Projected entangled-pair states can describe chiral topological states

We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free fermionic PEPS which show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians, and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version, Journal-Ref adde

Chiral projected entangled-pair state with topological order

We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.Comment: 11 pages, 7 figure

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Projection, Spatial Correlations, and Anisotropies in a Large and Complete Sample of Abell Clusters

An analysis of R >= 1 Abell clusters is presented for samples containing recent redshifts from the MX Northern Abell Cluster Survey. The newly obtained redshifts from the MX Survey as well as those from the ESO Nearby Abell Cluster Survey (ENACS) provide the necessary data for the largest magnitude-limited correlation analysis of rich clusters in the entire sky (excluding the galactic plane) to date. We find 19.4 <= r_0 <= 23.3 h^-1Mpc, -1.92 <= gamma <= -1.83 for four different subsets of Abell/ACO clusters, including a large sample (N=104) of cD clusters. We have used this dataset to look for line-of-sight anisotropies within the Abell/ACO catalogs. We show that the strong anisotropies present in previously studied Abell cluster datasets are not present in our R >= 1 samples. There are, however, indications of residual anisotropies which we show are the result of two elongated superclusters, Ursa Majoris and Corona Borealis, whose axes lie near the line-of-sight. After rotating these superclusters so that their semi-major axes are prependicular to the line-of-sight, we find no anisotropies as indicated by the correlation function. The amplitude and slope of the two-point correlation function remain the same before and after these rotations. We also remove a subset of R = 1 Abell/ACO clusters that show sizable foreground/background galaxy contamination and again find no change in the amplitude or slope of the correlation function. We conclude that the correlation length of R >= 1 Abell clusters is not artificially enhanced by line-of-sight anisotropies.Comment: 37 pages, 8 figures, AASTeX Accepted for publication in Ap

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems

Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices

We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free (Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs.Comment: 26 pages, LaTeX, published version (figure added

Lieb-Robinson Bounds for the Toda Lattice

We establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems

Como reduzir o colapso do albedo (Creasing) em frutos cítricos.

bitstream/item/136887/1/documento-364-com-capa.pd