82 research outputs found
Quasi-universal transient behavior of a nonequilibrium Mott insulator driven by an electric field
We use a self-consistent strong-coupling expansion for the self-energy
(perturbation theory in the hopping) to describe the nonequilibrium dynamics of
strongly correlated lattice fermions. We study the three-dimensional
homogeneous Fermi-Hubbard model driven by an external electric field showing
that the damping of the ensuing Bloch oscillations depends on the direction of
the field, and that for a broad range of field strengths, a long-lived
transient prethermalized state emerges. This long-lived transient regime
implies that thermal equilibrium may be out of reach of the time scales
accessible in present cold atom experiments, but shows that an interesting new
quasi-universal transient state exists in nonequilibrium governed by a
thermalized kinetic energy but not a thermalized potential energy. In addition,
when the field strength is equal in magnitude to the interaction between atoms,
the system undergoes a rapid thermalization, characterized by a different
quasi-universal behavior of the current and spectral function for different
values of the hopping.Comment: (5 pages, 5 figures, ReVTeX
Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory
We present a nonequilibrium strong-coupling approach to inhomogeneous systems
of ultracold atoms in optical lattices. We demonstrate its application to the
Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence
of a trap potential. Since the theory is formulated self-consistently, the
numerical implementation relies on a massively parallel evaluation of the
self-energy and the Green's function at each lattice site, employing thousands
of CPUs. While the computation of the self-energy is straightforward to
parallelize, the evaluation of the Green's function requires the inversion of a
large sparse matrix, with . As a crucial ingredient,
our solution heavily relies on the smallness of the hopping as compared to the
interaction strength and yields a widely scalable realization of a rapidly
converging iterative algorithm which evaluates all elements of the Green's
function. Results are validated by comparing with the homogeneous case via the
local-density approximation. These calculations also show that the
local-density approximation is valid in non-equilibrium setups without mass
transport.Comment: 14 pages, 9 figure
Thermodynamics of the Quantum Critical Point at Finite Doping in the 2D Hubbard Model: A Dynamical Cluster Approximation Study
We study the thermodynamics of the two-dimensional Hubbard model within the
dynamical cluster approximation. We use continuous time quantum Monte Carlo as
a cluster solver to avoid the systematic error which complicates the
calculation of the entropy and potential energy (double occupancy). We find
that at a critical filling, there is a pronounced peak in the entropy divided
by temperature, S/T, and in the normalized double occupancy as a function of
doping. At this filling, we find that specific heat divided by temperature,
C/T, increases strongly with decreasing temperature and kinetic and potential
energies vary like T^2 ln(T). These are all characteristics of quantum critical
behavior.Comment: 4 pages, 4 figures. Submitted to Phys. Rev. B Rapid Communications on
June 27, 200
Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model
Transport measurements on the cuprates suggest the presence of a quantum
critical point hiding underneath the superconducting dome near optimal hole
doping. We provide numerical evidence in support of this scenario via a
dynamical cluster quantum Monte Carlo study of the extended two-dimensional
Hubbard model. Single particle quantities, such as the spectral function, the
quasiparticle weight and the entropy, display a crossover between two distinct
ground states: a Fermi liquid at low filling and a non-Fermi liquid with a
pseudogap at high filling. Both states are found to cross over to a marginal
Fermi-liquid state at higher temperatures. For finite next-nearest-neighbor
hopping t' we find a classical critical point at temperature T_c. This
classical critical point is found to be associated with a phase separation
transition between a compressible Mott gas and an incompressible Mott liquid
corresponding to the Fermi liquid and the pseudogap state, respectively. Since
the critical temperature T_c extrapolates to zero as t' vanishes, we conclude
that a quantum critical point connects the Fermi-liquid to the pseudogap
region, and that the marginal-Fermi-liquid behavior in its vicinity is the
analogous of the supercritical region in the liquid-gas transition.Comment: 18 pages, 9 figure
Theoretical Description of Coherent Doublon Creation via Lattice Modulation Spectroscopy
Using a recently developed strong-coupling method, we present a comprehensive
theory for doublon production processes in modulation spectroscopy of a
three-dimensional system of ultracold fermionic atoms in an optical lattice
with a trap. The theoretical predictions compare well to the experimental time
traces of doublon production. For experimentally feasible conditions, we
provide a quantitative prediction for the presence of a nonlinear "two-photon"
excitation at strong modulation amplitudes.Comment: 5 pages, 5 figure
Role of the van Hove Singularity in the Quantum Criticality of the Hubbard Model
A quantum critical point (QCP), separating the non-Fermi liquid region from
the Fermi liquid, exists in the phase diagram of the 2D Hubbard model
[Vidhyadhiraja et. al, Phys. Rev. Lett. 102, 206407 (2009)]. Due to the
vanishing of the critical temperature associated with a phase separation
transition, the QCP is characterized by a vanishing quasiparticle weight. Near
the QCP, the pairing is enhanced since the real part of the bare d-wave p-p
susceptibility exhibits algebraic divergence with decreasing temperature,
replacing the logarithmic divergence found in a Fermi liquid [Yang et. al,
Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the
single-particle and transport properties near the QCP. We focus mainly on a van
Hove singularity (vHS) coming from the relatively flat dispersion that crosses
the Fermi level near the quantum critical filling. The flat part of the
dispersion orthogonal to the antinodal direction remains pinned near the Fermi
level for a range of doping that increases when we include a negative
next-near-neighbor hopping t' in the model. For comparison, we calculate the
bare d-wave pairing susceptibility for non-interacting models with the usual
two-dimensional tight binding dispersion and a hypothetical quartic dispersion.
We find that neither model yields a vHS that completely describes the critical
algebraic behavior of the bare d-wave pairing susceptibility. The resistivity,
thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in
the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A
negative next-near-neighbor hopping t' increases the doping region with
marginal Fermi liquid character. Both T and negative t' are relevant variables
for the QCP, and both the transport and the motion of the vHS with filling
suggest that they are qualitatively similar in their effect.Comment: 15 pages, 17 figure
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