A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.Comment: 20 pages, 6 figure

Quantum kk-core conduction on the Bethe lattice

Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the geometry also drives the onset of quantum conduction giving rise to a new universality class of Anderson localization transitions.Comment: 12 pgs., 6 fig

Level statistics for quantum kk-core percolation

Quantum $k$-core percolation is the study of quantum transport on $k$-core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. As the bond occupation probability, $p$, is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the lengthscale for the disorder, $l_d$, is much greater than the coherence length, $l_c$, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrate that for $k=3$ the metal-insulator transition (MIT) is discontinuous, suggesting a new universality class of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability $p$ and system size on a Bethe-like lattice. The level spacing analysis suggests that for $k=0$, $p_q$, the quantum percolation critical probability, is greater than $p_c$, the geometrical percolation critical probability, and the transition is continuous. In contrast, for $k=3$, $p_q=p_c$ and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new universality class of disorder-driven quantum MITs.Comment: 8 pages, 11 figure

Destruction of the Mott Insulating Ground State of Ca_2RuO_4 by a Structural Transition

We report a first-order phase transition at T_M=357 K in single crystal Ca_2RuO_4, an isomorph to the superconductor Sr_2RuO_4. The discontinuous decrease in electrical resistivity signals the near destruction of the Mott insulating phase and is triggered by a structural transition from the low temperature orthorhombic to a high temperature tetragonal phase. The magnetic susceptibility, which is temperature dependent but not Curie-like decreases abruptly at TM and becomes less temperature dependent. Unlike most insulator to metal transitions, the system is not magnetically ordered in either phase, though the Mott insulator phase is antiferromagnetic below T_N=110 K.Comment: Accepted for publication in Phys. Rev. B (Rapid Communications

Pinned Low Energy Electronic Excitation in Metal Exchanged Vanadium Oxide Nanoscrolls

We measured the optical properties of mixed valent vanadium oxide nanoscrolls and their metal exchanged derivatives in order to investigate the charge dynamics in these compounds. In contrast to the prediction of a metallic state for the metal exchanged derivatives within a rigid band model, we find that the injected charges in Mn$^{2+}$ exchanged vanadium oxide nanoscrolls are pinned. A low-energy electronic excitation associated with the pinned carriers appears in the far infrared and persists at low temperature, suggesting that the nanoscrolls are weak metals in their bulk form, dominated by inhomogeneous charge disproportionation and Madelung energy effects.Comment: 4 figure

Paired state in an integrable spin-1 boson model

An exactly solvable model describing the low density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.Comment: 6 pages, 1 figure, Revised versio

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.Comment: 4 pages, 4 figure

Field- and pressure-induced phases in Sr4_{4}Ru3_{3}O10_{10}: A spectroscopic investigation

We have investigated the magnetic-field- and pressure-induced structural and magnetic phases of the triple-layer ruthenate - Sr$_{4}$Ru$_{3}$O$_{10}$. Magnetic-field-induced changes in the phonon spectra reveal dramatic spin-reorientation transitions and strong magneto-elastic coupling in this material. Additionally, pressure-dependent Raman measurements at different temperatures reveal an anomalous negative Gruneisen-parameter associated with the B$_{1g}$ mode ($\sim$ 380 cm$^{-1}$) at low temperatures (T $<$ 75K), which can be explained consistently with the field dependent Raman data.Comment: 5 pages, 4 figures final version published in PRL 96, 067004 (2006

Metal-to-insulator transition and magnetic ordering in CaRu_{1-x}Cu_xO_3

CaRuO_3 is perovskite with an orthorhombic distortion and is believed to be close to magnetic ordering. Magnetic studies of single crystal and polycrystalline CaRu_{1-x}Cu_xO_3 (0\le x \le 15 at.%Cu) reveal that spin-glass-like transition develops for x\le 7 at.%Cu and obtained value for effective magnetic moment p_{eff}=3.55 mu_B for x=5 at.% Cu, single crystal, indicates presence of Ru^{5+}. At higher Cu concentrations more complex magnetic behaviors are observed. Electrical resistivity measured on polycrystalline samples shows metal-to-insulator transition (MIT) at 51 K for only 2 at.% Cu. Charge compensation, which is assumed to be present upon Cu^{2+/3+} substitution, induces appearance of Ru^{5+} and/or creation of oxygen vacancies in crystal structure. Since the observed changes in physical properties are completely attributable to the charge compensation, they cannot be related to behaviors of pure compound where no such mechanism is present. This study provides the criterion for "good" chemical probes for studying Ru-based perovskites.Comment: 12 pages, 7 figure

Evolution of Magnetism in Single-Crystal Honeycomb Iridates

We report the successful synthesis of single-crystals of the layered iridate, (Na$_{1-x}$Li$_{x}$)$_2$IrO$_3$, $0\leq x \leq 0.9$, and a thorough study of its structural, magnetic, thermal and transport properties. The new compound allows a controlled interpolation between Na$_2$IrO$_3$ and Li$_2$IrO$_3$, while maintaing the novel quantum magnetism of the honeycomb Ir$^{4+}$ planes. The measured phase diagram demonstrates a dramatic suppression of the N\'eel temperature, $T_N$, at intermediate $x$ suggesting that the magnetic order in Na$_2$IrO$_3$ and Li$_2$IrO$_3$ are distinct, and that at $x\approx 0.7$, the compound is close to a magnetically disordered phase that has been sought after in Na$_2$IrO$_3$ and Li$_2$IrO$_3$. By analyzing our magnetic data with a simple theoretical model we also show that the trigonal splitting, on the Ir$^{4+}$ ions changes sign from Na$_2$IrO$_3$ and Li$_2$IrO$_3$, and the honeycomb iridates are in the strong spin-orbit coupling regime, controlled by \jeff=1/2 moments.Comment: updated version with more dat