Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy

Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.Comment: 11 pages, 4 figure

Excited-state quantum phase transitions in a two-fluid Lipkin model

Background: Composed systems have became of great interest in the framework of the ground state quantum phase transitions (QPTs) and many of their properties have been studied in detail. However, in these systems the study of the so called excited-state quantum phase transitions (ESQPTs) have not received so much attention. Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is presented in this work. The study is performed through the Hamiltonian diagonalization for selected values of the control parameters in order to cover the most interesting regions of the system phase diagram. [Method:] A Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting boson model (IBM) is diagonalized for selected values of the parameters and properties such as the density of states, the Peres lattices, the nearest-neighbor spacing distribution, and the participation ratio are analyzed. Results: An overview of the spectrum of the two-fluid Lipkin model for selected positions in the phase diagram has been obtained. The location of the excited-state quantum phase transition can be easily singled out with the Peres lattice, with the nearest-neighbor spacing distribution, with Poincar\'e sections or with the participation ratio. Conclusions: This study completes the analysis of QPTs for the two-fluid Lipkin model, extending the previous study to excited states. The ESQPT signatures in composed systems behave in the same way as in single ones, although the evidences of their presence can be sometimes blurred. The Peres lattice turns out to be a convenient tool to look into the position of the ESQPT and to define the concept of phase in the excited states realm

Improved superposition schemes for approximate multi-caloron configurations

Two improved superposition schemes for the construction of approximate multi-caloron-anticaloron configurations, using exact single (anti)caloron gauge fields as underlying building blocks, are introduced in this paper. The first improvement deals with possible monopole-Dirac string interactions between different calorons with non-trivial holonomy. The second one, based on the ADHM formalism, improves the (anti-)selfduality in the case of small caloron separations. It conforms with Shuryak's well-known ratio-ansatz when applied to instantons. Both superposition techniques provide a higher degree of (anti-)selfduality than the widely used sum-ansatz, which simply adds the (anti)caloron vector potentials in an appropriate gauge. Furthermore, the improved configurations (when discretized onto a lattice) are characterized by a higher stability when they are exposed to lattice cooling techniques.Comment: New version accepted for publication in Nucl. Phys. B. Text partly shortened, changes in the introduction, new results added on the comparison with exact solution

Topological Properties of the QCD Vacuum at T=0 and T ~ T_c

We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories at zero temperature and of QCD at temperatures around the phase transition. To smooth out dislocations and the UV noise we cool the configurations with an action which has scale invariant instanton solutions for instanton size above about 2.3 lattice spacings. The corresponding "improved" topological charge stabilizes at an integer value after few cooling sweeps. At zero temperature the susceptibility calculated from this charge (about (195MeV)^4 for SU(2) and (185 MeV)^4 for SU(3)) agrees very well with the phenomenological expectation. At the minimal amount of cooling necessary to resolve the structure in terms of instantons and anti-instantons we observe a dense ensemble where the total number of peaks is by a factor 5-10 larger than the net charge. The average size observed for these peaks at zero temperature is about 0.4-0.45 fm for SU(2) and 0.5-0.6 fm for SU(3). The size distribution changes very little with further cooling, although in this process up to 90% of the peaks disappear by pair annihilation. For QCD we observe below T_c a reduction of the topological susceptibility as an effect of the dynamical fermions. Nevertheless also here the instantons form a dense ensemble with general characteristics similar to those of the quenched theory. A further drop in the susceptibility above T_c is also in rough agreement with what has been observed for pure SU(3). We see no clear signal for dominant formation of instanton - anti-instanton molecules.Comment: Latex, 7 pages, 4 figures (one colour). Contribution to the 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2-6, 199

Local topological and chiral properties of QCD

To elucidate the role played by instantons in chiral symmetry breaking, we explore their properties in full QCD, around the critical temperature. We study in particular spatial correlations between low-lying Dirac eigenmodes and instantons. Our measurements are compared with the predictions of instanton-based models.Comment: LATTICE98(confine), 3 pgs, 4 figures (3 color

What drives the helpfulness of online reviews? A deep learning study of sentiment analysis, pictorial content and reviewer expertise for mature destinations.

User-generated content (UGC) is a growing driver of destination choice. Drawing on dual-process theories on how individuals process information, this study focuses on the role of central and peripheral information processing routes in the formation of consumers’ perceptions of the helpfulness of online reviews. We carried out a two-step process to address the perceived helpfulness of user-generated content, a sentiment analysis using advanced machine-learning techniques (deep learning), and a regression analysis. We used a database of 2,023 comments posted on TripAdvisor about two iconic Venetian cultural attractions, St. Mark’s Square (an open, free attraction) and the Doge’s Palace (a museum which charges an entry fee). Following the application of deep-learning techniques, we first identified which factors influenced whether a review received a “helpful” vote by means of logistic regression. Second, we selected those reviews which received at least one helpful vote to identify, through linear regression, the significant determinants of TripAdvisor users’ voting behaviour. The results showed that reviewer expertise is an influential factor in both free and paid-for attractions, although the impact of central cues (sentiment polarity, subjectivity and pictorial content) is different in both attractions. Our study suggests that managers should look beyond individual ratings and focus on the sentiment analysis of online reviews, which are shown to be based on the nature of the attraction (free vs. paid-for)

Exact Matrix Product States for Quantum Hall Wave Functions

We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling properties of the real-space entanglement spectra on infinite cylinders. The real-space entanglement spectrum obeys a scaling form dictated by the edge conformal field theory, allowing us to accurately extract the two entanglement velocities of the Moore-Read state. In contrast, the orbital space spectrum is observed to scale according to a complex set of power laws that rule out a similar collapse.Comment: 10 pages and Appendix, v3 published versio