9,347 research outputs found
A class of quantum many-body states that can be efficiently simulated
We introduce the multi-scale entanglement renormalization ansatz (MERA), an
efficient representation of certain quantum many-body states on a D-dimensional
lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive
causal structure, the MERA allows for an exact evaluation of local expectation
values. It is also the structure underlying entanglement renormalization, a
coarse-graining scheme for quantum systems on a lattice that is focused on
preserving entanglement.Comment: 4 pages, 5 figure
Entanglement renormalization
In the context of real-space renormalization group methods, we propose a
novel scheme for quantum systems defined on a D-dimensional lattice. It is
based on a coarse-graining transformation that attempts to reduce the amount of
entanglement of a block of lattice sites before truncating its Hilbert space.
Numerical simulations involving the ground state of a 1D system at criticality
show that the resulting coarse-grained site requires a Hilbert space dimension
that does not grow with successive rescaling transformations. As a result we
can address, in a quasi-exact way, tens of thousands of quantum spins with a
computational effort that scales logarithmically in the system's size. The
calculations unveil that ground state entanglement in extended quantum systems
is organized in layers corresponding to different length scales. At a quantum
critical point, each rellevant length scale makes an equivalent contribution to
the entanglement of a block with the rest of the system.Comment: 4 pages, 4 figures, updated versio
Field-theory results for three-dimensional transitions with complex symmetries
We discuss several examples of three-dimensional critical phenomena that can
be described by Landau-Ginzburg-Wilson theories. We present an
overview of field-theoretical results obtained from the analysis of high-order
perturbative series in the frameworks of the and of the
fixed-dimension d=3 expansions. In particular, we discuss the stability of the
O(N)-symmetric fixed point in a generic N-component theory, the critical
behaviors of randomly dilute Ising-like systems and frustrated spin systems
with noncollinear order, the multicritical behavior arising from the
competition of two distinct types of ordering with symmetry O() and
O() respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200
Entanglement Entropy in Extended Quantum Systems
After a brief introduction to the concept of entanglement in quantum systems,
I apply these ideas to many-body systems and show that the von Neumann entropy
is an effective way of characterising the entanglement between the degrees of
freedom in different regions of space. Close to a quantum phase transition it
has universal features which serve as a diagnostic of such phenomena. In the
second part I consider the unitary time evolution of such systems following a
`quantum quench' in which a parameter in the hamiltonian is suddenly changed,
and argue that finite regions should effectively thermalise at late times,
after interesting transient effects.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200
The role of initial conditions in the ageing of the long-range spherical model
The kinetics of the long-range spherical model evolving from various initial
states is studied. In particular, the large-time auto-correlation and -response
functions are obtained, for classes of long-range correlated initial states,
and for magnetized initial states. The ageing exponents can depend on certain
qualitative features of initial states. We explicitly find the conditions for
the system to cross over from ageing classes that depend on initial conditions
to those that do not.Comment: 15 pages; corrected some typo
Entanglement of two blocks of spins in the critical Ising model
We compute the entropy of entanglement of two blocks of L spins at a distance
d in the ground state of an Ising chain in an external transverse magnetic
field. We numerically study the von Neumann entropy for different values of the
transverse field. At the critical point we obtain analytical results for blocks
of size L=1 and L=2. In the general case, the critical entropy is shown to be
additive when d goes to infinity. Finally, based on simple arguments, we derive
an expression for the entropy at the critical point as a function of both L and
d. This formula is in excellent agreement with numerical results.Comment: published versio
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
Dynamic crossover in the global persistence at criticality
We investigate the global persistence properties of critical systems relaxing
from an initial state with non-vanishing value of the order parameter (e.g.,
the magnetization in the Ising model). The persistence probability of the
global order parameter displays two consecutive regimes in which it decays
algebraically in time with two distinct universal exponents. The associated
crossover is controlled by the initial value m_0 of the order parameter and the
typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo
simulations of the two-dimensional Ising model with Glauber dynamics display
clearly this crossover. The measured exponent of the ultimate algebraic decay
is in rather good agreement with our theoretical predictions for the Ising
universality class.Comment: 5 pages, 2 figure
Entanglement entropy of two disjoint intervals in conformal field theory
We study the entanglement of two disjoint intervals in the conformal field
theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any
integer n is calculated as the four-point function of a particular type of
twist fields and the final result is expressed in a compact form in terms of
the Riemann-Siegel theta functions. In the decompactification limit we provide
the analytic continuation valid for all model parameters and from this we
extract the entanglement entropy. These predictions are checked against
existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos
corrected and refs adde
Entanglement entropy of random quantum critical points in one dimension
For quantum critical spin chains without disorder, it is known that the
entanglement of a segment of N>>1 spins with the remainder is logarithmic in N
with a prefactor fixed by the central charge of the associated conformal field
theory. We show that for a class of strongly random quantum spin chains, the
same logarithmic scaling holds for mean entanglement at criticality and defines
a critical entropy equivalent to central charge in the pure case. This
effective central charge is obtained for Heisenberg, XX, and quantum Ising
chains using an analytic real-space renormalization group approach believed to
be asymptotically exact. For these random chains, the effective universal
central charge is characteristic of a universality class and is consistent with
a c-theorem.Comment: 4 pages, 3 figure
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