149 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
Reply to the "Comment on 'Phase diagram of an impurity in the spin-1/2 chain: two channel Kondo effect versus Curie law'"
In a comment by A.A. Zvyagin the phase diagram in our Letter [Phys. Rev.
Lett. 86, 516 (2001)] was critisized of being incomplete and a new fixed point
was suggested. We show that this point is in fact not a fixed point and that
the phase diagram is correct as presented.Comment: Reply to a comment by A.A. Zvyagin. 1 page, 1 figure. The latest
version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/reply.pd
Critical entanglement of XXZ Heisenberg chains with defects
We study the entanglement properties of anisotropic open spin one-half
Heisenberg chains with a modified central bond. The entanglement entropy
between the two half-chains is calculated with the density-matrix
renormalization method (DMRG).We find a logarithmic behaviour with an effective
central charge c' varying with the length of the system. It flows to one in the
ferromagnetic region and to zero in the antiferromagnetic region of the model.
In the XX case it has a non-universal limit and we recover previous results.Comment: 8 pages, 15 figure
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
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
Local Magnetic Susceptibility of the Positive Muon in the Quasi 1D S=1/2 Antiferromagnet KCuF
We report muon spin rotation measurements of the local magnetic
susceptibility around a positive muon in the paramagnetic state of the quasi
one-dimensional spin 1/2 antiferromagnet KCuF. Signals from two distinct
sites are resolved which have a temperature dependent frequency shift which is
different than the magnetic susceptibility. This difference is attributed to a
muon induced perturbation of the spin 1/2 chain.Comment: 13 pages, 4 figures, The 2002 International Conference on Muon Spin
Rotation, Relaxation and Resonance, Virginia. US
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
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.
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