814 research outputs found
Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
The zero-temperature XX chain is studied with emphasis on the properties of a
block of spins inside the chain. We investigate the quantum fluctuations
resulting from the entanglement of the block with the rest of the chain using
analytical as well as numerical (density matrix renormalization group) methods.
It is found that the rest of the chain acts as a thermal environment and an
effective temperature can be introduced to describe the fluctuations. We show
that the effective temperature description is robust in the sense that several
independent definitions (through fluctuation dissipation theorem, comparing
with a finite temperature system) yield the same functional form in the limit
of large block size (). The effective temperature can also be shown
to satisfy the basic requirements on how it changes when two bodies of equal or
unequal temperatures are brought into contact.Comment: 19 pages, 7 figure
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
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
Critical Properties of the One-Dimensional Forest-Fire Model
The one-dimensional forest-fire model including lightnings is studied
numerically and analytically. For the tree correlation function, a new
correlation length with critical exponent \nu ~ 5/6 is found by simulations. A
Hamiltonian formulation is introduced which enables one to study the stationary
state close to the critical point using quantum-mechanical perturbation theory.
With this formulation also the structure of the low-lying relaxation spectrum
and the critical behaviour of the smallest complex gap are investigated
numerically. Finally, it is shown that critical correlation functions can be
obtained from a simplified model involving only the total number of trees
although such simplified models are unable to reproduce the correct
off-critical behaviour.Comment: 24 pages (plain TeX), 4 PostScript figures, uses psfig.st
On entanglement evolution across defects in critical chains
We consider a local quench where two free-fermion half-chains are coupled via
a defect. We show that the logarithmic increase of the entanglement entropy is
governed by the same effective central charge which appears in the ground-state
properties and which is known exactly. For unequal initial filling of the
half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde
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
Quantum Corner-Transfer Matrix DMRG
We propose a new method for the calculation of thermodynamic properties of
one-dimensional quantum systems by combining the TMRG approach with the corner
transfer-matrix method. The corner transfer-matrix DMRG method brings
reasonable advantage over TMRG for classical systems. We have modified the
concept for the calculation of thermal properties of one-dimensional quantum
systems. The novel QCTMRG algorithm is implemented and used to study two simple
test cases, the classical Ising chain and the isotropic Heisenberg model. In a
discussion, the advantages and challenges are illuminated.Comment: 17 pages, 15 figures, to appear in Int.J.Mod.Phys.
On the relation between entanglement and subsystem Hamiltonians
We show that a proportionality between the entanglement Hamiltonian and the
Hamiltonian of a subsystem exists near the limit of maximal entanglement under
certain conditions. Away from that limit, solvable models show that the
coupling range differs in both quantities and allow to investigate the effect.Comment: 7 pages, 2 figures version2: minor changes, typos correcte
- …