Elisa Ercolessi

Kitaev chains with long-range pairing.

We propose and analyze a generalization of the Kitaev chain for fermions with long-range p-wave pairing, which decays with distance as a power law with exponent α. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range (α > 1) or purely algebraically (α < 1). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small α. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.

Detecting a many-body mobility edge with quantum quenches

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from extended/ergodic (exhibiting extensive entanglement entropies and fluctuations) to localized (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using quantum-quench spectroscopy, namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

Discrete Abelian gauge theories for quantum simulations of QED

We study a lattice gauge theory in Wilson’s Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry , approximating the U(1) theory for large n. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss’s law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale

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

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Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models

. The time evolution of the entanglement entropy displays different regimes depending on the value of

On the geometry of mixed states and the Fisher information tensor

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Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of entanglement entropy and Schmidt gap.

Modular invariance in the gapped XYZ spin-1/2 chain

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)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.

A short course on quantum mechanics and methods of quantization

Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA(Dated: December 19, 2014)We discuss how to locate critical points in the Berezinskii-Kosterlitz-Thouless (BKT) universalityclass by means of gap-scaling analyses. While accurately determining such points using gap ex-trapolation procedures is usually challenging and inaccurate due to the exponentially small value ofthe gap in the vicinity of the critical point, we show that a generic gap-scaling analysis, includingthe e ects of logarithmic corrections, provides very accurate estimates of BKT transition pointsin a variety of spin and fermionic models. As a rst example, we show how the scaling proce-dure, combined with density-matrix-renormalization-group simulations, performs extremely well ina non-integrable spin-3=2 XXZ model, which is known to exhibit strong nite-size e ects. We thenanalyze the extended Hubbard model, whose BKT transition has been debated, nding results thatare consistent with previous studies based on the scaling of the Luttinger-liquid parameter. Finally,we investigate an anisotropic extended Hubbard model, for which we present the rst estimatesof the BKT transition line based on large-scale density-matrix-renormalization-group simulations.Our work demonstrates how gap-scaling analyses can help to locate accurately and ex0eciently BKTcritical points, without relying on model-dependent scaling assumptions.