Quantum Melting Research Articles

Vortex dynamics and Hall conductivity of hard-core bosons

Magneto-transport of hard core bosons (HCB) is studied using an XXZ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex hopping energy, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at 6.5x10-5 vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom ('vspin'), which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices, and magnet-transport of short coherence length superconductors.

Bose-Fermi solid and its quantum melting in a one-dimensional optical lattice

We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (NN) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized in the limit of weak intersite tunneling ($J$). When $J$ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through different procedures, depending on whether the crystalline order is dominated by the NN interaction between fermions or bosons. These properties are qualitatively different from the classical picture of solid-liquid phase transition.

Quantum Melting of Spin Ice: Emergent Cooperative Quadrupole and Chirality

Quantum melting of spin ice is proposed for pyrochlore-lattice magnets Pr2TM2O7 (TM=Ir, Zr, and Sn). The quantum superexchange Hamiltonian having a nontrivial magnetic anisotropy is derived on the basis of atomic non-Kramers magnetic doublets. The ground states exhibit a cooperative ferroquadrupole and pseudospin chirality, forming a magnetic analog of smectic liquid crystals. Our theory accounts for dynamic spin-ice behaviors experimentally observed in Pr2TM2O7.

Quantum Melting of Charge Ice and Non-Fermi-Liquid Behavior: An Exact Solution for the Extended Falicov-Kimball Model in the Ice-Rule Limit

An exact solution is obtained for a model of itinerant electrons coupled to ice-rule variables on the tetrahedron Husimi cactus, an analogue of the Bethe lattice of corner-sharing tetrahedra. It reveals a quantum critical point with the emergence of non-Fermi-liquid behavior in melting of the "charge ice" insulator. The electronic structure is compared with the numerical results for the pyrochlore-lattice model to elucidate the physics of electron systems interacting with the tetrahedron ice rule.

Quantum Melting of Valence-Bond Crystal Insulators and Novel Supersolid Phase at Commensurate Density

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence-Bond crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid or metallic phases under increasing hopping is investigated at T=0 K. We identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.

Quantum Phases of Cold Polar Molecules in 2D Optical Lattices

We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.

High Field Magnetism of the Spinel Oxide CoAl2O4

We report the results of magnetization and electron spin resonance (ESR) measurements on sintered samples of the spinel oxide CoAl2O4 in magnetic fields up to 53 T. In CoAl2O4, Co2+ (S=3/2) ions make a diamond lattice, indicating naively that no geometrical frustration takes place. This spinel oxide, however, is thought to be in the vicinity of a quantum melting point of the antiferromagnetically ordered state because of no sharp peak in the temperature dependence of specific heat. Magnetization curve at 4.2 K is almost linear in magnetic fields and a broad ESR signal was observed on a straight resonance line with g=2.26, implying an antiferromagnetic long range order or a well developed antiferromagnetic short range order with very small anisotropy.

Dynamic melting of driven vortex matter below 1 K

We report on measurements of a mode-locking resonance in amorphous Mo x Ge 1− x films at different temperatures T down to 0.8 K, which is well below the superconducting transition (6 K). We observe dynamic ordering of driven vortex matter for all the temperatures studied. As the field exceeds a certain critical field B c, dyn at fixed T, moving vortices do not exhibit dynamic ordering. At high T, this field B c, dyn ( T), so-called dynamic melting, nearly coincides with a characteristic field B c ( T) where the linear resistivity vanishes. At low T, however, B c, dyn ( T) is significantly suppressed compared to B c ( T), suggesting intrinsic quantum melting in the absence of pinning.

Effective interaction potential and superfluid–solid transition of spatially indirect excitons

Using an adiabatic approximation, we derive an effective interaction potential for spatially indirect excitons in quantum well structures. Using this potential and path integral Monte Carlo simulations, we study exciton crystallization and the quantum melting phase transition in a macroscopic system of 2D excitons. Furthermore, the superfluid fraction is calculated as a function of density and is shown to vanish upon crystallization.

Classical and quantum physics of hydrogen clusters

We present results of a comprehensive theoretical investigation of the low temperature(T) properties of clustersof para-hydrogen (p-H2), both pristine as well as doped with isotopic impurities (i.e., ortho-deuterium,o-D2). We study clusterscomprising up to N = 40 molecules, by means of quantum simulations based on the continuous-space Worm algorithm. Pristinep-H2 clusters are liquid-like and superfluid in the limit. The superfluid signal is uniform throughout these clusters; it is underlain bylong cycles of permutation of molecules. Clusters with more than 22 moleculesdisplay solid-like, essentially classical behavior at temperatures down toT∼1 K; some of them are seen to turn liquid-like at sufficiently lowT (quantum melting).

Mixed columnar-plaquette phase of hard-core bosons and its quantum melting

Mixed columnar-plaquette phase of hard-core bosons and its quantum melting

Quantum melting of a crystal of dipolar bosons

We investigate the behavior of dipolar bosons in two dimensions. We describe the large density crystalline limit analytically while we use quantum Monte Carlo to study the melting toward the Bose-Einstein condensate. We find strong evidence for a first order transition. We characterize the window of experimentally accessible parameters in the context of ultracold bosons and show that observing the quantum melting should be within grasp once one is able to form cold heteronuclear molecules. Close to the melting, we cannot conclude on the existence of a supersolid phase due to an insufficient overlap of our variational Bijl-Jastrow ansatz with the actual ground state.

