1,207 research outputs found
On single-copy entanglement
The largest eigenvalue of the reduced density matrix for quantum chains is
shown to have a simple physical interpretation and power-law behaviour in
critical systems. This is verified numerically for XXZ spin chains.Comment: 4 pages, 2 figures, note added, typo correcte
On the reduced density matrix for a chain of free electrons
The properties of the reduced density matrix describing an interval of N
sites in an infinite chain of free electrons are investigated. A commuting
operator is found for arbitrary filling and also for open chains. For a half
filled periodic chain it is used to determine the eigenfunctions for the
dominant eigenvalues analytically in the continuum limit. Relations to the
critical six-vertex model are discussed.Comment: 8 pages, small changes, Equ.(24) corrected, final versio
Calculation of reduced density matrices from correlation functions
It is shown that for solvable fermionic and bosonic lattice systems, the
reduced density matrices can be determined from the properties of the
correlation functions. This provides the simplest way to these quantities which
are used in the density-matrix renormalization group method.Comment: 4 page
Evolution of entanglement after a local quench
We study free electrons on an infinite half-filled chain, starting in the
ground state with a bond defect. We find a logarithmic increase of the
entanglement entropy after the defect is removed, followed by a slow relaxation
towards the value of the homogeneous chain. The coefficients depend
continuously on the defect strength.Comment: 14 pages, 9 figures, final versio
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
Real-space renormalization group approach for the corner Hamiltonian
We present a real-space renormalization group approach for the corner
Hamiltonian, which is relevant to the reduced density matrix in the density
matrix renormalization group. A set of self-consistent equations that the
renormalized Hamiltonian should satisfy in the thermodynamic limit is also
derived from the fixed point of the recursion relation for the corner
Hamiltonian. We demonstrate the renormalization group algorithm for the
XXZ spin chain and show that the results are consistent with the exact
solution. We further examine the renormalization group for the S=1 Heisenberg
spin chain and then discuss the nature of the eigenvalue spectrum of the corner
Hamiltonian for the non-integrable model.Comment: 7 page
Entanglement evolution after connecting finite to infinite quantum chains
We study zero-temperature XX chains and transverse Ising chains and join an
initially separate finite piece on one or on both sides to an infinite
remainder. In both critical and non-critical systems we find a typical increase
of the entanglement entropy after the quench, followed by a slow decay towards
the value of the homogeneous chain. In the critical case, the predictions of
conformal field theory are verified for the first phase of the evolution, while
at late times a step structure can be observed.Comment: 15 pages, 11 figure
Density-Matrix Spectra of Solvable Fermionic Systems
We consider non-interacting fermions on a lattice and give a general result
for the reduced density matrices corresponding to parts of the system. This
allows to calculate their spectra, which are essential in the DMRG method, by
diagonalizing small matrices. We discuss these spectra and their typical
features for various fermionic quantum chains and for the two-dimensional
tight-binding model.Comment: 12 pages and 9 figure
Density Matrices for a Chain of Oscillators
We consider chains with an optical phonon spectrum and study the reduced
density matrices which occur in density-matrix renormalization group (DMRG)
calculations. Both for one site and for half of the chain, these are found to
be exponentials of bosonic operators. Their spectra, which are correspondingly
exponential, are determined and discussed. The results for large systems are
obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure
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