Quantum Rotor Research Articles

Phase coherence in the Josephson-coupled stack of planar spin-charge separated condensates and the interlayer mechanism of high-Tcsuperconductivity

A system of spin-charge separated stack of two-dimensional condensates interacting via the interplane Josephson coupling E⊥J is studied in the only quantum rotor representation as a model of layered high-T c cuprates. Using de Gennes mapping onto S=1 pseudospin model the phase diagram is computed as a function of E⊥J which exhibits an intricate interplay between charge (e) and pair (2e) condensation. Experimental implications of the model pertaining to the condensation energy E c o n d , the behavior of the ratio E⊥ J/E c o n d , and the flux quantization are discussed.

REMARKS ON SYMMETRIES OF GENERALIZED ROTOR SPACE

We propose methods of analysis of the symmetries of the rotor space. A few examples of the point symmetries and their consequences for the state space of the quantum rotors are shortly considered.

Dielectric anomaly in coupled rotor systems

The correlated dynamics of coupled quantum rotors carrying electric dipole moment is theoretically investigated. The energy spectra of coupled rotors as a function of dipolar interaction energy is analytically solved. The calculated dielectric susceptibilities of the system show the peculiar temperature dependence different from that of isolated rotors.

Variational ansatz for the superfluid Mott-insulator transition in optical lattices

We develop a variational wave function for the ground state of a one-dimensional bosonic lattice gas. The variational theory is initially developed for the quantum rotor model and later on extended to the Bose- Hubbard model. This theory is compared with quasi-exact numerical results obtained by Density Matrix Renormalization Group (DMRG) studies and with results from other analytical approximations. Our approach accurately gives local properties for strong and weak interactions, and it also describes the crossover from the superfluid phase to the Mott-insulator phase.

Magnetic Quantum Rotors

A new quantum system, magnetic quantum rotors, is presented. A magnetic rotor—a rotor possessing nonzero spin—is exemplified by the oxygen molecule. Of the exchange, spin-orbital, and spin-figure interactions contributed by the spin degree of freedoms only the latter was taken into consideration in this study. Phase diagrams of magnetic quantum linear rotors in a crystal field are studied for a system where all angular momentum states are allowed (all-J system) and for one where angular momentum is restricted to have odd values (odd-J system). It is found that depending on the crystal field and the value of the spin-figure coupling constant the orientational phase transition line can display a set of critical points (one, two, three or none in the case of the all-J systems and one, two or no critical points in the case of the odd-J systems) which are responsible for the topology of the phase diagram.

Absence of phase stiffness in the quantum rotor phase glass

We analyze here the consequence of local rotational-symmetry breaking in the quantum spin (or phase) glass state of the quantum random rotor model. By coupling the spin glass order parameter directly to a vector potential, we are able to compute whether the system is resilient (that is, possesses a phase stiffness) to a uniform rotation in the presence of random anisotropy. We show explicitly that the O(2) vector spin glass has no electromagnetic response indicative of a superconductor at mean-field and beyond, suggesting the absence of phase stiffness. This result confirms our earlier finding [Phys. Rev. Lett. 89, 027001 (2002)] that the phase glass is metallic, due to the main contribution to the conductivity arising from fluctuations of the superconducting order parameter. In addition, our finding that the spin stiffness vanishes in the quantum rotor glass is consistent with the absence of a transverse stiffness in the Heisenberg spin glass found by Feigelman and Tsvelik [Sov. Phys. JETP 50, 1222 (1979)].

CH3NH3 + as a quantum and classical rotor

Spin-lattice relaxation time T 1 is determined for protons in three polycrystals (CH3NH3)5Bi2Cl11, (CD3NH3)5Bi2Cl11 and (CH3ND3)5Bi2Cl11. The temperature dependence of the relaxation times obtained for (CH3NH3)5Bi2Cl11 and (CD3NH3)5Bi2Cl11 are interpreted as a result of correlated motions of the three-proton groups of the monomethylammonium cation. 2H NMR lines of (CD3NH3)3Sb2Br9 have been recorded between 5 K and 291 K using solid echo method. The 2H NMR line shape analysis shows that characteristic shape of tunnelling methyl group appears at about 25 K and coming down with temperature up to 5 K is more distinct. From theoretical calculation, it has been found that in the quadrupolar constants is 161.3 kHz and tunnelling frequency is above 3 MHz.

