91 research outputs found
Topological Order and Quantum Criticality
In this chapter we discuss aspects of the quantum critical behavior that
occurs at a quantum phase transition separating a topological phase from a
conventionally ordered one. We concentrate on a family of quantum lattice
models, namely certain deformations of the toric code model, that exhibit
continuous quantum phase transitions. One such deformation leads to a
Lorentz-invariant transition in the 3D Ising universality class. An alternative
deformation gives rise to a so-called conformal quantum critical point where
equal-time correlations become conformally invariant and can be related to
those of the 2D Ising model. We study the behavior of several physical
observables, such as non-local operators and entanglement entropies, that can
be used to characterize these quantum phase transitions. Finally, we briefly
consider the role of thermal fluctuations and related phase transitions, before
closing with a short overview of field theoretical descriptions of these
quantum critical points.Comment: 24 pages, 7 figures, chapter of the book "Understanding Quantum Phase
Transitions", edited by Lincoln D. Carr (CRC Press / Taylor and Francis,
2010); v2: updated reference
Magnetic Monopoles in Spin Ice
Electrically charged particles, such as the electron, are ubiquitous. By
contrast, no elementary particles with a net magnetic charge have ever been
observed, despite intensive and prolonged searches. We pursue an alternative
strategy, namely that of realising them not as elementary but rather as
emergent particles, i.e., as manifestations of the correlations present in a
strongly interacting many-body system. The most prominent examples of emergent
quasiparticles are the ones with fractional electric charge e/3 in quantum Hall
physics. Here we show that magnetic monopoles do emerge in a class of exotic
magnets known collectively as spin ice: the dipole moment of the underlying
electronic degrees of freedom fractionalises into monopoles. This enables us to
account for a mysterious phase transition observed experimentally in spin ice
in a magnetic field, which is a liquid-gas transition of the magnetic
monopoles. These monopoles can also be detected by other means, e.g., in an
experiment modelled after the celebrated Stanford magnetic monopole search.Comment: (6 pages, 6 figures) v2: fig 3 replaced with colour version. For the
high-definition version of the paper click
http://www-thphys.physics.ox.ac.uk/user/ClaudioCastelnovo/Publications/papersub.pd
Toric-boson model: Toward a topological quantum memory at finite temperature
We discuss the existence of stable topological quantum memory at finite
temperature. At stake here is the fundamental question of whether it is, in
principle, possible to store quantum information for macroscopic times without
the intervention from the external world, that is, without error correction. We
study the toric code in two dimensions with an additional bosonic field that
couples to the defects, in the presence of a generic environment at finite
temperature: the toric-boson model. Although the coupling constants for the
bare model are not finite in the thermodynamic limit, the model has a finite
spectrum. We show that in the topological phase, there is a finite temperature
below which open strings are confined and therefore the lifetime of the memory
can be made arbitrarily (polynomially) long in system size. The interaction
with the bosonic field yields a long-range attractive force between the end
points of open strings but leaves closed strings and topological order intact.Comment: updated to published versio
Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates
We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. We argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d-wave superconducting pairing amplitude when antiferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.This work was supported, in part, by the Engineering and Physical Sciences Research Council (EPSRC) Grant No. EP/M007065/1 (C.Ca. and G.G.), and by DOE Grant No. DE-FG02- 06ER46316 (C.Ch.)
Neural network wave functions and the sign problem
Neural quantum states (NQS) are a promising approach to study many-body
quantum physics. However, they face a major challenge when applied to lattice
models: Convolutional networks struggle to converge to ground states with a
nontrivial sign structure. We tackle this problem by proposing a neural network
architecture with a simple, explicit, and interpretable phase ansatz, which can
robustly represent such states and achieve state-of-the-art variational
energies for both conventional and frustrated antiferromagnets. In the latter
case, our approach uncovers low-energy states that exhibit the Marshall sign
rule and are therefore inconsistent with the expected ground state. Such states
are the likely cause of the obstruction for NQS-based variational Monte Carlo
to access the true ground states of these systems. We discuss the implications
of this observation and suggest potential strategies to overcome the problem.Comment: 12 pages, 7 figures. v3: authors' final versio
Entanglement negativity and sudden death in the toric code at finite temperature
We study the fate of quantum correlations at finite temperature in the two
dimensional toric code using the logarithmic entanglement negativity. We are
able to obtain exact results that give us insight into how thermal excitations
affect quantum entanglement. The toric code has two types of elementary
excitations (defects) costing different energies. We show that an
density of the lower energy defect is required to degrade the
zero-temperature entanglement between two subsystems in contact with one
another. However, one type of excitation alone is not sufficient to kill all
quantum correlations, and an density of the higher energy
defect is required to cause the so-called sudden death of the negativity.
Interestingly, if the energy cost of one of the excitations is taken to
infinity, quantum correlations survive up to arbitrarily high temperatures, a
feature that is likely shared with other quantum spin liquids and frustrated
systems in general, when projected down to their low energy states. We
demonstrate this behaviour both for small subsystems, where we can prove that
the negativity is a necessary and sufficient condition for separability, as
well as for extended subsystems, where it is only a sufficient condition. We
further observe that the negativity per boundary degree of freedom at a given
temperature increases (parametrically) with the size of the boundary, and that
quantum correlations between subsystems with extended boundaries are more
robust to thermal fluctuations
Vison crystal in quantum spin ice on the breathing pyrochlore lattice
Recent excitement in the quantum spin ice community has come from the
experimental discovery of pseudospin- breathing pyrochlores, including
BaYbZnO, in which inversion symmetry is broken by the `up'
and `down' tetrahedra taking different physical sizes. We show here that the
often-neglected coupling between Kramers ions, in combination with
the breathing nature of the lattice, can produce an imaginary ring flip term.
This can lead to an unconventional ' phase', corresponding to a
maximally dense packing of visons on the lattice. Coherent dynamics persists in
all phases, together with its emergent QED description, in a manner reminiscent
of fragmentation in spinon crystals. We characterize the enlarged QSI phase
diagram and its excitations, showing that the imaginary ring flip acts both as
a chemical potential for visons and as an effective three-photon vertex akin to
strong light-matter coupling. The novel coupling causes a structured
high-energy continuum to emerge above the photon dispersion, which is naturally
interpreted as three photon up-conversion in a nonlinear optical crystal.Comment: 26 pages, 21 figure
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