364 research outputs found
Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime
We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional
half-filled Hubbard model in the "spin-disordered regime", which is
characterized by the temperature being much larger than the magnetic energy
scale but small compared to the Mott-Hubbard gap. In this regime the
thermodynamics of the Hubbard model can be thought of in terms of gapped
charged excitations with an effective dispersion and spin degrees of freedom
that only contribute entropically. In particular, the internal energy and the
effective dispersion become essentially independent of temperature. An
interpretation of this regime in terms of a putative interacting-electron
system at zero temperature leads to a metal-insulator transition at a finite
interaction strength above which the gap opens linearly. We relate these
observations to studies of the Mott-Hubbard transition in the limit of infinite
dimensions.Comment: 15 pages, 3 figure
Random dispersion approximation for the Hubbard model
We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard
transition in the Hubbard model at half band filling. The RDA becomes exact for
the Hubbard model in infinite dimensions. We implement the RDA on finite chains
and employ the Lanczos exact diagonalization method in real space to calculate
the ground-state energy, the average double occupancy, the charge gap, the
momentum distribution, and the quasi-particle weight. We find a satisfactory
agreement with perturbative results in the weak- and strong-coupling limits. A
straightforward extrapolation of the RDA data for lattice results in
a continuous Mott-Hubbard transition at . We discuss the
significance of a possible signature of a coexistence region between insulating
and metallic ground states in the RDA that would correspond to the scenario of
a discontinuous Mott-Hubbard transition as found in numerical investigations of
the Dynamical Mean-Field Theory for the Hubbard model.Comment: 10 pages, 11 figure
Metal-insulator transition in the Edwards model
To understand how charge transport is affected by a background medium and
vice versa we study a two-channel transport model which captures this interplay
via a novel, effective fermion-boson coupling. By means of (dynamical) DMRG we
prove that this model exhibits a metal-insulator transition at half-filling,
where the metal typifies a repulsive Luttinger liquid and the insulator
constitutes a charge density wave. The quantum phase transition point is
determined consistently from the calculated photoemission spectra, the scaling
of the Luttinger liquid exponent, the charge excitation gap, and the
entanglement entropy.Comment: 4 pages, 3 figures, contributions to SCES 201
Tomonaga-Luttinger parameters for doped Mott insulators
The Tomonaga--Luttinger parameter determines the critical behavior
in quasi one-dimensional correlated electron systems, e.g., the exponent
for the density of states near the Fermi energy. We use the numerical
density-matrix renormalization group method to calculate from the
slope of the density-density correlation function in momentum space at zero
wave vector. We check the accuracy of our new approach against exact results
for the Hubbard and XXZ Heisenberg models. We determine in the phase
diagram of the extended Hubbard model at quarter filling, , and
confirm the bosonization results on the critical
line and at infinitesimal doping of the
charge-density-wave (CDW) insulator for all interaction strengths. The doped
CDW insulator exhibits exponents only for small doping and strong
correlations.Comment: 7 pages, 4 figure
Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model
We use continuous-time quantum Monte Carlo simulations to study retardation
effects in the metallic, quarter-filled Holstein model in one dimension. Based
on results which include the one- and two-particle spectral functions as well
as the optical conductivity, we conclude that with increasing phonon frequency
the ground state evolves from one with dominant diagonal order---2k_F charge
correlations---to one with dominant off-diagonal fluctuations, namely s-wave
pairing correlations. In the parameter range of this crossover, our numerical
results support the existence of a spin gap for all phonon frequencies. The
crossover can hence be interpreted in terms of preformed pairs corresponding to
bipolarons, which are essentially localised in the Peierls phase, and
"condense" with increasing phonon frequency to generate dominant pairing
correlations.Comment: 11 pages, 5 figure
Ising Deconfinement Transition Between Feshbach-Resonant Superfluids
We investigate the phase diagram of bosons interacting via Feshbach-resonant
pairing interactions in a one-dimensional lattice. Using large scale density
matrix renormalization group (DMRG) and field theory techniques we explore the
atomic and molecular correlations in this low-dimensional setting. We provide
compelling evidence for an Ising deconfinement transition occurring between
distinct superfluids and extract the Ising order parameter and correlation
length of this unusual superfluid transition. This is supported by results for
the entanglement entropy which reveal both the location of the transition and
critical Ising degrees of freedom on the phase boundary.Comment: 4 pages, 4 figure
Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approach
We reexamine the nature of the metallic phase of the one-dimensional
half-filled Holstein model of spinless fermions. To this end we determine the
Tomonaga-Luttinger-liquid correlation parameter by large-scale
density-matrix renormalisation-group (DMRG) calculations, exploiting (i) the
leading-order scaling relations between the ground-state energy and the
single-particle excitation gap and (ii) the static charge structure factor in
the long-wavelength limit. While both approaches give almost identical results
for intermediate-to-large phonon frequencies, we find contrasting behaviour in
the adiabatic regime: (i) (attractive) versus (ii)
(repulsive). The latter result for the correlation exponent is corroborated by
data obtained for the momentum distribution function , which puts the
existence of an attractive metallic state in the spinless fermion Holstein
model into question. We conclude that the scaling relation must be modified in
the presence of electron-phonon interactions with noticeable retardation.Comment: 6 pages, 5 figures, revised versio
Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians
We explore the Mott insulating state of single-band bosonic pairing
Hamiltonians using analytical approaches and large scale density matrix
renormalization group calculations. We focus on the second Mott lobe which
exhibits a magnetic quantum phase transition in the Ising universality class.
We use this feature to discuss the behavior of a range of physical observables
within the framework of the 1D quantum Ising model and the strongly anisotropic
Heisenberg model. This includes the properties of local expectation values and
correlation functions both at and away from criticality. Depending on the
microscopic interactions it is possible to achieve either antiferromagnetic or
ferromagnetic exchange interactions and we highlight the possibility of
observing the E8 mass spectrum for the critical Ising model in a longitudinal
magnetic field.Comment: 14 pages, 15 figure
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