127 research outputs found
Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
We present an algorithm to study mixed-state dynamics in one-dimensional
quantum lattice systems. The algorithm can be used, e.g., to construct thermal
states or to simulate real time evolutions given by a generic master equation.
Its two main ingredients are (i) a superoperator renormalization scheme to
efficiently describe the state of the system and (ii) the time evolving block
decimation (TEBD) technique to efficiently update the state during a time
evolution. The computational cost of a simulation increases significantly with
the amount of correlations between subsystems but it otherwise depends only
linearly in the system size. We present simulations involving quantum spins and
fermions in one spatial dimension.Comment: See also F. Verstraete et al. cond-mat/040642
INTEGRASI ANALITICAL HIERARCHY PROCESS-FUZZY DALAM PEMILIHAN SUPPLIER
This study discusses the selection of wood raw material suppliers using the AHP-F method. Problems by UD. Bless Furniture is the difficulty of determining which supplier has good performance in terms of price, quality, service, delivery, quantity determination, location as well as guarantees and claims. With many competitors and different raw material prices from each supplier. Many raw materials such as wood cracks are hollow and broken at the ends of the wood, the color of the wood, and the shape of the wood. Delivery plans that are often complained by companies where delivery is not according to the schedule in the agreement. The results of data processing carried out by the AHP fuzzy method show that the criteria that become a priority in supplier selection are the price criteria which have a weight of 0.47. By taking into account the seven criteria above, it is obtained that the supplier recommended being prioritized as the best supplier based on the highest priority weight, namely supplier C with a weight of 0,39 then supplier A with a weight of 0,37 and the third is supplier B with a weight of 0,24
Friedel Oscillations and Charge Density Waves in Chains and Ladders
The density matrix renormalization group method for ladders works much more
efficiently with open boundary conditions. One consequence of these boundary
conditions is groundstate charge density oscillations that often appear to be
nearly constant in magnitude or to decay only slightly away from the
boundaries. We analyse these using bosonization techniques, relating their
detailed form to the correlation exponent and distinguishing boundary induced
generalized Friedel oscillations from true charge density waves. We also
discuss a different approach to extracting the correlation exponent from the
finite size spectrum which uses exclusively open boundary conditions and can
therefore take advantage of data for much larger system sizes. A general
discussion of the Friedel oscillation wave-vectors is given, and a convenient
Fourier transform technique is used to determine it. DMRG results are analysed
on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the
existence of a long-ranged charge density wave state in the t-J ladder at a
filling of n=0.75 and near J/t \approx 0.25.Comment: Revtex, 15 pages, 15 postscript figure
Efficient simulation of one-dimensional quantum many-body systems
We present a numerical method to simulate the time evolution, according to a
Hamiltonian made of local interactions, of quantum spin chains and systems
alike. The efficiency of the scheme depends on the amount of the entanglement
involved in the simulated evolution. Numerical analysis indicate that this
method can be used, for instance, to efficiently compute time-dependent
properties of low-energy dynamics of sufficiently regular but otherwise
arbitrary one-dimensional quantum many-body systems.Comment: 4 pages, 1 figur
Block-Spin Approach to Electron Correlations
We consider an expansion of the ground state wavefunction of quantum lattice
many-body systems in a basis whose states are tensor products of block-spin
wavefunctions. We demonstrate by applying the method to the antiferromagnetic
spin-1/2 chain that by selecting the most important many-body states the
technique affords a severe truncation of the Hilbert space while maintaining
high accuracy.Comment: 17 pages, 3 Postscript figure
Entanglement in quantum critical phenomena
Quantum phase transitions occur at zero temperature and involve the
appearance of long-range correlations. These correlations are not due to
thermal fluctuations but to the intricate structure of a strongly entangled
ground state of the system. We present a microscopic computation of the scaling
properties of the ground-state entanglement in several 1D spin chain models
both near and at the quantum critical regimes. We quantify entanglement by
using the entropy of the ground state when the system is traced down to
spins. This entropy is seen to scale logarithmically with , with a
coefficient that corresponds to the central charge associated to the conformal
theory that describes the universal properties of the quantum phase transition.
Thus we show that entanglement, a key concept of quantum information science,
obeys universal scaling laws as dictated by the representations of the
conformal group and its classification motivated by string theory. This
connection unveils a monotonicity law for ground-state entanglement along the
renormalization group flow. We also identify a majorization rule possibly
associated to conformal invariance and apply the present results to interpret
the breakdown of density matrix renormalization group techniques near a
critical point.Comment: 5 pages, 2 figure
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
Exact bounds on the ground-state energy of the infinite-U Hubbard model
We give upper and lower bounds for the ground-state energy of the infinite-U
Hubbard model. In two dimensions, using these bounds we are able to rule out
the possibility of phase separation between the undoped-insulating state and an
hole-rich state.Comment: 2 pages, 1 figure, to appear in Phys. Rev.
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
Phase diagram of an impurity in the spin-1/2 chain: two channel Kondo effect versus Curie law
We consider a magnetic s=1/2 impurity in the antiferromagnetic spin chain as
a function of two coupling parameters: the symmetric coupling of the impurity
to two sites in the chain and the coupling between the two sites .
By using field theory arguments and numerical calculations we can identify all
possible fixed points and classify the renormalization flow between them, which
leads to a non-trivial phase diagram. Depending on the detailed choice of the
two (frustrating) coupling strengths, the stable phases correspond either to a
decoupled spin with Curie law behavior or to a non-Fermi liquid fixed point
with a logarithmically diverging impurity susceptibility as in the two channel
Kondo effect. Our results resolve a controversy about the renormalization flow.Comment: 5 pages in revtex format including 4 embedded figures (using epsf).
The latest version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/phase-diagram.pd
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