13,083 research outputs found
Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
A systematic analysis is performed for quantum phase transitions in a
two-dimensional anisotropic spin 1/2 anti-ferromagnetic XYX model in an
external magnetic field. With the help of an innovative tensor network
algorithm, we compute the fidelity per lattice site to demonstrate that the
field-induced quantum phase transition is unambiguously characterized by a
pinch point on the fidelity surface, marking a continuous phase transition. We
also compute an entanglement estimator, defined as a ratio between the
one-tangle and the sum of squared concurrences, to identify both the
factorizing field and the critical point, resulting in a quantitative agreement
with quantum Monte Carlo simulation. In addition, the local order parameter is
"derived" from the tensor network representation of the system's ground state
wave functions.Comment: 4+ pages, 3 figure
Cosmological Effects of Nonlinear Electrodynamics
It will be shown that a given realization of nonlinear electrodynamics, used
as source of Einstein's equations, generates a cosmological model with
interesting features, namely a phase of current cosmic acceleration, and the
absence of an initial singularity, thus pointing to a way to solve two
important problems in cosmology
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
Ground state fidelity from tensor network representations
For any D-dimensional quantum lattice system, the fidelity between two ground
state many-body wave functions is mapped onto the partition function of a
D-dimensional classical statistical vertex lattice model with the same lattice
geometry. The fidelity per lattice site, analogous to the free energy per site,
is well-defined in the thermodynamic limit and can be used to characterize the
phase diagram of the model. We explain how to compute the fidelity per site in
the context of tensor network algorithms, and demonstrate the approach by
analyzing the two-dimensional quantum Ising model with transverse and parallel
magnetic fields.Comment: 4 pages, 2 figures. Published version in Physical Review Letter
A non-separability measure for spatially disjoint vectorial fields
Vectorial forms of structured light that are non-separable in their spatial and polarisation degrees of freedom have become topical of late, with an extensive toolkit for their creation and control. In contrast, the toolkit for quantifying their non-separability, the inhomogeneity of the polarisation structure, is less developed and in some cases fails altogether. To overcome this, here we introduce a new measure for vectorial light, which we demonstrate both theoretically and experimentally. We consider the general case where the local polarisation homogeneity can vary spatially across the field, from scalar to vector, a condition that can arise naturally if the composite scalar fields are path separable during propagation, leading to spatially disjoint vectorial light. We show how the new measure correctly accounts for the local path-like separability of the individual scalar beams, which can have varying degrees of disjointness, even though the global vectorial field remains intact. Our work attempts to address a pressing issue in the analysis of such complex light fields, and raises important questions on spatial coherence in the context of vectorially polarised light
Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
The logarithmic violations of the area law, i.e. an "area law" with
logarithmic correction of the form , for entanglement
entropy are found in both 1D gapless system and for high dimensional free
fermions. The purpose of this work is to show that both violations are of the
same origin, and in the presence of Fermi liquid interactions such behavior
persists for 2D fermion systems. In this paper we first consider the
entanglement entropy of a toy model, namely a set of decoupled 1D chains of
free spinless fermions, to relate both violations in an intuitive way. We then
use multi-dimensional bosonization to re-derive the formula by Gioev and Klich
[Phys. Rev. Lett. 96, 100503 (2006)] for free fermions through a low-energy
effective Hamiltonian, and explicitly show the logarithmic corrections to the
area law in both cases share the same origin: the discontinuity at the Fermi
surface (points). In the presence of Fermi liquid (forward scattering)
interactions, the bosonized theory remains quadratic in terms of the original
local degrees of freedom, and after regularizing the theory with a mass term we
are able to calculate the entanglement entropy perturbatively up to second
order in powers of the coupling parameter for a special geometry via the
replica trick. We show that these interactions do not change the leading
scaling behavior for the entanglement entropy of a Fermi liquid. At higher
orders, we argue that this should remain true through a scaling analysis.Comment: 18 pages, accepted version with major updat
Evangelical Visitor- October 2, 1911. Vol. XXV. No. 20.
Evangelical Visitor published in Harrisburg, Pa., for the exposition of true, practical piety and devoted to the spread of evangelical truths and the unity of the church. Published in the interest of the church of the Brethren in Christ on October 2, 1911. Vol. XXV. No. 20
Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wave function. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin-1/2 XYX model in an external magnetic field, and the quantum spin-1 XXZ model with single-ion anisotropy. All these models have symmetry group Z(2) and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states
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