Monte Carlo simulation of an strongly coupled XY model in three dimensions

Many experimental studies, over the past two decades, have constantly reported a novel critical behavior for the transition from Smectic-A phase of liquid crystals to Hexatic-B phase with non-XY critical exponents. However according to symmetry arguments this transition must belong to XY universality class. Using an optimized Monte Carlo simulation technique based on multi-histogram method, we have investigated phase diagram of a coupled XY model, proposed by Bruinsma and Aeppli (PRL {\bf 48}, 1625 (1982)), in three dimensions. The simulation results demonstrate the existence of a tricritical point for this model, in which two different orderings are established simultaneously. This result verifies the accepted idea the large specific heat anomaly exponent observed for SmA-HexB transition could be due to the occurrence of this transition in the vicinity of a tricritical poin

Comparing different modes of quantum state transfer in a XXZ spin chain

We study the information transferring ability of a spin-1/2 XXZ Hamiltonian for two different modes of state transfer, namely, the well studied attaching scenario and the recently proposed measurement induced transport. The latter one has been inspired by recent achievements in optical lattice experiments for local addressability of individual atoms and their time evolution when only local rotations and measurements are available and local control of the Hamiltonian is very limited. We show that while measurement induced transport gives higher fidelity for quantum state transfer around the isotropic Heisenberg point, its superiority is less pronounced in non-interacting free fermionic XX phase. Moreover, we study the quality of state transfer in the presence of thermal fluctuations and environmental interactions and show that measurement scheme gives higher fidelity for low temperatures and weak interaction with environment.Comment: 6 pages, 5 figure

Exactly solvable spin chain models corresponding to BDI class of topological superconductors

We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes which are in turn related to an integer winding number. We further find a general relation between the winding number and the number of Majorana fermions at the ends of an open chain. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification (A. Altland, M. R. Zirnbauer, Phys. Rev. B (1997) 55 1142) of topological superconductors. We show that time reversal (TR) symmetry of the spin variables translates into a peculiar particle-hole transformation in the language of Jordan-Wigner (JW) fermions that is accompanied by a {\pi} shift in the wave vector ($\pi$PH). Presence of $\pi$PH symmetry restricts the winding number of TR symmetric extensions of XY to odd integers. The {\pi}PH operator may serve in further detailed classification of topological superconductors.Comment: title modified, size reduce

Quantum phase diagram of J1−J2J_1-J_2 Heisenberg S=1/2S=1/2 antiferromagnet in honeycomb lattice: a modified spin wave study

Using modified spin wave (MSW) method, we study the $J_1-J_2$ Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For symmetric $S=1/2$ model, with the same couplings for all the equivalent neighbors, we find three phase in terms of frustration parameter ${\bar\alpha=J_2/J_1}$: (1) a commensurate collinear ordering with staggered magnetization (N{\'e}el.I state) for $0\leq{\bar\alpha}\lesssim 0.207$ , (2) a magnetically gapped disordered state for $0.207\lesssim{\bar\alpha}\lesssim 0.369$, preserving all the symmetries of the Hamiltonian and lattice, hence by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (N{\'e}el.II state), for $0.396\lesssim{\bar\alpha}\leq 1$. We also explore the phase diagram of distorted $J_1-J_2$ model with $S=1/2$. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal (VBC) phase in addition to the previously three phases found for undistorted model

Diversity enhanced synchronization in a small-world network of phase oscillators

In this work, we study the synchronization of a group of phase oscillators (rotors) in the small-world (SW) networks. The distribution of intrinsic angular frequency of the rotors are given by a Lorenz probability density function with zero mean and the width $\gamma$, and their dynamics are governed by the Kuramoto model. We find that the partially synchronized states of identical oscillators (with $\gamma=0)$ in the SW network, become more synchronized when $\gamma$ increases up to an optimum value, where the synchrony in the system reaches a maximum and then start to fall. We discuss that the reason for this "{\it diversity enhanced synchronization}" is the weakening and destruction of topological defects presented in the partially synchronized attractors of the Kuramoto model in SW network of identical oscillators. We also show that introducing the diversity in the intrinsic frequency of the rotary agents makes the fully synchronized state in the SW networks, more fragile than the one in the random networks.Comment: The paper needs a major revisio

