2,768 research outputs found
Non-extensive entropy from incomplete knowledge of Shannon entropy?
In this paper we give an interpretation of Tsallis' nonextensive statistical
mechanics based upon the information-theoretic point of view of Luzzi et al.
[cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis'
entropy to be not a fundamental concept but rather a derived one, stemming from
an incomplete knowledge of the system, not taking properly into account its
interaction with the environment. This interpretation seems to avoid some
problems occurring with the original interpretation of Tsallis statistics.Comment: v.4. 11 pages. Title changed. Content substantially changed: added
discussion of several points raised by various referees and readers; Also
reference made to work by Luzzi, Vasconcellos, Galvao Ramos. Physica Scripta,
to appea
Entanglement renormalization of anisotropic XY model
The renormalization group flows of the one-dimensional anisotropic XY model
and quantum Ising model under a transverse field are obtained by different
multiscale entanglement renormalization ansatz schemes. It is shown that the
optimized disentangler removes the short-range entanglement by rotating the
system in the parameter space spanned by the anisotropy and the magnetic field.
It is understood from the study that the disentangler reduces the entanglement
by mapping the system to another one in the same universality class but with
smaller short range entanglement. The phase boundary and corresponding critical
exponents are calculated using different schemes with different block sizes,
look-ahead steps and truncation dimensions. It is shown that larger truncation
dimension leads to more accurate results and that using larger block size or
look-ahead step improve the overall calculation consistency.Comment: 5 pages, 3 figure
On the entanglement entropy for a XY spin chain
The entanglement entropy for the ground state of a XY spin chain is related
to the corner transfer matrices of the triangular Ising model and expressed in
closed form.Comment: 4 pages, 2 figure
Two-Point Entanglement Near a Quantum Phase Transition
In this work, we study the two-point entanglement S(i,j), which measures the
entanglement between two separated degrees of freedom (ij) and the rest of
system, near a quantum phase transition. Away from the critical point, S(i,j)
saturates with a characteristic length scale , as the distance |i-j|
increases. The entanglement length agrees with the correlation length.
The universality and finite size scaling of entanglement are demonstrated in a
class of exactly solvable one dimensional spin model. By connecting the
two-point entanglement to correlation functions in the long range limit, we
argue that the prediction power of a two-point entanglement is universal as
long as the two involved points are separated far enough.Comment: published versio
Geometric entanglement from matrix product state representations
An efficient scheme to compute the geometric entanglement per lattice site
for quantum many-body systems on a periodic finite-size chain is proposed in
the context of a tensor network algorithm based on the matrix product state
representations. It is systematically tested for three prototypical critical
quantum spin chains, which belong to the same Ising universality class. The
simulation results lend strong support to the previous claim [Q.-Q. Shi, R.
Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008
(2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82},
180406R (2010)] that the leading finite-size correction to the geometric
entanglement per lattice site is universal, with its remarkable connection to
the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally
invariant boundary condition.Comment: 4+ pages, 3 figure
The Entanglement Entropy of Solvable Lattice Models
We consider the spin k/2 analogue of the XXZ quantum spin chain. We compute
the entanglement entropy S associated with splitting the infinite chain into
two semi-infinite pieces. In the scaling limit, we find S ~ c_k/6
(ln(xi))+ln(g)+... . Here xi is the correlation length and c_k=3k/(k+2) is the
central charge associated with the sl_2 WZW model at level k. ln(g) is the
boundary entropy of the WZW model. Our result extends previous observations and
suggests that this is a simple and perhaps rather general way both of
extracting the central charge of the ultraviolet CFT associated with the
scaling limit of a solvable lattice model, and of matching lattice and CFT
boundary conditions.Comment: 6 pages; connection with boundary entropy of Affleck and Ludwig added
in revised version and notation slightly change
Entanglement entropy in collective models
We discuss the behavior of the entanglement entropy of the ground state in
various collective systems. Results for general quadratic two-mode boson models
are given, yielding the relation between quantum phase transitions of the
system (signaled by a divergence of the entanglement entropy) and the
excitation energies. Such systems naturally arise when expanding collective
spin Hamiltonians at leading order via the Holstein-Primakoff mapping. In a
second step, we analyze several such models (the Dicke model, the two-level BCS
model, the Lieb-Mattis model and the Lipkin-Meshkov-Glick model) and
investigate the properties of the entanglement entropy in the whole parameter
range. We show that when the system contains gapless excitations the
entanglement entropy of the ground state diverges with increasing system size.
We derive and classify the scaling behaviors that can be met.Comment: 11 pages, 7 figure
Ground-state fidelity of Luttinger liquids: A wave functional approach
We use a wave functional approach to calculate the fidelity of ground states
in the Luttinger liquid universality class of one-dimensional gapless quantum
many-body systems. The ground-state wave functionals are discussed using both
the Schrodinger (functional differential equation) formulation and a path
integral formulation. The fidelity between Luttinger liquids with Luttinger
parameters K and K' is found to decay exponentially with system size, and to
obey the symmetry F(K,K')=F(1/K,1/K') as a consequence of a duality in the
bosonization description of Luttinger liquids.Comment: 13 pages, IOP single-column format. Sec. 3 expanded with discussion
of short-distance cut-off. Some typos corrected. Ref. 44 in v2 is now
footnote 2 (moved by copy editor). Published versio
Chiral critical behavior in two dimensions from five-loop renormalization-group expansions
We analyse the critical behavior of two-dimensional N-vector spin systems
with noncollinear order within the five-loop renormalization-group
approximation. The structure of the RG flow is studied for different N leading
to the conclusion that the chiral fixed point governing the critical behavior
of physical systems with N = 2 and N = 3 does not coincide with that given by
the 1/N expansion. We show that the stable chiral fixed point for ,
including N = 2 and N = 3, turns out to be a focus. We give a complete
characterization of the critical behavior controlled by this fixed point, also
evaluating the subleading crossover exponents. The spiral-like approach of the
chiral fixed point is argued to give rise to unusual crossover and
near-critical regimes that may imitate varying critical exponents seen in
numerous physical and computer experiments.Comment: 17 pages, 12 figure
Entanglement Entropy dynamics in Heisenberg chains
By means of the time-dependent density matrix renormalization group algorithm
we study the zero-temperature dynamics of the Von Neumann entropy of a block of
spins in a Heisenberg chain after a sudden quench in the anisotropy parameter.
In the absence of any disorder the block entropy increases linearly with time
and then saturates. We analyze the velocity of propagation of the entanglement
as a function of the initial and final anisotropies and compare, wherever
possible, our results with those obtained by means of Conformal Field Theory.
In the disordered case we find a slower (logarithmic) evolution which may
signals the onset of entanglement localization.Comment: 15 pages, 9 figure
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