184 research outputs found
Flux quench in a system of interacting spinless fermions in one dimension
We study a quantum quench in a one-dimensional spinless fermion model
(equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched
off. This quench is equivalent to imposing a pulse of electric field and
therefore generates an initial particle current. This current is not a
conserved quantity in presence of a lattice and interactions and we investigate
numerically its time-evolution after the quench, using the infinite
time-evolving block decimation method. For repulsive interactions or large
initial flux, we find oscillations that are governed by excitations deep inside
the Fermi sea. At long times we observe that the current remains non-vanishing
in the gapless cases, whereas it decays to zero in the gapped cases. Although
the linear response theory (valid for a weak flux) predicts the same long-time
limit of the current for repulsive and attractive interactions (relation with
the zero-temperature Drude weight), larger nonlinearities are observed in the
case of repulsive interactions compared with that of the attractive case.Comment: 10 pages, 10 figures; v2: Added references. Figures are refined and
animations are added. Corrected typos. Published versio
Magnon bands of N-leg integer-spin antiferromagnetic systems in the weak interchain-coupling regime
Using the exact results of the O(3) nonlinear sigma model (NLSM) and a few
quantitative numerical data for integer-spin antiferromagnetic (AF) chains, we
systematically estimate all magnon excitation energies of N-leg integer-spin AF
ladders and tubes in the weak-interchain-coupling regime. Our method is based
on a first-order perturbation theory for the strength of the interchain
coupling. It can deal with any kind of interchain interactions, in principle.
We confirm that results of the perturbation theory are in good agreement with
those of a quantum Monte Carlo simulation and with our recent study based on a
saddle-point approximation of the NLSM [Phys. Rev. B 72, 104438 (2005)]. Our
theory further supports the existence of a Haldane (gapped) phase even in a
d-dimensional (d\geq 2) spatially anisotropic integer-spin AF model, if the
exchange coupling in one direction is sufficiently strong compared with those
in all the other directions. The strategy in this paper is applicable to other
N-leg systems consisting of gapped chains which low-energy physics is exactly
or quantitatively known.Comment: 11 pages, 4 figures, Revtex, published version, see also
cond-mat/0506049 (PRB72, 104438 (2005)
Power dissipation for systems with junctions of multiple quantum wires
We study power dissipation for systems of multiple quantum wires meeting at a
junction, in terms of a current splitting matrix (M) describing the junction.
We present a unified framework for studying dissipation for wires with either
interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi liquid
leads) or non-interacting electrons. We show that for a given matrix M, the
eigenvalues of M^T M characterize the dissipation, and the eigenvectors
identify the combinations of bias voltages which need to be applied to the
different wires in order to maximize the dissipation associated with the
junction. We use our analysis to propose and study some microscopic models of a
dissipative junction which employ the edge states of a quantum Hall liquid.
These models realize some specific forms of the M-matrix whose entries depends
on the tunneling amplitudes between the different edges.Comment: 9 pages, 4 figures; made several minor changes; this is the published
versio
An Electron Spin Resonance Selection Rule for Spin-Gapped Systems
The direct electron spin resonance (ESR) absorption between a singlet ground
state and the triplet excited states of spin gap systems is investigated. Such
an absorption, which is forbidden by the conservation of the total spin quantum
number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya
interaction. We show a selection rule in the presence of this interaction,
using the exact numerical diagonalization of the finite cluster of the
quasi-one-dimensional bond-alternating spin system. The selection rule is also
modified into a suitable form in order to interpret recent experimental results
on CuGeO and NaVO.Comment: 5 pages, Revtex, with 6 eps figures, to appear in J. Phys. Soc. Jpn.
Vol. 69 No. 11 (2000
Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances
We study the effect that resistive regions have on the conductance of a
quantum wire with interacting electrons which is connected to Fermi liquid
leads. Using the bosonization formalism and a Rayleigh dissipation function to
model the power dissipation, we use both scattering theory and Green's function
techniques to derive the DC conductance. The resistive regions are generally
found to lead to incoherent transport. For a single wire, we find that the
resistance adds in series to the contact resistance of h/e^2 for spinless
electrons, and the total resistance is independent of the Luttinger parameter
K_W of the wire. We numerically solve the bosonic equations to illustrate what
happens when a charge density pulse is incident on the wire; the results depend
on the parameters of the resistive and interacting regions in interesting ways.
For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless
current splitting matrix to model the junction. For a junction of three wires
connected to Fermi liquid leads, there are two families of such matrices; we
find that the conductance matrix generally depends on K_W for one family but is
independent of K_W for the other family, regardless of the resistances present
in the system.Comment: 6 pages, 3 figures; added a discussion of time reversal invariance;
this is the published versio
Non-perturbative approach to Luttinger's theorem in one dimension
The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide
range of models of interacting electrons and localized spins in one-dimensional
lattice. The existence of a low-energy state is generally proved except for
special commensurate fillings where a gap may occur. Moreover, the crystal
momentum of the constructed low-energy state is , where is the
Fermi momentum of the non-interacting model, corresponding to Luttinger's
theorem. For the Kondo lattice model, our result implies that must be
calculated by regarding the localized spins as additional electrons.Comment: Note added on the rigorous proof given by H. Tasaki; also added some
references; 5 pages, REVTEX (no figure
Renormalization group study of the Kondo problem at a junction of several Luttinger wires
We study a system consisting of a junction of N quantum wires, where the
junction is characterized by a scalar S-matrix, and an impurity spin is coupled
to the electrons close to the junction. The wires are modeled as weakly
interacting Tomonaga-Luttinger liquids. We derive the renormalization group
equations for the Kondo couplings of the spin to the electronic modes on
different wires, and analyze the renormalization group flows and fixed points
for different values of the initial Kondo couplings and of the junction
S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We
generally find that the Kondo couplings flow towards large and
antiferromagnetic values in one of two possible ways. For the Griffiths
S-matrix, we study one of the strong coupling flows by a perturbative expansion
in the inverse of the Kondo coupling; we find that at large distances, the
system approaches the ferromagnetic fixed point of the decoupled S-matrix. For
the decoupled S-matrix with antiferromagnetic Kondo couplings and weak
inter-electron interactions, the flows are to one of two strong coupling fixed
points in which all the channels are strongly coupled to each other through the
impurity spin. But strong inter-electron interactions, with K_\rho < N/(N+2),
stabilize a multi-channel fixed point in which the coupling between different
channels goes to zero. We have also studied the temperature dependence of the
conductance at the decoupled and Griffiths S-matrices.Comment: Revtex4, 16 pages including 6 figure
Ordered phase and phase transitions in the three-dimensional generalized six-state clock model
We study the three-dimensional generalized six-state clock model at values of
the energy parameters, at which the system is considered to have the same
behavior as the stacked triangular antiferromagnetic Ising model and the
three-state antiferromagnetic Potts model. First, we investigate ordered phases
by using the Monte Carlo twist method (MCTM). We confirmed the existence of an
incompletely ordered phase (IOP1) at intermediate temperature, besides the
completely ordered phase (COP) at low-temperature. In this intermediate phase,
two neighboring states of the six-state model mix, while one of them is
selected in the low temperature phase. We examine the fluctuation the mixing
rate of the two states in IOP1 and clarify that the mixing rate is very stable
around 1:1.
The high temperature phase transition is investigated by using
non-equilibrium relaxation method (NERM). We estimate the critical exponents
beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY
universality class. The low temperature phase transition is found to be of
first-order by using MCTM and the finite-size-scaling analysis
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