27 research outputs found
Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas
We analyze the extrapolation to the thermodynamic limit of Fermi liquid
properties of the homogeneous electron gas in two and three dimensions. Using
field theory, we explicitly calculate finite-size effects of the total energy,
the renormalization factor, and the effective mass at the Fermi surface within
the random phase approximation (RPA) and discuss the validity for general
metallic systems.Comment: 6 page
Renormalization factor and effective mass of the two-dimensional electron gas
We calculate the momentum distribution of the Fermi liquid phase of the
homogeneous, two-dimensional electron gas. We show that, close to the Fermi
surface, the momentum distribution of a finite system with electrons
approaches its thermodynamic limit slowly, with leading order corrections
scaling as . These corrections dominate the extrapolation of the
renormalization factor, , and the single particle effective mass, , to
the infinite system size. We show how convergence can be improved analytically.
In the range , we get a lower renormalization factor and
a higher effective mass, , compared to the perturbative RPA values.Comment: 4 pages, 3 figure
The kagome antiferromagnet: a chiral topological spin liquid ?
Inspired by the recent discovery of a new instability towards a chiral phase
of the classical Heisenberg model on the kagome lattice, we propose a specific
chiral spin liquid that reconciles different, well-established results
concerning both the classical and quantum models. This proposal is analyzed in
an extended mean-field Schwinger boson framework encompassing time reversal
symmetry breaking phases which allows both a classical and a quantum phase
description. At low temperatures, we find quantum fluctuations favor this
chiral phase, which is stable against small perturbations of second and third
neighbor interactions. For spin-1/2 this phase may be, beyond mean-field, a
chiral gapped spin liquid. Such a phase is consistent with Density Matrix
Renormalization Group results of Yan et al. (Science 322, 1173 (2011)).
Mysterious features of the low lying excitations of exact diagonalization
spectra also find an explanation in this framework. Moreover, thermal
fluctuations compete with quantum ones and induce a transition from this flux
phase to a planar zero flux phase at a non zero value of the renormalized
temperature (T/S^2), reconciling these results with those obtained for the
classical system.Comment: 4 pages, 4 figures, 1 tabl
Optimized Periodic Coulomb Potential in Two Dimension
The 1/r Coulomb potential is calculated for a two dimensional system with
periodic boundary conditions. Using polynomial splines in real space and a
summation in reciprocal space we obtain numerically optimized potentials which
allow us efficient calculations of any periodic (long-ranged) potential up to
high precision. We discuss the parameter space of the optimized potential for
the periodic Coulomb potential. Compared to the analytic Ewald potential, the
optimized potentials can reach higher precisions by up to several orders of
magnitude. We explicitly give simple expressions for fast calculations of the
periodic Coulomb potential where the summation in reciprocal space is reduced
to a few terms
Emergent Potts order in the kagom\'e Heisenberg model
Motivated by the physical properties of Vesignieite
BaCuVO(OH), we study the Heisenberg model on the
kagom\'e lattice, that is proposed to describe this compound for and
. The nature of the classical ground state and the possible phase
transitions are investigated through analytical calculations and parallel
tempering Monte Carlo simulations. For and
, the ground states are not all related by an
Hamiltonian symmetry. Order appears at low temperature via the order by
disorder mechanism, favoring colinear configurations and leading to an emergent
Potts parameter. This gives rise to a finite temperature phase
transition. Effect of quantum fluctuations are studied through linear spin wave
approximation and high temperature expansions of the model. For
between and , the ground state goes
through a succession of semi-spiral states, possibly giving rise to multiple
phase transitions at low temperatures
Effect of perturbations on the kagome antiferromagnet at all temperatures
The ground state of the kagome Heisenberg antiferromagnet is now
recognized as a spin liquid, but its precise nature remains unsettled, even if
more and more clues point towards a gapless spin liquid. We use high
temperature series expansions (HTSE) to extrapolate the specific heat
and the magnetic susceptibility over the full temperature range,
using an improved entropy method with a self-determination of the ground state
energy per site . Optimized algorithms give the HTSE coefficients up to
unprecedented orders (20 in ) and as exact functions of the magnetic
field. Three extrapolations are presented for different low- behaviors of
: exponential (for a gapped system), linear or quadratic (for two
different types of gapless spin liquids). We study the effects of various
perturbations to the Heisenberg Hamiltonian: Ising anisotropy,
Dzyaloshinskii-Moriya interactions, second and third neighbor interactions, and
randomly distributed magnetic vacancies. We propose an experimental
determination of , which could be non zero, from measurements
under different magnetic fields.Comment: Main article of 7 pages and 5 figures, Supplemental Material of 42
page