Quantum effects in the thermal conductivity of solid krypton–methane solutions

The dynamic interaction of a quantum rotor with its crystalline environment has been studied by measurement of the thermal conductivity of the Kr1−c(CH4)c solid solutions at c=0.05–0.75 in the temperature region 2–40 K. The thermal resistance of the solutions was mainly determined by the resonance scattering of phonons on CH4 molecules with the nuclear spin I=1 (the nuclear spin of the T species). The influence of the nuclear spin conversion on the temperature dependence of the thermal conductivity κ(T) leads to a well-defined minimum on κ(T). The temperature of the minimum depends on the CH4 concentration. It was shown that the nonmonotonic increase of the anisotropic molecular field with the CH4 concentration is caused by a compensation effect due to corrections in the mutual orientations of the neighboring rotors at c κ>0.5. The temperature dependence or Kr1−c(CH4)c is described within the Debye model of thermal conductivity taking into account the lower limit of the phonon mean free path. It is shown that phonon–rotation coupling is responsible for the anomalous temperature dependence of the thermal resistance at varying temperature. It increases strongly when the quantum character of the CH4 rotation at low temperatures changes to a classical one at high temperatures. A thermal conductivity jump (a sharp increase in κ(T) within a narrow temperature range) was also observed. The temperature position of the jump varies from 9.7 to 8.4 K when the CH4 concentration changes from 0.25 to 0.45.

Directed geometrical worm algorithm applied to the quantum rotor model.

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm the Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part, is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore, we show how correlation functions C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and undirected geometrical worm algorithms. Results for autocorrelation times and Green's functions are presented for the quantum rotor model.

SO(5) superconductor in a Zeeman magnetic field

In this paper we present calculations of the SO(5) quantum rotor theory of high- T c superconductivity in Zeeman magnetic field. We use the spherical approach for five-component quantum rotors in three-dimensional lattice to obtain formula for the specific heat and present temperature dependencies of this quantity for different values of magnetic field. Our results are in qualitative agreement with relevant experiments on high- T c cuprates.

Cluster Monte Carlo algorithm for the quantum rotor model.

We propose a highly efficient "worm"-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with mu=0, the algorithm yields high- precision estimates for the critical point K(c)=0.333 05(5) and the correlation length exponent nu=0.670(3). For the disordered case, mu=1 / 2+/-1 / 2, we find nu=1.15(10).

Phase phonon spectrum and melting in a quantum rotor model with diagonal disorder

We study the zero-temperature ($T = 0$) quantum rotor model with on-site disorder in the charging energy. Such a model may serve as an idealized Hamiltonian for an array of Josephson-coupled small superconducting grains, or superfluid $^4$He in a disordered environment. In the approximation of small-amplitude phase fluctuations, the Hamiltonian maps onto a system of coupled harmonic oscillators with on-site disorder. We study the effects of disorder in this harmonic regime, using the coherent potential approximation (CPA), obtaining the density of states and the lifetimes of the spin-wave-like excitations for several choices of the parameters which characterize the disorder. Finally, we estimate the parameters characterizing the $T = 0$ quantum melting of the phase order, using a suitable Lindemann criterion.

Novel phase behavior in quantum rotors

A system of quantum linear rotors in a crystal field is found to display a novel type of phase diagram. At a certain value of the crystal field a discontinuity point appears at the orientational phase transition line. As the crystal field increases this point splits into two critical points with a single-phase-state discontinuity (“hole”) between them. This remarkable feature is common both for a system where all angular momentum states are allowed and for one where the angular momentum is restricted to have even values despite the fact that general aspects of the transformations induced by the crystal field differ considerably for the two systems.

