arXiv subjects

Elisa Ercolessi

Publications and source records attributed to Elisa Ercolessi.

49 records · Page 3Linked to original sources

arXiv2013

Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems

Within a geometrical context, we derive an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two-level mixed and three-level pure state systems and then apply it to the novel case of U(3), that is for arbitrarily mixed three-level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a q-trit considering also all possible degenerate subcases.

quant-ph↗

arXiv2012

Exact entanglement entropy of the XYZ model and its sine-Gordon limit

We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the 1+1 dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.

hep-th↗

arXiv2012

Critical properties and Rényi entropies of the spin-3/2 XXZ chain

We discuss entanglement and critical properties of the spin-3/2 XXZ chain in its entire gapless region. Employing density-matrix renormalization group calculations combined with different methods based on level spectroscopy, correlation functions and entanglement entropies, we determine the sound velocity and the Luttinger parameter of the model as a function of the anisotropy parameter. Then, we focus on entanglement properties by systematically studying the behavior of Rényi entropies under both open and periodic boundary conditions, providing further evidence of recent findings about entanglement entropies of excited states in conformal field theory.

cond-mat.str-el↗

arXiv2012

Correlation Length and Unusual Corrections to the Entanglement Entropy

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Renyi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 Conformal Field Theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path-dependent in phase-space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain.

hep-th↗

arXiv2011

Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain

We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.

cond-mat.stat-mech↗

arXiv2010

From the Equations of Motion to the Canonical Commutation Relations

The problem of whether or not the equations of motion of a quantum system determine the commutation relations was posed by E.P.Wigner in 1950. A similar problem (known as "The Inverse Problem in the Calculus of Variations") was posed in a classical setting as back as in 1887 by H.Helmoltz and has received great attention also in recent times. The aim of this paper is to discuss how these two apparently unrelated problems can actually be discussed in a somewhat unified framework. After reviewing briefly the Inverse Problem and the existence of alternative structures for classical systems, we discuss the geometric structures that are intrinsically present in Quantum Mechanics, starting from finite-level systems and then moving to a more general setting by using the Weyl-Wigner approach, showing how this approach can accomodate in an almost natural way the existence of alternative structures in Quantum Mechanics as well.

quant-ph↗

arXiv2000

Spin-1 Antiferromagnetic Heisenberg Chains in an External Staggered Field

We present in this paper a nonlinear sigma-model analysis of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. After rediscussing briefly and extending previous results for the staggered magnetization curve, the core of the paper is a novel calculation, at the tree level, of the Green functions of the model. We obtain precise results for the elementary excitation spectrum and in particular for the spin gaps in the transverse and longitudinal channels. It is shown that, while the spectral weight in the transverse channel is exhausted by a single magnon pole, in the longitudinal one, besides a magnon pole a two-magnon continuum appears as well whose weight is a stedily increasing function of the applied field, while the weight of the magnon decreases correspondingly. The balance between the two is governed by a sum rule that is derived and discussed. A detailed comparison with the present experimental and numerical (DMRG) status of the art as well as with previous analytical approaches is also made.

cond-mat.str-el↗

arXiv2000

Integer-spin Heisenberg Chains in a Staggered Magnetic Field. A Nonlinear $σ$-Model Approach

We present here a nonlinear sigma-model (NL$σ$M) study of a spin-1 antiferromagnetic Heisenberg chain in an external commensurate staggered magnetic field. We find, already at the mean-field level, excellent agreement with recent and very accurate Density Matrix Renormalization Group (DMRG) studies, and that up to the highest values of the field for which a comparison is possible, for the staggered magnetization and the transverse spin gap. Qualitative but not quantitative agreement is found between the NL$σ$M predictions for the longitudinal spin gap and the DMRG results. The origin of the discrepancies is traced and discussed. Our results allow for extensions to higher-spin chains that have not yet been studied numerically, and the predictions for a spin-2 chain are presented and discussed. Comparison is also made with previous theoretical approaches that led instead to predictions in disagreement with the DMRG results.

cond-mat.str-el↗

arXiv1999

Mixed Phases for the t-J Model

We study the competition between non-magnetic (dimer or flux) states and short-range antiferromagnetically ordered RVB states in the t-J model and present a finite temperature phase diagram. We show that, for a wide range of temperatures and dopings, the stable phase results to be a state in which both the flux and the RVB parameters are nonzero.

cond-mat.str-el↗

arXiv1997

Phase Separation and Three-site Hopping in the 2-dimensional t-J Model

We study the t-J model with the inclusion of the so called three-site term which comes out from the t/U --> 0 expansion of the Hubbard model. We find that this singlet pair hopping term has no qualitative effect on the structure of the pure mean field phase diagram for nonmagnetic states. In accordance with experimental data on high-T_c materials and some numerical studies, we also find wide regions of phase coexistence whenever the coupling J is greater than a critical value J_c. We show that J_c varies linearly with the temperature T, going to zero at T=0.

cond-mat.str-el↗

arXiv1996

A New Phase Diagram for the t-J Model

We study the so-called nonmagnetic phases (dimer and flux states) in the t-J model below half filling. We present a new phase diagram, at zero and finite temperature, that includes broad areas of phase coexistence (dimer-flux or flux-uniform), in accordance with experimental and numerical data on the possibility of separation into hole-rich and hole-poor regions. We also briefly comment on some techniques used in the literature to discuss phase separation in the t-J model.

cond-mat.str-el↗

arXiv1996

Noncommutative Lattices and the Algebra of their Continuous Functions

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for their use in quantum physics. Posets are truly noncommutative spaces, or {\it noncommutative lattices}, since they can be realized as structure spaces of noncommutative $C^*$-algebras. These noncommutative algebras play the same role of the algebra of continuous functions ${\cal C}(M)$ on a Hausdorff topological space $M$ and can be thought of as algebras of operator valued functions on posets. In this article, we will review some mathematical results that establish a duality between finite posets and a certain class of C$^*$-algebras. We will see that the algebras in question are all postliminal approximately finite dimensional (AF) algebras.

q-alg↗

arXiv1996

K-Theory of Noncommutative Lattices

Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their $K$-theory. We shall do it algebraically, by studying the algebraic $K$-theory of the associated algebras of `continuous functions' which turn out to be noncommutative approximately finite dimensional (AF) $C^*$-algebra . We also work out several examples.

q-alg↗