1,093 research outputs found
Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding to the fixed points. We relate them to the states
possessing zero correlation length, saturation of the area law, as well as to
those which generate ground states of local and commuting Hamiltonians. For
mixed states, we introduce the concept of renormalization fixed points and
characterize the corresponding tensors. We also relate them to concepts like
finite correlation length, saturation of the area law, as well as to those
which generate Gibbs states of local and commuting Hamiltonians. One of the
main result of this work is that the resulting fixed points can be associated
to the boundary theories of two-dimensional topological states, through the
bulk-boundary correspondence introduced by Cirac et al. in 2011.Comment: 63 pages, Annals of Physics (2016). Accepted versio
Nonlocal resources in the presence of Superselection Rules
Superselection rules severely alter the possible operations that can be
implemented on a distributed quantum system. Whereas the restriction to local
operations imposed by a bipartite setting gives rise to the notion of
entanglement as a nonlocal resource, the superselection rule associated with
particle number conservation leads to a new resource, the \emph{superselection
induced variance} of local particle number. We show that, in the case of pure
quantum states, one can quantify the nonlocal properties by only two additive
measures, and that all states with the same measures can be asymptotically
interconverted into each other by local operations and classical communication.
Furthermore we discuss how superselection rules affect the concepts of
majorization, teleportation and mixed state entanglement.Comment: 4 page
Supersolid Helium at High Pressure
We have measured the pressure dependence of the supersolid fraction by a
torsional oscillator technique. Superflow is found from 25.6 bar up to 136.9
bar. The supersolid fraction in the low temperature limit increases from 0.6 %
at 25.6 bar near the melting boundary up to a maximum of 1.5% near 55 bar
before showing a monotonic decrease with pressure extrapolating to zero near
170 bar.Comment: 4 pages, 4 figure
Using exercise to protect physical and mental health in youth at risk for psychosis.
A large body of literature has demonstrated that exercise interventions can improve a broad range of outcomes in people with established schizophrenia, including reducing psychiatric symptoms, increasing cognitive functioning, and improving physical health. Furthermore, these benefits seem just as pronounced in first-episode psychosis. However, there have been few clinical studies to date examining the effects of exercise in those found to be âat-riskâ of psychosis, particularly for those meeting the criteria for âClinical High Riskâ (CHR) state (a classification which includes both those meeting the âultra-high risk for psychosisâ criteria and/or those with âatrisk mental statesâ). This is surprising, as a proportion of those in the CHR state go on to develop psychotic disorders, and a growing body of evidence suggests that early interventions in this period have significant potential to improve the course of illness. In this article, we shall review the existing literature for i) exercise as an adjunctive intervention for those treated for psychosis; ii) exercise as a standalone intervention in CHR groups; and iii) the rationale and supportive evidence for widescale use of exercise to preserve physical and mental health in those identified as at risk for psychosis. From this, we will put forth how the CHR phase represents an under-researched but highly-suitable timepoint for administering structured exercise interventions, in order to improve physical, psychological and neurocognitive outcomes; while also potentially reducing the odds of transition to full-threshold psychotic disorders. Following this, directions, recommendations and considerations around both the clinical implementation and future research around exercise in CHR individuals will be discussed
Edge theories in Projected Entangled Pair State models
We study the edge physics of gapped quantum systems in the framework of
Projected Entangled Pair State (PEPS) models. We show that the effective
low-energy model for any region acts on the entanglement degrees of freedom at
the boundary, corresponding to physical excitations located at the edge. This
allows us to determine the edge Hamiltonian in the vicinity of PEPS models, and
we demonstrate that by choosing the appropriate bulk perturbation, the edge
Hamiltonian can exhibit a rich phase diagram and phase transitions. While for
models in the trivial phase any Hamiltonian can be realized at the edge, we
show that for topological models, the edge Hamiltonian is constrained by the
topological order in the bulk which can e.g. protect a ferromagnetic Ising
chain at the edge against spontaneous symmetry breaking.Comment: 5 pages, 4 figure
Transfer Matrices and Excitations with Matrix Product States
We investigate the relation between static correlation functions in the
ground state of local quantum many-body Hamiltonians and the dispersion
relations of the corresponding low energy excitations using the formalism of
tensor network states. In particular, we show that the Matrix Product State
Transfer Matrix (MPS-TM) - a central object in the computation of static
correlation functions - provides important information about the location and
magnitude of the minima of the low energy dispersion relation(s) and present
supporting numerical data for one-dimensional lattice and continuum models as
well as two-dimensional lattice models on a cylinder. We elaborate on the
peculiar structure of the MPS-TM's eigenspectrum and give several arguments for
the close relation between the structure of the low energy spectrum of the
system and the form of static correlation functions. Finally, we discuss how
the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at
zero temperature. We present a renormalization group argument for obtaining
finite bond dimension approximations of MPS, which allows to reinterpret
variational MPS techniques (such as the Density Matrix Renormalization Group)
as an application of Wilson's Numerical Renormalization Group along the virtual
(imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure
Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh
Xcompact3D is a Fortran 90â95 open-source framework designed for fast and accurate simulations of turbulent flows, targeting CPU-based supercomputers. It is an evolution of the flow solver Incompact3D which was initially designed in France in the mid-90âs for serial processors to solve the incompressible NavierâStokes equations. Incompact3D was then ported to parallel High Performance Computing (HPC) systems in the early 2010âs. Very recently the capabilities of Incompact3D have been extended so that it can now tackle more flow regimes (from incompressible flows to compressible flows at low Mach numbers), resulting in the design of a new user-friendly framework called Xcompact3D. The present manuscript presents an overview of Xcompact3D with a particular focus on its functionalities, its ready-to-run simulations and a few case studies to demonstrate its impact
Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
In this paper, we do a complete classification of valence-bond crystals
(VBCs) on the kagome lattice based on general arguments of symmetry only and
thus identify many new VBCs for different unit cell sizes. For the spin-1/2
Heisenberg antiferromagnet, we study the relative energetics of competing
gapless spin liquids (SLs) and VBC phases within the class of
Gutzwiller-projected fermionic wave functions using variational Monte Carlo
techniques, hence implementing exactly the constraint of one fermion per site.
By using a state-of-the-art optimization method, we conclusively show that the
U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and
36-site unit cell VBCs. This stability is also preserved on addition of a
next-nearest-neighbor super-exchange coupling of both antiferromagnetic and
ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is
stabilized on addition of a very small next-nearest-neighbor FM super-exchange
coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group
symmetry as that obtained in an effective quantum dimer model study. It breaks
reflection symmetry, has a nontrivial flux pattern and is a strong dimerization
of the uniform RVB SL.Comment: 16 pages, 25 figures. Invited paper for Focus issue on "Quantum Spin
Liquids" of the New Journal of Physic
Preparation and verification of tensor network states
We consider a family of tensor network states defined on regular lattices that come with a natural definition of an adiabatic path to prepare them. This family comprises relevant classes of states, such as injective matrix product and projected entangled-pair states, and some corresponding to classical spin models. We show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semidefinite programming. This allows one to check whether the adiabatic preparation can be performed efficiently with a scalable effort. We also derive a set of observables whose expectation values can be easily determined and that form a complete set, in the sense that they uniquely characterize the state. We identify a subset of those observables which can be efficiently computed if one has access to the quantum state and local measurements, and analyze how they can be used in verification procedures
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