4,135 research outputs found
Spin density wave selection in the one-dimensional Hubbard model
The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard
model is calculated, constrained to uniform phases, which have no charge
density modulation. The allowed solutions are saturated ferromagnetism (FM), a
spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The
DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices.
FM occurs for small filling, SSDW in most of the remainder of the phase
diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling.
Itinerant electrons lift the degeneracy with respect to canting angle in the
DSDW. The Hartree-Fock states are metallic except at multiples of a quarter
filling. Near half filling the uniform SSDW phase is unstable against phase
separation into a half-filled antiferromagnetic phase and a hole-rich SSDW
phase. The dependence of the ground state wave number on chemical potential is
conjectured to be a staircase. Comparison is made with higher dimensional
Hubbard models and the Heisenberg model.Comment: 15 pages LaTeX, 5 Postscript figures in uuencoded file. To appear in
J Phys: Condensed Matter. Requires files ioplppt.sty, iopl10.sty, iopl12.sty
(available at http://www.ioppublishing.com/Journals/texstyle.html
Phase-space path-integral calculation of the Wigner function
The Wigner function W(q,p) is formulated as a phase-space path integral,
whereby its sign oscillations can be seen to follow from interference between
the geometrical phases of the paths. The approach has similarities to the
path-centroid method in the configuration-space path integral. Paths can be
classified by the mid-point of their ends; short paths where the mid-point is
close to (q,p) and which lie in regions of low energy (low P function of the
Hamiltonian) will dominate, and the enclosed area will determine the sign of
the Wigner function. As a demonstration, the method is applied to a sequence of
density matrices interpolating between a Poissonian number distribution and a
number state, each member of which can be represented exactly by a discretized
path integral with a finite number of vertices. Saddle point evaluation of
these integrals recovers (up to a constant factor) the WKB approximation to the
Wigner function of a number state.Comment: 16 pages. Small number of typos corrected, including sign in eq A2
Exact Classical Effective Potential
A quantum spin system can be modelled by an equivalent classical system, with
an effective Hamiltonian obtained by integrating all non-zero frequency modes
out of the path integral. The effective Hamiltonian H_eff(S_i) derived from the
coherent-state integral is highly singular: the quasiprobability density
exp(-beta H_eff), a Wigner function, imposes quantisation through derivatives
of delta functions. This quasiprobability is the distribution of the
time-averaged lower symbol of the spin in the coherent-state integral. We
relate the quantum Monte Carlo minus-sign problem to the non-positivity of this
quasiprobability, both analytically and by Monte Carlo integration.Comment: 4 page
Pseudogap in high-temperature superconductors from realistic Fr\"ohlich and Coulomb interactions
It has been recently shown that the competition between unscreened Coulomb
and Fr\"{o}hlich electron-phonon interactions can be described in terms of a
short-range spin exchange and an effective on-site interaction
in the framework of the polaronic -- model. This
model, that provides an explanation for high temperature superconductivity in
terms of Bose-Einstein condensation (BEC) of small and light bipolarons, is now
studied as a charged Bose-Fermi mixture. Within this approximation, we show
that a gap between bipolaron and unpaired polaron bands results in a strong
suppression of low-temperature spin susceptibility, specific heat and tunneling
conductance, signaling the presence of normal state pseudogap without any
assumptions on preexisting orders or broken symmetries in the normal state of
the model.Comment: 5 pages, 5 figure
Coherent-state path integral calculation of the Wigner function
We consider a set of operators hat{x}=(hat{x}_1,..., hat{x}_N) with diagonal representatives P(n) in the space of generalized coherent states |n>; hat{x}=int dn P(n) |n>_L over polygonal paths with L vertices {n_1...L}. The distribution of the path centroid bar{P}=(1/L) sum_{i=1}^{L}P(n_i) tends to the Wigner function W(x), the joint distribution for the operators: W(x)=lim_{L->infinity} _{L}. This result is proved in the case where the Hamiltonian commutes with hat{x}. The Wigner function is non-positive if the dominant paths with path centroid in a certain region have Berry phases close to odd multiples of pi. For finite L the path centroid distribution is a Wigner function convolved with a Gaussian of variance inversely proportional to L. The results are illustrated by numerical calculations of the spin Wigner function from SU(2) coherent states. The relevance to the quantum Monte Carlo sign problem is also discussed
Angular distribution of photoelectrons at 584A using polarized radiation
Photoelectron angular distributions for Ar, Xe, N2, O2, CO, CO2, and NH3 were obtained at 584 A by observing the photoelectrons at a fixed angle and simply rotating the plane of polarization of a highly polarized photon source. The radiation from a helium dc glow discharge source was polarized (84%) using a reflection type polarizer
Time Discretization of Functional Integrals
Numerical evaluation of functional integrals usually involves a finite (L-slice) discretization of the imaginary-time axis. In the auxiliary-field method, the L-slice approximant to the density matrix can be evaluated as a function of inverse temperature at any finite L as , if the density matrix in the static approximation is known. We investigate the convergence of the partition function , the internal energy and the density of states (the inverse Laplace transform of ), as . For the simple harmonic oscillator, is a normalized truncated Fourier series for the exact density of states. When the auxiliary-field approach is applied to spin systems, approximants to the density of states and heat capacity can be negative. Approximants to the density matrix for a spin-1/2 dimer are found in closed form for all L by appending a self-interaction to the divergent Gaussian integral and analytically continuing to zero self-interaction. Because of this continuation, the coefficient of the singlet projector in the approximate density matrix can be negative. For a spin dimer, is an even function of the coupling constant for L<3: ferromagnetic and antiferromagnetic coupling can be distinguished only for , where a Berry phase appears in the functional integral. At any non-zero temperature, the exact partition function is recovered as
Unconventional pairing in bipolaronic theories
Various mechanisms have been put forward for cuprate superconductivity, which
fit largely into two camps: spin-fluctuation and electron-phonon (el-ph)
mechanisms. However, in spite of a large effort, electron-phonon interactions
are not fully understood away from clearly defined limits. To this end, we use
a numerically exact algorithm to simulate the binding of bipolarons. We present
the results of a continuous-time quantum Monte-Carlo (CTQMC) algorithm on a
tight-binding lattice, for bipolarons with arbitrary interaction range in the
presence of strong coulomb repulsion. The algorithm is sufficiently efficient
that we can discuss properties of bipolarons with various pairing symmetries.
We investigate the effective mass and binding energies of singlet and triplet
real-space bipolarons for the first time, and discuss the extensions necessary
to investigate -symmetric pairs.Comment: Submitted to M2S-HTSC VIII, Dresden 2006, 2 page
Effects of lattice geometry and interaction range on polaron dynamics
We study the effects of lattice type on polaron dynamics using a
continuous-time quantum Monte-Carlo approach. Holstein and screened Froehlich
polarons are simulated on a number of different Bravais lattices. The effective
mass, isotope coefficients, ground state energy and energy spectra, phonon
numbers, and density of states are calculated. In addition, the results are
compared with weak and strong coupling perturbation theory. For the Holstein
polaron, it is found that the crossover between weak and strong coupling
results becomes sharper as the coordination number is increased. In higher
dimensions, polarons are much less mobile at strong coupling, with more phonons
contributing to the polaron. The total energy decreases monotonically with
coupling. Spectral properties of the polaron depend on the lattice type
considered, with the dimensionality contributing to the shape and the
coordination number to the bandwidth. As the range of the electron-phonon
interaction is increased, the coordination number becomes less important, with
the dimensionality taking the leading role.Comment: 16 pages, 12 figure
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