57 research outputs found
Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories
We investigate both numerically and analytically the behaviour of a spin-1
antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic
field. Extensive DMRG studies of chains up to N=80 sites extend previous
analyses and exhibit the well known phenomenon of the closure of the Haldane
gap at a lower critical field H_c1. We obtain an estimate of the gap below
H_c1. Above the lower critical field, when the correlation functions exhibit
algebraic decay, we obtain the critical exponent as a function of the net
magnetization as well as the magnetization curve up to the saturation (upper
critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry
of the model is explicitly broken by the field, the Haldane phase of the model
is still well described by an SO(3) nonlinear sigma-model. A mean-field theory
is developed for the latter and its predictions are compared with those of the
numerical analysis and with the existing literature.Comment: 11 pages, 4 eps figure
Rapidly-converging methods for the location of quantum critical points from finite-size data
We analyze in detail, beyond the usual scaling hypothesis, the finite-size
convergence of static quantities toward the thermodynamic limit. In this way we
are able to obtain sequences of pseudo-critical points which display a faster
convergence rate as compared to currently used methods. The approaches are
valid in any spatial dimension and for any value of the dynamic exponent. We
demonstrate the effectiveness of our methods both analytically on the basis of
the one dimensional XY model, and numerically considering c = 1 transitions
occurring in non integrable spin models. In particular, we show that these
general methods are able to locate precisely the onset of the
Berezinskii-Kosterlitz-Thouless transition making only use of ground-state
properties on relatively small systems.Comment: 9 pages, 2 EPS figures, RevTeX style. Updated to published versio
Quantum criticality as a resource for quantum estimation
We address quantum critical systems as a resource in quantum estimation and
derive the ultimate quantum limits to the precision of any estimator of the
coupling parameters. In particular, if L denotes the size of a system and
\lambda is the relevant coupling parameters driving a quantum phase transition,
we show that a precision improvement of order 1/L may be achieved in the
estimation of \lambda at the critical point compared to the non-critical case.
We show that analogue results hold for temperature estimation in classical
phase transitions. Results are illustrated by means of a specific example
involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a
specific exampl
Stable particles in anisotropic spin-1 chains
Motivated by field-theoretic predictions we investigate the stable
excitations that exist in two characteristic gapped phases of a spin-1 model
with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a
region close to the phase boundary where a stable breather exists besides the
stable particles, that form the Haldane triplet at the Heisenberg isotropic
point. The numerical data, obtained by means of the Density Matrix
Renormalization Group, confirm this picture in the so-called large-D phase for
which we give also a quantitative analysis of the bound states using standard
perturbation theory. However, the situation turns out to be considerably more
intricate in the Haldane phase where, to the best of our data, we do not
observe stable breathers contrarily to what could be expected from the
sine-Gordon model, but rather only the three modes predicted by a novel
anisotropic extension of the Non-Linear Sigma Model studied here by means of a
saddle-point approximation.Comment: 8 pages, 7 eps figures, svjour clas
Optimal quantum estimation in spin systems at criticality
It is a general fact that the coupling constant of an interacting many-body
Hamiltonian do not correspond to any observable and one has to infer its value
by an indirect measurement. For this purpose, quantum systems at criticality
can be considered as a resource to improve the ultimate quantum limits to
precision of the estimation procedure. In this paper, we consider the
one-dimensional quantum Ising model as a paradigmatic example of many-body
system exhibiting criticality, and derive the optimal quantum estimator of the
coupling constant varying size and temperature. We find the optimal external
field, which maximizes the quantum Fisher information of the coupling constant,
both for few spins and in the thermodynamic limit, and show that at the
critical point a precision improvement of order is achieved. We also show
that the measurement of the total magnetization provides optimal estimation for
couplings larger than a threshold value, which itself decreases with
temperature.Comment: 8 pages, 4 figure
Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements
The vacuum angle renormalization is studied for a toy model of a
quantum particle moving around a ring, threaded by a magnetic flux .
Different renormalization group (RG) procedures lead to the same generic RG
flow diagram, similar to that of the quantum Hall effect. We argue that the
renormalized value of the vacuum angle may be observed if the particle's
position is measured with finite accuracy or coupled to additional slow
variable, which can be viewed as a coordinate of a second (heavy) particle on
the ring. In this case the renormalized appears as a magnetic flux
this heavy particle sees, or the Berry phase, associated with its slow
rotation.Comment: 4 pages, 2 figure
Luttinger liquid behavior in spin chains with a magnetic field
Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic
field are Luttinger liquids, whose parameters depend on the actual
magnetization of the chain. Here we present precise numerical estimates of the
Luttinger liquid dressed charge , which determines the critical exponents,
by calculating the magnetization and quadrupole operator profiles for
and S=1 chains using the density matrix renormalization group method. Critical
amplitudes and the scattering length at the chain ends are also determined.
Although both systems are Luttinger liquids the characteristic parameters
differ considerably.Comment: Final version, 6 pages, 6 EPS figure
Numerical Calculation of the Fidelity for the Kondo and the Friedel-Anderson Impurities
The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are
calculated numerically. The ground states of both systems are calculated with
the FAIR (Friedel artificially inserted resonance) theory. The ground state in
the interacting systems is compared with a nullstate in which the interaction
is zero. The different multi-electron states are expressed in terms of Wilson
states. The use of N Wilson states simulates the use of a large effective
number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals
whether one has an Anderson orthogonality catastrophe at zero energy. The
results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the
Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding
plot for the symmetric FA impurity saturates for large N_{eff} when the level
spacing at the Fermi level is of the order of the singlet-triplet excitation
energy. The behavior of the fidelity allows one to determine the phase shift of
the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a,
05.30.-
Particle Content of the Nonlinear Sigma Model with Theta-Term: a Lattice Model Investigation
Using new as well as known results on dimerized quantum spin chains with
frustration, we are able to infer some properties on the low-energy spectrum of
the O(3) Nonlinear Sigma Model with a topological theta-term. In particular,
for sufficiently strong coupling, we find a range of values of theta where a
singlet bound state is stable under the triplet continuum. On the basis of
these results, we propose a new renormalization group flow diagram for the
Nonlinear Sigma Model with theta-term.Comment: 10 pages, 5 figures .eps, iopart format, submitted to JSTA
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