882 research outputs found
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
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
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
On the continuum limit of the entanglement Hamiltonian
We consider the entanglement Hamiltonian for an interval in a chain of free fermions in its ground state and show that the lattice expression goes over into the conformal one if one includes the hopping to distant neighbours in the continuum limit. For an infinite chain, this can be done analytically for arbitrary fillings and is shown to be the consequence of the particular structure of the entanglement Hamiltonian, while for finite rings or temperatures the result is based on numerical calculations
Entanglement in the XX spin chain with an energy current
We consider the ground state of the XX chain that is constrained to carry a
current of energy. The von Neumann entropy of a block of neighboring spins,
describing entanglement of the block with the rest of the chain, is computed.
Recent calculations have revealed that the entropy in the XX model diverges
logarithmically with the size of the subsystem. We show that the presence of
the energy current increases the prefactor of the logarithmic growth. This
result indicates that the emergence of the energy current gives rise to an
increase of entanglement.Comment: 4 pages, 4 figure
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
Exact results for the entanglement across defects in critical chains
We consider fermionic and bosonic quantum chains where a defect separates two
subsystems and compare the corresponding entanglement spectra. With these, we
calculate their R\'enyi entanglement entropies and obtain analytical formulae
for the continuously varying coefficient of the leading logarithmic term. For
the bosonic case we also present numerical results.Comment: 17 pages, 6 figures, some remarks adde
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
change
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