arXiv subjects

F. J. Burnell

Publications and source records attributed to F. J. Burnell.

43 records · Page 3Linked to original sources

arXiv2009

Devil's staircases and supersolids in a one-dimensional dipolar Bose gas

We consider a single-component gas of dipolar bosons confined in a one-dimensional optical lattice, where the dipoles are aligned such that the long-ranged dipolar interactions are maximally repulsive. In the limit of zero inter-site hopping and sufficiently large on-site interaction, the phase diagram is a complete devil's staircase for filling fractions between 0 and 1, wherein every commensurate state at a rational filling is stable over a finite interval in chemical potential. We perturb away from this limit in two experimentally motivated directions involving the addition of hopping and a reduction of the onsite interaction. The addition of hopping alone yields a phase diagram, which we compute in perturbation theory in the hopping, where the commensurate Mott phases now compete with the superfluid. Further softening of the onsite interaction yields alternative commensurate states with double occupancies which can form a staircase of their own, as well as one-dimensional "supersolids" which simultaneously exhibit discrete broken symmetries and superfluidity.

cond-mat.other↗

arXiv2008

Scenario for Fractional Quantum Hall Effect in Bulk Isotropic Materials

We investigate the possibility of a strongly correlated Fractional Quantum Hall (FQH) state in bulk three dimensional isotropic (not layered) materials. We find that a FQH state can exist at low densities only if it is accompanied by a staging transition in which the electrons re-organize themselves in layers, perpendicular to the magnetic field, at distances of order the magnetic length apart. The Hartree energy associated to the staging transition is off-set by the correlation Fock energy of the 3D FQH state. We obtain the phase diagram of bulk electrons in a magnetic field subject to Coulomb interactions as a function of carrier density and lattice constant. At very low densities, the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilized by phonon correlations.

cond-mat.mes-hall↗

arXiv2008

Monopole Flux State on the Pyrochlore Lattice

The ground state of a spin 1/2 nearest neighbor quantum Heisenberg antiferromagnet on the pyrochlore lattice is investigated using a large $N$ SU(N) fermionic mean field theory. We find several mean field states, of which the state of lowest energy upon Gutzwiller projection, is a parity and time reversal breaking chiral phase with a unit monopole flux exiting each tetrahedron. This "monopole flux" state has a Fermi surface consisting of 4 lines intersecting at a point. At mean field the low-energy excitations about the Fermi surface are gapless spinons. An analysis using the projective symmetry group of this state suggests that the state is stable to small fluctuations which neither induce a gap, nor alter the unusual Fermi surface.

cond-mat.str-el↗

arXiv2008

Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations

We study a family of Hamiltonians of fermions hopping on a set of lattices in the presence of a background gauge field. The lattices are constructed by decorating the root lattices of various Lie algebras with their minuscule representations. The Hamiltonians are, in momentum space, themselves elements of the Lie algebras in these same representations. We describe various interesting aspects of the spectra--which exhibit a family resemblance to the Dirac spectrum, and in many cases are able to relate them to known facts about the relevant Lie algebras. Interestingly, various realizable lattices such as the kagomé and pyrochlore can be given this Lie algebraic interpretation and the particular flux Hamiltonians arise as mean-field Hamiltonians for spin-1/2 Heisenberg models on these lattices.

cond-mat.str-el↗

arXiv2008

Classical Antiferromagnetism on Torquato-Stillinger Packings

Torquato and Stillinger have constructed a new family of frustrated lattices by unusually high dilution of close packed structures while preserving structural stability. We show that an infinite subclass of these structures has an underlying topology that greatly simplifies determination of their magnetic phase structure for nearest neighbor antiferromagnetism interactions and O(N) spins.

cond-mat.str-el↗

arXiv2003

Chaos in a Relativistic 3-body Self-Gravitating System

We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to their non-relativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of non-linearity in the system. We find numerical evidence for a countably infinite class of non-chaotic orbits, yielding a fractal structure in the outer regions of the Poincare plot.

gr-qc↗

arXiv2003

Chaos in an Exact Relativistic 3-body Self-Gravitating System

We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly determined in terms of the four coordinate and momentum degrees of freedom in the system. Non-relativistically these degrees of freedom can be rewritten in terms of a single particle moving in a two-dimensional hexagonal well. We find the exact relativistic generalization of this potential, along with its post-Newtonian approximation. We then specialize to the equal mass case and numerically solve the equations of motion that follow from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining orbits in both the hexagonal and 3-body representations of the system, and plot the Poincare sections as a function of the relativistic energy parameter $η$. We find two broad categories of periodic and quasi-periodic motions that we refer to as the annulus and pretzel patterns, as well as a set of chaotic motions that appear in the region of phase-space between these two types. Despite the high degree of non-linearity in the relativistic system, we find that the the global structure of its phase space remains qualitatively the same as its non-relativisitic counterpart for all values of $η$ that we could study. However the relativistic system has a weaker symmetry and so its Poincare section develops an asymmetric distortion that increases with increasing $η$. For the post-Newtonian system we find that it experiences a KAM breakdown for $η\simeq 0.26$: above which the near integrable regions degenerate into chaos.

gr-qc↗