Melting of antiferromagnetic ordering in spinel oxide CoAl{sub 2}O{sub 4}

The magnetic and thermal properties of the spinel oxides CoB{sub 2}O{sub 4} have been studied for B = Rh, Co and Al. The compounds consist of magnetic Co{sup 2+} (S = 3/2) in the A site and non-magnetic B{sup 3+} in the B site, which form diamond and pyrochlore sublattices, respectively. We found that the ratio of the Curie-Weiss temperature to the magnetic ordering temperature, {theta}{sub CW}/T{sub N}, depends strongly on B{sup 3+} cations. CoRh{sub 2}O{sub 4} was a typical antiferromagnet with {theta}{sub CW}/T{sub N} = 31 K/25 K = 1.2. The ratio was enhanced up to {theta}{sub CW}/T{sub N} = 110 K/30 K = 3.7 for Co{sub 3}O{sub 4} (B = Co) and {theta}{sub CW}/T* = 89 K/9 K = 10 for CoAl{sub 2}O{sub 4}, indicating the evolution of magnetic frustration. The specific heat for CoAl{sub 2}O{sub 4} exhibited a broad peak at T* = 9 K and T{sup 2.5} behaviour at low temperatures, suggesting the most frustrated magnet CoAl{sub 2}O{sub 4} is in the critical vicinity of a quantum melting point of the antiferromagnetically ordered state.

Static structure factor and quantum melting of vortex lattices in two-dimensional Bose-Einstein condensates

The first-order quantum corrections to the static structure factor of vortex lattices in a rapidly rotating quasi-two-dimensional Bose-Einstein condensate are calculated. Furthermore, we estimate the melting filling fraction by using a criterion similar to that used in thermal melting related to the Debye-Waller factor of the smallest reciprocal lattice vector.

Melting of antiferromagnetic ordering in spinel oxideCoAl2O4

The magnetic and thermal properties of the spinel oxidesCoB2O4 have beenstudied for B = Rh, Co and Al. The compounds consist of magneticCo2+ (S = 3/2) in the A siteand non-magnetic B3+ in the B site, which form diamond and pyrochlore sublattices, respectively. We found thatthe ratio of the Curie–Weiss temperature to the magnetic ordering temperature,|ΘCW|/TN, depends stronglyon B3+ cations.CoRh2O4 was a typicalantiferromagnet with |ΘCW|/TN = 31 K/25 K = 1.2. Theratio was enhanced up to |ΘCW|/TN = 110 K/30 K = 3.7 for Co3O4 (B = Co)and |ΘCW|/T* = 89 K/9 K = 10 for CoAl2O4, indicating the evolution of magnetic frustration. The specific heat forCoAl2O4 exhibited abroad peak at T* = 9 K and T2.5 behaviour at low temperatures, suggesting the most frustrated magnetCoAl2O4 is in the critical vicinity of a quantum melting point of the antiferromagnetically orderedstate.

Structure, superfluidity, and quantum melting of hydrogen clusters

We present results of a theoretical study of para-hydrogen and ortho-deuterium clusters at low temperature (0.5 K < T < 3.5 K), based on Path Integral Monte Carlo simulations. Clusters of size up to N=21 para-hydrogen molecules are nearly entirely superfluid at T < 1 K. For 21 < N < 30, the superfluid response displays strong variations with N, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solid- to liquid-like as T tends to 0. Melting is caused by quantum exchanges of molecules. The largest para-hydrogen cluster for which a significant superfluid response is observed comprises 27 molecules. Evidence of a finite superfluid response is presented for ortho-deuterium clusters of size up to 14 molecules. Magic numbers are observed, at which both types of clusters feature pronounced stability.

Simulations of atomic gases on frustrated optical lattices

We present results form quantum Monte Carlo simulations of ultra-cold bosonic atoms on frustrated optical lattices such as the triangular and the kagome lattice. For the triangular lattice case a supersolid state of matter emerges, resulting from a novel order-by-disorder effect in the quantum regime. On the kagome lattice no supersolid appears, instead the atoms form exotic valence-bond-solids with local bosonic resonances. The quantum melting of these solids into the superfluid takes place at weakly first-order quantum phase transitions. Relevant algorithmic improvements which allow for large-scale simulations of such systems are mentioned as well as possible experimental realizations of these scenarios based on current experimental advances in quantum optics.

Coulomb crystal and quantum melting in electron–hole plasmas of semiconductors under high pressure

AbstractA phase diagram for variable hole to electron mass ratio of two‐component Coulomb crystals is presented as result of the first‐principle computer simulations. A critical mass ratio for the existence of quantum Coulomb crystals is of the order of 80 in three dimensions. At very low temperature the electron–hole system with decreasing hole mass can form antiferromagnetic crystal structure composed by two perfect hole lattices each consisting of the holes with the same spin projections. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

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.

Frenkel-Kontorova model with cold trapped ions

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. Quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.