Noise-induced Synchronization in Small World Network of Phase Oscillators

A small-world network (SW) of similar phase oscillators, interacting according to the Kuramoto model is studied numerically. It is shown that deterministic Kuramoto dynamics on the SW networks has various stable stationary states. This can be attributed to the "defect patterns" in a SW network which is inherited to it from deformation of "helical patterns" in its parent regular one. Turning on an uncorrelated random force, causes the vanishing of the defect patterns, hence increasing the synchronization among oscillators for intermediate noise intensities. This phenomenon which is called "stochastic synchronization" generally observed in some natural networks like brain neuronal network.Comment: 6 page

The effects of noise and time delay on the synchronization of the Kuramoto model in small-world networks

We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of each node. For this model, similar to the constant coupling studied before, we find the existence of various attractors corresponding to the different defect patterns and also the noise enhanced synchronization when driven by an external uncorrelated white noise. We also investigate the synchronization of the model with homogenous time-delay in the phase couplings. For a given intrinsic frequency and coupling constant, upon varying the time delay we observe the existence a partially synchronized state with defect patterns which transforms to an incoherent phase characterized by randomly phase locked states. By further increasing of the time delay, this phase again undergoes a transition to another patterned partially synchronized state. We show that the transition between theses phases are discontinuous and moreover in each phase the average frequency of the oscillators decreases by increasing the time delay and shows an upward jump at the transition points.Comment: 8 pages, 10 figure

Zero Temperature Phase Diagram of the Classical Kane-Mele-Heisenberg Model

The classical phase diagram of the Kane-Mele-Heisenberg model is obtained by three complementary methods: Luttinger-Tisza, variational minimization, and the iterative minimization method. Six distinct phases were obtained in the space of the couplings. Three phases are commensurate with long-range ordering, planar N{\'e}el states in horizontal plane (phase.I), planar states in the plane vertical to the horizontal plane (phase.VI) and collinear states normal to the horizontal plane (phase.II). However the other three, are infinitely degenerate due to the frustrating competition between the couplings, and characterized by a manifold of incommensurate wave-vectors. These phases are, planar helical states in horizontal plane (phase.III), planar helical states in a vertical plane (phase.IV) and non-coplanar states (phase.V). Employing the linear spin-wave analysis, it is found that the quantum fluctuations select a set of symmetrically equivalent states in phase.III, through the quantum order-by-disorder mechanism. Based on some heuristic arguments is argued that the same scenario may also occur in the other two frustrated phases VI and V.Comment: 13 page

Perfect quantum excitation energy transport via single edge perturbation in a complete network

We consider quantum excitation energy transport (EET) in a network of two-state nodes in the Markovian approximation by employing the Lindblad formulation. We find that EET from an initial site, where the excitation is inserted to the sink, is generally inefficient due to the inhibition of transport by localization of the excitation wave packet in a symmetric, fully-connected network. We demonstrate that the EET efficiency can be significantly increased up to %100 by perturbing hopping transport between the initial node and the one connected directly to the sink, while the rate of energy transport is highest at a finite value of the hopping parameter. We also show that prohibiting hopping between the other nodes which are not directly linked to the sink does not improve the efficiency. We show that external dephasing noise in the network plays a constructive role for EET in the presence of localization in the network, while in the absence of localization it reduces the efficiency of EET.Comment: 6 pages, 6 figure

Valence Bond Phases in S=1/2S=1/2 Kane-Mele-Heisenberg Model

The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical limit~\cite{zare}, contains disordered regions in the coupling space, as the result of to competition among different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phase in the quantum limit, for a $S=1/2$. Employing exact diagonalization (ED) in $S_z$ and nearest neighbor valence bond (NNVB) bases, bond and plaquette valence bond mean field theories, We show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystal(PVBC) and staggered dimerized (SD) phases.Comment: 8 pages, 9 figures, 52 reference