SO(5) superconductor in a Zeeman magnetic field: Phase diagram and thermodynamic properties

In this paper we present calculations of the SO(5) quantum rotor theory of high-${T}_{c}$ superconductivity in a Zeeman magnetic field. We use the spherical approach for five-component quantum rotors in a three-dimensional lattice to obtain formulas for the critical lines, free energy, entropy, specific heat, and present temperature dependences of these quantities for different values of the magnetic field. Our results are in qualitative agreement with relevant experiments on high-${T}_{c}$ cuprates.

Quantum impurity solvers using a slave rotor representation

We introduce a representation of electron operators as a product of a spin-carrying fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a method is proposed for solving multiorbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Green's functions, which can be derived from a controlled saddle point in the limit of a large number of field components. In contrast to some finite-$U$ extensions of the noncrossing approximation, the method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low frequency. We demonstrate that this impurity solver can be applied in the context of dynamical mean-field theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.

Phase glass is a Bose metal: a new conducting state in two dimensions.

In the quantum rotor model with random exchange interactions having a nonzero mean, three phases, a (i) phase (Bose) glass, (ii) superfluid, and (iii) Mott insulator, meet at a bicritical point. We demonstrate that proximity to the bicritical point and the coupling between the energy landscape and the dissipative degrees of freedom of the phase glass lead to a metallic state at T = 0. Consequently, the phase glass is unique in that it represents a concrete example of a metallic state that is mediated by disorder, even in 2D. We propose that the experimentally observed metallic phase which intervenes between the insulator and the superconductor in a wide range of thin films is in actuality a phase glass.

Thermodynamic properties of theSO(5) model of high-Tc superconductivity

In this paper we present calculations of thermodynamic functionswithin Zhang's SO(5) quantum rotor theory of high-Tcsuperconductivity. Using the spherical approach for three-dimensional quantum rotors we derive explicit analyticalformulae for entropy and specific heat related to the latticeversion of the SO(5) nonlinear quantum sigma model. We presentthe temperature dependence of these quantities for varioussettings of relevant control parameters (quantum fluctuationsand chemical potential). We find our results in overall qualitativeagreement with basic thermodynamics of high-Tc cuprates.

Resonant coupling of free quantum rotors in inclusion compounds.

NH3 groups in certain Hofmann clathrates form almost free one-dimensional quantum rotors with energy levels E(n) = n(2)B and angular momentum n (planck constant), where n = 0, +/-1, +/-2,.... Recent neutron scattering experiments revealed a surprising temperature dependence for the linewidths of the n = 0 <--> 1, 0 <--> 2, and 1 <--> 2 transitions. We propose a novel line broadening mechanism based on rotor-rotor coupling and obtain a simple analytic expression for the widths that depends on the rotor level occupation and on the 3-proton spin degeneracies of initial and final states. Our model provides, without adjustable parameters, a good fit both to the temperature dependence of the observed widths and to their relative magnitude.

A heuristic quantum dissipation algorithm applied to new neutron scattering data of the free ammonia rotations in the Ni–Ni–biphenyl Hofmann clathrate

This is a joint effort of an experimental and a theoretical group to understand neutron scattering linewidths of almost free quantum rotors. In the first part we introduce a new method for simulating the dynamics of small quantum systems at finite temperatures. Thermal fluctuations are implemented through a stochastic perturbation potential, which drives the system to thermal equilibrium. It is modeled in analogy to the classical Langevin equation. In the second part we present neutron scattering data for the NH3-rotor in Ni–Ni–2C12H10 Hofmann clathrates. By comparison of the experimental with the simulated data we find a classical behavior for the coupling strength of the phonons to the rotor.

Resonant coupling of free quantum rotors in inclusion compounds

Resonant coupling of free quantum rotors in inclusion compounds