4,308 research outputs found

### Solution of the fermionic entanglement problem with interface defects

We study the ground-state entanglement of two halves of a critical transverse
Ising chain, separated by an interface defect. From the relation to a
two-dimensional Ising model with a defect line we obtain an exact expression
for the continuously varying effective central charge. The result is relevant
also for other fermionic chains.Comment: 15 pages, 6 figures, changed title and minor modifications in
published 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 $L$ 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 ($L\to\infty$). 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

### 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

### Casimir Terms and Shape Instabilities for Two-Dimensional Critical Systems

We calculate the universal part of the free energy of certain finite two-
dimensional regions at criticality by use of conformal field theory. Two
geometries are considered: a section of a circle ("pie slice") of angle \phi
and a helical staircase of finite angular (and radial) extent. We derive some
consequences for certain matrix elements of the transfer matrix and corner
transfer matrix. We examine the total free energy, including non- universal
edge free energy terms, in both cases. A new, general, Casimir instability
toward sharp corners on the boundary is found; other new instability behavior
is investigated. We show that at constant area and edge length, the rectangle
is unstable against small curvature.Comment: 15 pages PostScript, accepted for publication in Z. Phys.

### Surface and bulk entanglement in free-fermion chains

We consider free-fermion chains where full and empty parts are connected by a
transition region with narrow surfaces. This can be caused by a linear
potential or by time evolution from a step-like initial state. Entanglement
spectra, entanglement entropies and fluctuations are determined for subsystems
either in the surface region or extending into the bulk. In all cases there is
logarithmic behaviour in the subsystem size, but the prefactors in the surface
differ from those in the bulk by 3/2. A previous fluctuation result is
corrected and a general scaling formula is inferred from the data.Comment: 14 pages, 6 figures, minor changes, references adde

### 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

- …