Quantum Rotor Model Research Articles

Excitonic Phase Transition in the Extended Three-Dimensional Falicov–Kimball Model

We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov-Kimball (EFKM) model with the tunable Coulomb interaction $U$ between both species. By lowering the temperature, the electron-hole system may become unstable with respect to the formation of the excitons, i.e, electron-hole pairs at temperature $T=T_{\Delta}$, exhibiting a gap $\Delta$ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formula for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.

Quantum Rotor Model for a Bose-Einstein Condensate of Dipolar Molecules

We show that a Bose-Einstein condensate of heteronuclear molecules in the regime of small and static electric fields is described by a quantum rotor model for the macroscopic electric dipole moment of the molecular gas cloud. We solve this model exactly and find the symmetric, i.e., rotationally invariant, and dipolar phases expected from the single-molecule problem, but also an axial and planar nematic phase due to many-body effects. Investigation of the wave function of the macroscopic dipole moment also reveals squeezing of the probability distribution for the angular momentum of the molecules.

Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges

We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.

Quantum Monte Carlo calculation of entanglement Rényi entropies for generic quantum systems

We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy.

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.

Quantum criticality for extended nodes on a Bethe lattice in the large connectivity limit

Theoretical description of anisotropic systems, such as layered superconductors and coupled spin chains, is often a challenge due to the different natures of interactions along different directions. As a model of such a system, we present an analytical study of $d$-dimensional ``nodes'' arranged as the vertices of a Bethe lattice, where each node has nonzero spatial dimension and is described by an $O(N)$ quantum rotor model, and there is hopping between neighboring nodes. In the limit of large connectivity on the Bethe lattice, the hopping can be treated by constructing a self-consistent effective action for a single node. This procedure is akin to dynamical mean field theory, but generalized so that spatial as well as quantum fluctuations are taken into account on each node. The quantum phase transition is studied using this effective action for both infinite and finite $N$. The importance of the Perron-Frobenius uniform mode on the Bethe lattice is discussed, and its elimination via an ``infinite-range hopping'' term shifts the transition, leading to nontrivial critical behavior. We calculate critical exponents and find that the internode hopping reduces the upper and lower critical dimensions each by 1, indicating that---at least for the purposes of quantum criticality---the large number of internode couplings is similar to adding a single extra dimension to the theory describing a single node.

Quantum phase slips in one-dimensional superfluids in a periodic potential

We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\Gamma$. When the flow momentum $p$ is small, we find that the nucleation rate per unit length increases algebraically with $p$ as $\Gamma/L \propto p^{2K-2}$, where $L$ is the system size and $K$ is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulae of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.

A Ground State Monte Carlo Approach for Studies of Dipolar Systems with Rotational Degrees of Freedom

We have developed a path integral ground state Monte Carlo (PIGSMC) algorithm for quantum simulations of rotating dipolar molecules, using a highly accurate sixth-order algorithm. The method allows us to calculate unbiased estimates of ground state properties of dipolar molecules in a variety of geometries, with or without an external electric field. To demonstrate the capability of the approach, we calculate the orientational phase diagram of a one dimensional lattice system of rotating point dipoles in the absence of any external electric fields. We find that for finite lattice size, this system exhibits an order–disorder transition at finite dipolar interaction strength in contrast to the well-known orientational disorder of the corresponding one dimensional O(3) quantum rotor models. Comparison of the quantum Monte Carlo results with a self-consistent field estimate of the phase transition shows the emergence of an ordered phase at non-zero dipolar strength, confirming the symmetry breaking role of the anisotropic dipole–dipole interaction.

Quantum rotor theory of spinor condensates in tight traps

In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensates. In a previous work [R. Barnett et al., Phys. Rev. A 82, 031602(R) (2010)] it was shown that there is an exact mapping of a spin-one condensate of fixed particle number with quadratic Zeeman interaction onto a quantum rotor model. Since the rotor model has an unbounded spectrum from above, it has many more eigenstates than the original bosonic model. Here we show that for each subset of states with fixed spin ${F}_{z}$, the physical rotor eigenstates are always those with the lowest energy. We classify three distinct physical limits of the rotor model: the Rabi, Josephson, and Fock regimes. The last regime corresponds to a fragmented condensate and is thus not captured by the Bogoliubov theory. We next consider the semiclassical limit of the rotor problem and make connections with the quantum wave functions through the use of the Husimi distribution function. Finally, we describe how to extend the analysis to higher-spin systems and derive a rotor model for the spin-two condensate. Theoretical details of the rotor mapping are also provided here.

Antiferromagnetic spinor condensates are quantum rotors

We establish a theoretical correspondence between spin-one antiferromagnetic spinor condensates in an external magnetic field and quantum rotor models in an external potential. We show that the rotor model provides a conceptually clear picture of the possible phases and dynamical regimes of the antiferromagnetic condensate. We also show that this mapping simplifies calculations of the condensate's spectrum and wavefunctions. We use the rotor mapping to describe the different dynamical regimes recently observed in $^{23}$Na condensates. We also suggest a way to experimentally observe quantum mechanical effects (collapse and revival) in spinor condensates.

Phase Transitions in the Two-Dimensional Quantum Rotor Model at Finite Temperature

Phase Transitions in the Two-Dimensional Quantum Rotor Model at Finite Temperature

Triaxial rotor model description ofE2properties inOs186,188,190,192

The triaxial rotor model with independent inertia and electric quadrupole tensors is applied to the description of the extensive set of $E2$ matrix elements available for $^{186,188,190,192}\mathrm{Os}$. Most large and medium transition $E2$ matrix elements can be reproduced to within $~10%,$ and most diagonal elements to within $~30%$. Most small transition matrix elements can be reproduced to within $~30%,$ and they support the interference effect exhibited by the model between the inertia and $E2$ tensors: this is a new feature of quantum rotor models. The diagonal $E2$ matrix elements at higher spins in the $K=2$ band are extremely sensitive to admixtures of higher $K$ values: the low experimental values in $^{190,192}\mathrm{Os}$ indicate significant admixtures of $K=4$ components. Attention is given to the ${K}^{\ensuremath{\pi}}={4}^{+}$ bands in these nuclei and the controversial issue of whether they are of quadrupole or hexadecapole nature.

Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensionalquantum rotor model

The ground state of the quantum rotor model in two dimensions with random phase frustrationis investigated. Extensive Monte Carlo simulations are performed on the corresponding(2+1)-dimensional classical model under the entropic sampling scheme. For weak quantumfluctuation, the system is found to be in a phase glass phase characterized by a finitecompressibility and a finite value for the Edwards–Anderson order parameter, signifyinglong-range phase rigidity in both spatial and imaginary time directions. The scalingproperties of the model near the transition to the gapped, Mott insulator state withvanishing compressibility are analyzed. At the quantum critical point, the dynamicexponent is greater than one. Correlation length exponents in the spatial and imaginary timedirections are given by and , respectively; both assume values greater than 0.6723 of the pure case. We speculate thatthe phase glass phase is superconducting rather than metallic in the zero-currentlimit.

Finite-Temperature Phase Transitions in a Two-Dimensional Boson Hubbard Model

We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of a quantum rotor model and construct the corresponding phase diagram. Compressibility shows a thermally activated gapped behavior in the insulating regime. Finite-size scaling of the superfluid stiffness clearly shows the nature of the Kosterlitz-Thouless transition. The transition temperature T(c) confirms a scaling relation T(c) proportional, rho(0)(x), with x=1.0. Some evidence of anomalous quantum behavior at low temperatures is presented.

Matrix product states algorithms and continuous systems

A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be applied to a wide variety of situations. As a first test, we show how it provides reliable results in the computation of fundamental properties of a chain of quantum harmonic oscillators achieving off-critical and critical relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use it to study the ground state properties of the quantum rotor model in one spatial dimension, a model that can be mapped to the Mott insulator limit of the 1-dimensional Bose-Hubbard model. At the quantum critical point, the central charge associated to the underlying conformal field theory can be computed with good accuracy by measuring the finite-size corrections of the ground state energy. Examples of MPS-computations both in the finite-size regime and in the thermodynamic limit are given. The precision of our results are found to be comparable to those previously encountered in the MPS studies of, for instance, quantum spin chains. Finally, we present a spin-off application: an iterative technique to efficiently get numerical solutions of partial differential equations of many variables. We illustrate this technique by solving Poisson-like equations with precisions of the order of 10^(-7).

Quantum phase transitions of the diluted O(3) rotor model

We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte Carlo simulations. This system has two quantum phase transitions: a generic one for small dilutions and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law scaling. We relate our findings to a recent classification of phase transitions with quenched disorder according to the rare region dimensionality, and we discuss experiments in disordered quantum magnets.

Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model

As an example of ordering due to quantum fluctuations, we examine the nearest-neighbor antiferromagnetic quantum $O(n)$ rotor model on the pyrochlore lattice. Classically, this system remains disordered even at zero temperature; we find that adding quantum fluctuations induces an ordered phase that survives to positive temperature, and we determine how its phase diagram scales with the coupling constant and the number of spin components. We demonstrate, using quantum Monte Carlo simulations, that this phase has long-range spin-nematic order, and that the phase transition into it appears to be first order.

Dynamical correlations and quantum phase transition in the quantum Potts model

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension.Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix {\gf deep} in the gapped phases is shown to take a simple {\gf exchange} form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while {\gf far from the quantum critical point} we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay functions exhibit a {\em diffusive character}. {\gf We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition.} Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.

Vortex glass is a metal: Unified theory of the magnetic-field and disorder-tuned Bose metals

We consider the disordered quantum rotor model in the presence of a magnetic field. We analyze the transport properties in the vicinity of the multicritical point between the superconductor, phase glass and paramagnetic phases. We find that the magnetic field leaves metallic transport of bosons in the glassy phase in tact. In the vicinity of the vicinity of the superconductivity-to-Bose metal transition, the resistitivy turns on as $(H-H_c)^{2}$ with $H_c$. This functional form is in excellent agreement with the experimentally observed turn-on of the resistivity in the metallic state in MoGe, namely $R\approx R_c(H-H_c)^\mu$, $1<\mu<3$. The metallic state is also shown to presist in three spatial dimensions. In addition, we also show that the metallic state remains intact in the presence of Ohmic dissipation in spite of recent claims to the contrary. As the phase glass in $d=3$ is identical to the vortex glass, we conclude that the vortex glass is, in actuality, a metal rather than a superconductor at T=0. Our analysis unifies the recent experiments on vortex glass systems in which the linear resistivity remained non-zero below the putative vortex glass transition and the experiments on thin films in which a metallic phase has been observed to disrupt the direct transition from a superconductor to an insulator.

Correlation effects of quantum rotors in Ge crystals

We address the accurate treatment of dipolar interaction effects between oxygen defects in Ge crystals on the low-temperature properties of bulk systems. On the basis of a quantum rotor model, we reveal that the interaction between adjacent oxygen defects generates nontrivial low-lying excitations that result in power-law specific heats below 0.1 K . In addition, a peculiar hump is observed for the dielectric susceptibilities at approximately 1 K . Further, we contend that the predicted power-law specific heats are well described by the two-level tunneling theory, which is based on the random distribution of interacting oxygen defects in Ge samples.