Scale Quantum Monte Carlo Simulations Research Articles

Dynamical exponent of a quantum critical itinerant ferromagnet: A Monte Carlo study

We consider the effect of the coupling between 2D quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions.A common belief is that near a $q=0$ ferromagnetic transition, fermions induce an $\Omega/q$ Landau damping of rotors (i.e., the dynamical critical exponent is $z=3$) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy $\Sigma\propto \omega^{2/3}$. This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies.Here we show that for the XY case the behavior is different.We report the results of large scale quantum Monte Carlo simulations,which show that at small frequencies $z=2$ and $\Sigma\propto \omega^{1/2}$. We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces $1/q$ in the Landau damping by a constant. We discuss the implication of these results to experiments.

Dimensional reduction of helium-4 inside argon-plated MCM-41 nanopores

The angstrom-scale coherence length describing the superfluid wavefunction of helium-4 at low temperatures has prevented its preparation in a truly one-dimensional geometry. Mesoporous ordered silica-based structures, such as the molecular sieve MCM-41, offer a promising avenue towards physical confinement, but the minimal pore diameters that can be chemically synthesized have proven to be too large to reach the quasi-one-dimensional limit. We present an active nano-engineering approach to this problem by pre-plating MCM-41 with a single, well controlled layer of Ar gas before filling the pores with helium. The structure inside the pore is investigated via experimental adsorption isotherms and neutron scattering measurements that are in agreement with large scale quantum Monte Carlo simulations. The results demonstrate angstrom and kelvin scale tunability of the effective confinement potential experienced by 4He atoms inside the MCM-41, with the Ar layer reducing the diameter of the confining media into a regime where a number of solid layers surround a one-dimensional quantum liquid.

Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model

New magnetization plateaus and supersolid phases are identified in an extended Shastry–Sutherland model – with additional longer range interactions and exchange anisotropy – over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Using a plaquette representation and exact mapping of ground state configurations in the Ising limit, supplemented by large scale quantum Monte Carlo simulations to include the effects of exchange interactions, we have identified several magnetization plateaus and associated spin supersolid phases. Our methods enable us to elucidate the underlying structure and mechanism of formation of the supersolid phases, thus gaining deeper understanding into their emergence from competing interactions. Additionally, in this regime we find evidence of a fractional plateau at 1∕9 saturation magnetization, which may hold the clue to understanding the fractional plateau in TmB4 that exhibits magnetic hysteresis.

Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice.

We use large scale quantum MonteCarlo simulations to study an extended Hubbard model of hard core bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at 1/3 filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. We present a theory in terms of an easy plane noncompact CP^{1} gauge theory describing the phase transition at 1/3 filling. Utilizing large scale quantum MonteCarlo simulations with parallel tempering in the canonical ensemble up to 15552 spins, we provide evidence that the phase transition is continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality.

Magnons in a two-dimensional transverse-field XXZ model

The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin wave theory to investigate the resulting canted antiferromagnet. The small and large field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free $XY$ antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a non-zero field, where magnon degeneracy appears as a result of restoration of an U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for $S=1/2$ via large scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign-problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.

Effective spin physics in two-dimensional cavity QED arrays

We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya’s enumeration theorem.

Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice.

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).

Rydberg Polaritons in a Cavity: A Superradiant Solid

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum MonteCarlo simulations.

A LUTTINGER LIQUID CORE INSIDE HELIUM-4 FILLED NANOPORES

As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.

Extended Bose-Hubbard model on a honeycomb lattice

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large scale quantum Monte Carlo simulations. We present the ground state phase diagrams for both the hard-core case and the soft-core case. For the hard-core case, the transition between $\rho=1/2$ solid and the superfluid is first order and the supersolid state is unstable towards phase separation. For the soft-core case, due to the presence of the multiple occupation, a stable particle induced supersolid (SS-p) phase emerges when $1/2<\rho<1$. The transition from the solid at $\rho=1/2$ to the SS-p is second order with the superfluid density scaling as $ \rho_{s} \sim \rho-1/2 $. The SS-p has the same diagonal order as the solid at $ \rho=1/2 $. As the chemical potential increasing further, the SS-p will turn into a solid where two bosons occupying each site of a sublattice through a first order transition. We also calculate the critical exponents of the transition between $\rho=1/2$ solid and superfluid at the Heisenberg point for the hard core case. We find the dynamical critical exponent $z=0.15$, which is smaller than results obtained on smaller lattices. This indicates that $ z $ approaches zero in the thermodynamic limit, so the transition is also first order even at the Heisenberg point.

Hard-Core Bosons on the Kagome Lattice: Valence-Bond Solids and Their Quantum Melting

Using large scale quantum Monte Carlo simulations and dual vortex theory, we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest-neighbor repulsion. In contrast with the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half filling, two novel solid phases emerge at densities rho=1/3 and rho=2/3. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.

Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

We study properties of ultracold bosonic atoms in one-, two-, and three-dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose-Hubbard model in parabolic confining potentials. Our results indicate that local properties of the atoms can be accessed by probing the system's response to local potential perturbations. Furthermore, we show how the formation of Mott insulating regions is reflected in the momentum distribution of the atoms, amenable to experimental detection. We disprove previous claims concerning the relevance of fine structure in the momentum distribution function. Furthermore, we discuss limitations of local density approximations for confined systems, and demonstrate the absence of quantum criticality due to the inhomogenous potential. Instead, we show that quantum critical behavior can be observed in flat confining potentials. Our results indicate that the experimental detection of the Mott transition in moderately sized optical lattices would be significantly eased in flat confinement potentials.