10 research outputs found
Non-linear feedback effects in coupled Boson-Fermion systems
We address ourselves to a class of systems composed of two coupled subsystems
without any intra-subsystem interaction: itinerant Fermions and localized
Bosons on a lattice. Switching on an interaction between the two subsystems
leads to feedback effects which result in a rich dynamical structure in both of
them. Such feedback features are studied on the basis of the flow equation
technique - an infinite series of infinitesimal unitary transformations - which
leads to a gradual elimination of the inter-subsystem interaction. As a result
the two subsystems get decoupled but their renormalized kinetic energies become
mutually dependent on each other. Choosing for the inter - subsystem
interaction a charge exchange term (the Boson-Fermion model) the initially
localized Bosons acquire itinerancy through their dependence on the
renormalized Fermion dispersion. This latter evolves from a free particle
dispersion into one showing a pseudogap structure near the chemical potential.
Upon lowering the temperature both subsystems simultaneously enter a
macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a
soundwave like dispersion while the Fermions develop a true gap in their
dispersion. The essential physical features described by this technique are
already contained in the renormalization of the kinetic terms in the respective
Hamiltonians of the two subsystems. The extra interaction terms resulting in
the process of iteration only strengthen this physics. We compare the results
with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.
Universal asymptotic behavior in flow equations of dissipative systems
Based on two dissipative models, universal asymptotic behavior of flow
equations for Hamiltonians is found and discussed. Universal asymptotic
behavior only depends on fundamental bath properties but not on initial system
parameters, and the integro-differential equations possess an universal
attractor. The asymptotic flow of the Hamiltonian can be characterized by a
non-local differential equation which only depends on one parameter -
independent of the dissipative system or truncation scheme. Since the fixed
point Hamiltonian is trivial, the physical information is completely
transferred to the transformation of the observables. This yields a more stable
flow which is crucial for the numerical evaluation of correlation functions.
Furthermore, the low energy behavior of correlation functions is determined
analytically. The presented procedure can also be applied if relevant
perturbations are present as is demonstrated by evaluating dynamical
correlation functions for sub-Ohmic environments. It can further be generalized
to other dissipative systems.Comment: 15 pages, 9 figures; to appear in Phys. Rev.
Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains
Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an
asymptotically exact renormalization group. Randomness is found to induce a
quantum phase transition between two random-singlet phases. In the strong
randomness phase the effective spins at low energies are S_eff=3/2, while in
the weak randomness phase the effective spins are S_eff=1/2. Separating them is
a quantum critical point near which there is a non-trivial mixture of S=1/2,
S=1, and S=3/2 effective spins at low temperatures.Comment: 4 pages, 3 figures. Typos correcte
On the Geodesic Nature of Wegner's Flow
Wegner's method of flow equations offers a useful tool for diagonalizing a
given Hamiltonian and is widely used in various branches of quantum physics.
Here, generalizing this method, a condition is derived, under which the
corresponding flow of a quantum state becomes geodesic in a submanifold of the
projective Hilbert space, independently of specific initial conditions. This
implies the geometric optimality of the present method as an algorithm of
generating stationary states. The result is illustrated by analyzing some
physical examples.Comment: 8 pages, no figures. The version published in Foundations of Physic
Real-Time-RG Analysis of the Dynamics of the Spin-Boson Model
Using a real-time renormalization group method we determine the complete
dynamics of the spin-boson model with ohmic dissipation for coupling strengths
. We calculate the relaxation and dephasing time, the
static susceptibility and correlation functions. Our results are consistent
with quantum Monte Carlo simulations and the Shiba relation. We present for the
first time reliable results for finite cutoff and finite bias in a regime where
perturbation theory in or in tunneling breaks down. Furthermore, an
unambigious comparism to results from the Kondo model is achieved.Comment: 4 pages, 5 figures, 1 tabl
Criticality of the Mean-Field Spin-Boson Model: Boson State Truncation and Its Scaling Analysis
The spin-boson model has nontrivial quantum phase transitions at zero
temperature induced by the spin-boson coupling. The bosonic numerical
renormalization group (BNRG) study of the critical exponents and
of this model is hampered by the effects of boson Hilbert space
truncation. Here we analyze the mean-field spin boson model to figure out the
scaling behavior of magnetization under the cutoff of boson states . We
find that the truncation is a strong relevant operator with respect to the
Gaussian fixed point in and incurs the deviation of the exponents
from the classical values. The magnetization at zero bias near the critical
point is described by a generalized homogeneous function (GHF) of two variables
and . The universal function has a
double-power form and the powers are obtained analytically as well as
numerically. Similarly, is found to be a GHF of
and . In the regime , the truncation produces no effect.
Implications of these findings to the BNRG study are discussed.Comment: 9 pages, 7 figure
Truncation errors in self-similar continuous unitary transformations
Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the framework of the S-CUT and obtain rigorous error bounds for the ground state energy and the highest excited level. These bounds can be lowered exploiting symmetries of the Hamiltonian. We illustrate our approach with results for a toy model of two interacting hard-core bosons and the dimerized S=1/2 Heisenberg chain. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011