the spin-chirality-related Hall effect. Our results are potentially relevant to the thermal enhancement of anomalous Hall effect often seen in experiments.Comment: 5 pages, 3 figure

Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations

We study superfluid (SF) states of strongly interacting Bose-Bose mixtures with equal mass and intra-component interaction in optical lattices both in the presence and absence of a barrier potential (BP). We show that the SF order parameters obey the two-component nonlinear Schroedinger equation (NLSE) with not only cubic but also quintic nonlinearity in the vicinity of the first-order transitions to the Mott insulators with even fillings. In the case of no BP, we analyze solitary-wave (SW) solutions of the cubic-quintic NLSE. When the SF state changes from a ground state to a metastable one, a standard dark SW turns into a bubble-like dark SW, which has a non-vanishing density dip and no pi phase kink even in the case of a standing SW. It is shown that the former and latter SW are dynamically unstable against an out-of-phase fluctuation and an in-phase fluctuation, respectively, and the dynamical instabilities are weakened when one approaches the transition point. We find that the size and the inertial mass of the SW diverge at the first-order transition point. We suggest that the divergence of the inertial mass may be detected through measurement of the relation between the velocity and the phase jump of the SW. In the presence of BP, we reveal that when the barrier strength exceeds a certain critical value, the SF state that was metastable without the barrier is destabilized towards complete disjunction of the SF. The presence of the critical BP strength indicates that the strong BP qualitatively changes the criticality near the metastability limit of the SF state. We derive critical behaviors of the density, the compressibility, and the critical current near the metastability limit induced by the BP. It is also found that the relation between the supercurrent and the phase jump across the BP exhibits a peculiar behavior, owing to the non-topological nature of the bubble-like SW.Comment: 25 pages, 19 figure

Lock-in of a Chiral Soliton Lattice by Itinerant Electrons

Chiral magnets often show intriguing magnetic and transport properties associated with their peculiar spin textures. A typical example is a chiral soliton lattice, which is found in monoaxial chiral magnets, such as CrNb$_3$S$_6$ and Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$ in an external magnetic field perpendicular to the chiral axis. Here, we theoretically investigate the electronic and magnetic properties in the chiral soliton lattice by a minimal itinerant electron model. Using variational calculations, we find that the period of the chiral soliton lattice can be locked at particular values dictated by the Fermi wave number, in stark contrast to spin-only models. We discuss this behavior caused by the spin-charge coupling as a possible mechanism for the lock-in discovered in Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$. We also show that the same mechanism leads to the spontaneous formation of the chiral soliton lattice even in the absence of the magnetic field.Comment: 4 pages, 4 figure

Quantum tricriticality at the superfluid-insulator transition of binary Bose mixtures

Quantum criticality near a tricritical point (TCP) is studied in the two-component Bose-Hubbard model on square lattices. The existence of quantum TCP on a boundary of superfluid-insulator transition is confirmed by quantum Monte Carlo simulations. Moreover, we analytically derive the quantum tricritical behaviors on the basis of an effective field theory. We find two significant features of the quantum tricriticality, that are the chemical potential dependence of the superfluid transition temperature and a strong density fluctuation. We suggest that these features are directly observable in existing experimental setups of Bose-Bose mixtures in optical lattices.Comment: 5+10 pages, 5 figure

Antiferromagnetic Kitaev Interactions in Polar Spin-Orbit Mott Insulators

A bond-directional anisotropic exchange interaction, called the Kitaev interaction, is a promising route to realize quantum spin liquids. The Kitaev interactions were found in Mott insulators with the strong spin-orbit coupling, in the presence of quantum interference between indirect electron transfers. Here we theoretically propose a different scenario by introducing a polar structural asymmetry that unbalances the quantum interference. We show that the imbalance activates additional exchange processes and gives rise to a dominant antiferromagnetic Kitaev interaction, in stark contrast to the conventional ferromagnetic ones. We demonstrate by ab initio calculations that polar Ru trihalides with multiple anions, $\alpha$-RuH$_{3/2}X_{3/2}$ ($X$=Cl and Br), exhibit the antiferromagnetic Kitaev interaction whose magnitude is several times larger compared to existing candidates. Our proposal opens the way for materializing the Kitaev spin liquids in unexplored parameter regions.Comment: 8 pages, 6 figures, 4 table

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii-Moriya interaction

Monoaxial chiral magnets can form a noncollinear twisted spin structure called the chiral helimagnetic state. We study magnetic properties of such a chiral helimagnetic state, with emphasis on the effect of itinerant electrons. Modeling a monoaxial chiral helimagnet by a one-dimensional Kondo lattice model with the Dzyaloshinskii--Moriya interaction, we perform a variational calculation to elucidate the stable spin configuration in the ground state. We obtain a chiral helimagnetic state as a candidate for the ground state, whose helical pitch is modulated by the model parameters: the Kondo coupling, the Dzyaloshinski--Moriya interaction, and electron filling.Comment: 3 pages, 2 figure