346 research outputs found
The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
We consider the finite temperature metal-insulator transition in the half
filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A
new method for calculating the Dynamical Mean Field Theory fixpoint surface in
the phase diagram is presented and shown to be free from the convergence
problems of standard forward recursion. The fixpoint equation is then analyzed
using dynamical systems methods. On the fixpoint surface the eigenspectra of
its Jacobian is used to characterize the hysteresis boundaries of the first
order transition line and its second order critical end point. The critical
point is shown to be a cusp catastrophe in the parameter space, opening a
pitchfork bifurcation along the first order transition line, while the
hysteresis boundaries are shown to be saddle-node bifurcations of two merging
fixpoints. Using Landau theory the properties of the critical end point is
determined and related to the critical eigenmode of the Jacobian. Our findings
provide new insights into basic properties of this intensively studied
transition.Comment: 11 pages, 12 figures, 1 tabl
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Clustering in mixing flows
We calculate the Lyapunov exponents for particles suspended in a random
three-dimensional flow, concentrating on the limit where the viscous damping
rate is small compared to the inverse correlation time. In this limit Lyapunov
exponents are obtained as a power series in epsilon, a dimensionless measure of
the particle inertia. Although the perturbation generates an asymptotic series,
we obtain accurate results from a Pade-Borel summation. Our results prove that
particles suspended in an incompressible random mixing flow can show pronounced
clustering when the Stokes number is large and we characterise two distinct
clustering effects which occur in that limit.Comment: 5 pages, 1 figur
Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
The density matrix renormalization group (``DMRG'') discovered by White has
shown to be a powerful method to understand the properties of many one
dimensional quantum systems. In the case where renormalization eventually
converges to a fixed point we show that quantum states in the thermodynamic
limit with periodic boundary conditions can be simply represented by a special
type of product ground state with a natural description of Bloch states of
elementary excitations that are spin-1 solitons. We then observe that these
states can be rederived through a simple variational ansatz making no reference
to a renormalization construction. The method is tested on the spin-1
Heisenberg model.Comment: 13 pages uuencoded compressed postscript including figure
Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix
In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that
the many-particle eigenvalues and eigenstates of the many-body density matrix
of a block of sites cut out from an infinite chain of
noninteracting spinless fermions can all be constructed out of the one-particle
eigenvalues and one-particle eigenstates respectively. In this paper we
developed a statistical-mechanical analogy between the density matrix
eigenstates and the many-body states of a system of noninteracting fermions.
Each density matrix eigenstate corresponds to a particular set of occupation of
single-particle pseudo-energy levels, and the density matrix eigenstate with
the largest weight, having the structure of a Fermi sea ground state,
unambiguously defines a pseudo-Fermi level. We then outlined the main ideas
behind an operator-based truncation of the density matrix eigenstates, where
single-particle pseudo-energy levels far away from the pseudo-Fermi level are
removed as degrees of freedom. We report numerical evidence for scaling
behaviours in the single-particle pseudo-energy spectrum for different block
sizes and different filling fractions \nbar. With the aid of these
scaling relations, which tells us that the block size plays the role of an
inverse temperature in the statistical-mechanical description of the density
matrix eigenstates and eigenvalues, we looked into the performance of our
operator-based truncation scheme in minimizing the discarded density matrix
weight and the error in calculating the dispersion relation for elementary
excitations. This performance was compared against that of the traditional
density matrix-based truncation scheme, as well as against a operator-based
plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb,
graphicx and mathrsfs package
Exact ground states for two new spin-1 quantum chains, new features of matrix product states
We use the matrix product formalism to find exact ground states of two new
spin-1 quantum chains with nearest neighbor interactions. One of the models,
model I, describes a one-parameter family of quantum chains for which the
ground state can be found exactly. In certain limit of the parameter, the
Hamiltonian turns into the interesting case . The other model which we label as model II, corresponds to a
family of solvable three-state vertex models on square two dimensional
lattices. The ground state of this model is highly degenerate and the matrix
product states is a generating state of such degenerate states. The simple
structure of the matrix product state allows us to determine the properties of
degenerate states which are otherwise difficult to determine. For both models
we find exact expressions for correlation functions.Comment: 22 pages, references added, accepted for publication in European
Physics Journal
A class of ansatz wave functions for 1D spin systems and their relation to DMRG
We investigate the density matrix renormalization group (DMRG) discovered by
White and show that in the case where the renormalization eventually converges
to a fixed point the DMRG ground state can be simply written as a ``matrix
product'' form. This ground state can also be rederived through a simple
variational ansatz making no reference to the DMRG construction. We also show
how to construct the ``matrix product'' states and how to calculate their
properties, including the excitation spectrum. This paper provides details of
many results announced in an earlier letter.Comment: RevTeX, 49 pages including 4 figures (macro included). Uuencoded with
uufiles. A complete postscript file is available at
http://fy.chalmers.se/~tfksr/prb.dmrg.p
Heterogeneity in Blood Pressure Response to 4 Antihypertensive Drugs: A Randomized Clinical Trial
Importance: Hypertension is the leading risk factor for premature death worldwide. Multiple blood pressure-lowering therapies are available but the potential for maximizing benefit by personalized targeting of drug classes is unknown. Objective: To investigate and quantify the potential for targeting specific drugs to specific individuals to maximize blood pressure effects. Design, Setting, and Participants: A randomized, double-blind, repeated crossover trial in men and women with grade 1 hypertension at low risk for cardiovascular events at an outpatient research clinic in Sweden. Mixed-effects models were used to assess the extent to which individuals responded better to one treatment than another and to estimate the additional blood pressure lowering achievable by personalized treatment. Interventions: Each participant was scheduled for treatment in random order with 4 different classes of blood pressure-lowering drugs (lisinopril [angiotensin-converting enzyme inhibitor], candesartan [angiotensin-receptor blocker], hydrochlorothiazide [thiazide], and amlodipine [calcium channel blocker]), with repeated treatments for 2 classes. Main Outcomes and Measures: Ambulatory daytime systolic blood pressure, measured at the end of each treatment period. Results: There were 1468 completed treatment periods (median length, 56 days) recorded in 270 of the 280 randomized participants (54% men; mean age, 64 years). The blood pressure response to different treatments varied considerably between individuals (P <.001), specifically for the choices of lisinopril vs hydrochlorothiazide, lisinopril vs amlodipine, candesartan vs hydrochlorothiazide, and candesartan vs amlodipine. Large differences were excluded for the choices of lisinopril vs candesartan and hydrochlorothiazide vs amlodipine. On average, personalized treatment had the potential to provide an additional 4.4 mm Hg-lower systolic blood pressure. Conclusions and Relevance: These data reveal substantial heterogeneity in blood pressure response to drug therapy for hypertension, findings that may have implications for personalized therapy. Trial Registration: ClinicalTrials.gov Identifier: NCT02774460
The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
We have adjusted the Density Matrix Renormalization method to handle two
dimensional systems of limited width. The key ingredient for this extension is
the incorporation of symmetries in the method. The advantage of our approach is
that we can force certain symmetry properties to the resulting ground state
wave function. Combining the results obtained for system sizes up-to and finite size scaling, we derive the phase transition point and the
critical exponent for the gap in the Ising model in a Transverse Field on a two
dimensional square lattice.Comment: 9 pages, 8 figure
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