1,502 research outputs found

### Finite-size scaling exponents and entanglement in the two-level BCS model

We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio

### Violation of area-law scaling for the entanglement entropy in spin 1/2 chains

Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure

### Matrix Product States Algorithms and Continuous Systems

A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio

### A Generic Renormalization Method in Curved Spaces and at Finite Temperature

Based only on simple principles of renormalization in coordinate space, we
derive closed renormalized amplitudes and renormalization group constants at 1-
and 2-loop orders for scalar field theories in general backgrounds. This is
achieved through a generic renormalization procedure we develop exploiting the
central idea behind differential renormalization, which needs as only inputs
the propagator and the appropriate laplacian for the backgrounds in question.
We work out this generic coordinate space renormalization in some detail, and
subsequently back it up with specific calculations for scalar theories both on
curved backgrounds, manifestly preserving diffeomorphism invariance, and at
finite temperature.Comment: 15pp., REVTeX, UB-ECM-PF 94/1

### Ground state entanglement in quantum spin chains

A microscopic calculation of ground state entanglement for the XY and
Heisenberg models shows the emergence of universal scaling behavior at quantum
phase transitions. Entanglement is thus controlled by conformal symmetry. Away
from the critical point, entanglement gets saturated by a mass scale. Results
borrowed from conformal field theory imply irreversibility of entanglement loss
along renormalization group trajectories. Entanglement does not saturate in
higher dimensions which appears to limit the success of the density matrix
renormalization group technique. A possible connection between majorization and
renormalization group irreversibility emerges from our numerical analysis.Comment: 26 pages, 16 figures, added references, minor changes. Final versio

### Time-optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries

Motivated by experimental limitations commonly met in the design of solid
state quantum computers, we study the problems of non-local Hamiltonian
simulation and non-local gate synthesis when only homogeneous local unitaries
are performed in order to tailor the available interaction. Homogeneous (i.e.
identical for all subsystems) local manipulation implies a more refined
classification of interaction Hamiltonians than the inhomogeneous case, as well
as the loss of universality in Hamiltonian simulation. For the case of
symmetric two-qubit interactions, we provide time-optimal protocols for both
Hamiltonian simulation and gate synthesis.Comment: 7 page

### Area law and vacuum reordering in harmonic networks

We review a number of ideas related to area law scaling of the geometric
entropy from the point of view of condensed matter, quantum field theory and
quantum information. An explicit computation in arbitrary dimensions of the
geometric entropy of the ground state of a discretized scalar free field theory
shows the expected area law result. In this case, area law scaling is a
manifestation of a deeper reordering of the vacuum produced by majorization
relations. Furthermore, the explicit control on all the eigenvalues of the
reduced density matrix allows for a verification of entropy loss along the
renormalization group trajectory driven by the mass term. A further result of
our computation shows that single-copy entanglement also obeys area law
scaling, majorization relations and decreases along renormalization group
flows.Comment: 15 pages, 6 figures; typos correcte

### Simulation of many-qubit quantum computation with matrix product states

Matrix product states provide a natural entanglement basis to represent a
quantum register and operate quantum gates on it. This scheme can be
materialized to simulate a quantum adiabatic algorithm solving hard instances
of a NP-Complete problem. Errors inherent to truncations of the exact action of
interacting gates are controlled by the size of the matrices in the
representation. The property of finding the right solution for an instance and
the expected value of the energy are found to be remarkably robust against
these errors. As a symbolic example, we simulate the algorithm solving a
100-qubit hard instance, that is, finding the correct product state out of ~
10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow
growth of the average minimum time to solve hard instances with
highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio

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