Giacomo Gori

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Verified

Giacomo verified their affiliation via an institutional email.

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• PhD
• PostDoc at Heidelberg University

Ultracold gases provide an excellent platform for the realization of quantum interferometers. In the case of implementations based on Bose-Einstein condensates in double well potentials, an effective two-mode model allows to study how the interactions among particles affect the sensitivity of the interferometer. In this work we review the propertie...

Ground-state entanglement properties in the 1D antiferromagnetic spin-1 Heisenberg model with external magnetic field B and single-ion anisotropy D are investigated. The logarithmic negativity for nearest and non-nearest neighbor sites on finite chains is obtained. The resulting phase diagram is discussed in the B - D plane, and a line where the en...

In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile ϕ, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Δϕ. The latter can be fixed fr...

Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables such a...

Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables su...

We apply the critical geometry approach for bounded critical phenomena [1] to $3d$ percolation. The functional shape of the order parameter profile $\phi$ is related via the fractional Yamabe equation to its scaling dimension $\Delta_{\phi}$. We obtain $\Delta_{\phi}= 0.4785(7)$ from which the anomalous dimension $\eta$ is found to be $\eta=-0.0431...

We study the connection between the magnetization profiles of models described by a scalar field with marginal interaction term in a bounded domain and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization...

A bstract We study the critical properties of the 3 d O (2) universality class in bounded domains through Monte Carlo simulations of the clock model. We use an improved version of the latter, chosen to minimize finite-size corrections at criticality, with 8 orientations of the spins and in the presence of vacancies. The domain chosen for the simula...

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting...

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting...

Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks, a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this...

We study the connection between the magnetization profiles of $O(N)$ models in a bounded domain at the upper critical dimension and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization profiles at the upp...

Allowing to relate exactly the behaviour of a wide range of real interacting systems with abstract mathematical models, the theory of universality is one of the core successes of modern physics. Over the years, many of such interacting systems have been conveniently mapped into networks, physical architectures on top of which collective and in part...

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of eithe...

We study the non-linear beam splitter in matter-wave interferometers using ultracold quantum gases in a double-well configuration in presence of non-local interactions inducing inter-well density-density coupling, as they can be realized, e.g., with dipolar gases. We explore this effect after considering different input states, in the form of eithe...

In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase dia...

In this paper we study an Ising spin chain with short-range competing interactions in presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic phase diagram...

We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$. $\gamma(x)$ is chosen in order to have a scalar curvature to be constant and negative, the proper notion of curvat...

A bstract We study renormalization group (RG) fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes. We employ the functional perturbative renormalization group (FPRG) approach and the ϵ-expansion in d = d c − ϵ . The upper critical dimensions relevant to our analysis are $$ {d}_c=6,4,\raisebox{1ex}{$1...

We study renormalization group (RG) fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes. We employ the functional perturbative renormalization group (FPRG) approach and the $\epsilon$-expansion in $d=d_c-\epsilon$. The upper critical dimensions relevant to our analysis are $d_c = 6,4,\frac{10}{3},3,\...

A bstract We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional Q -color Potts model. We also provide analogous results for the limit Q → 1 that corresponds to percolation where the observable has a logarithmic singularity. Our conjectures are tested against Monte Carlo simulations s...

We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation where the observable has a logarithmic singularity. Our conjectures are tested against Monte Carlo simulations...

Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic singularities. We check our prediction using Monte Carlo simulations on a triangular lattice, showing excellent ag...

Based on conformal symmetry we propose an exact formula for the four-point connectivities of FK clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic singularities. We check our prediction using Monte Carlo simulations on a triangular lattice, showing excellent ag...

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $\sigma$ the critical value $C_{c}$ at which percolation occurs. The critical expone...

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $\sigma$ the critical value $C_{c}$ at which percolation occurs. The critical expone...

We deal with the problem of studying the effective theories and the symmetries of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and intere...

The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we study three dimensional percolation at criticality in bounded domains. Both on discrete and continuous models...

We show how the area law for entanglement entropy may be violated by free fermions on a lattice, and we look for conditions leading to the emergence of a volume law.We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets A and ¯ A is given,...

We show how a violation of the area law for the entanglement entropy may emerge in fermionic lattices, and investigate when a volume law is obtained. We first consider long-range couplings with power-law exponent, showing that it is not (only) the long-range-ness that matters, but rather the topology of the Fermi surface: as a (pathological) exampl...

We study the occurrence of modulational instabilities in lattices with non-local, power-law hoppings and interactions. Choosing as a case study the discrete nonlinear Schr\"odinger equation, we consider one-dimensional chains with power-law decaying interactions (with exponent \alpha) and hoppings (with exponent \beta): an extensive energy is obtai...

We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation functions. As an application, we reconstruct the couplings of chain Ising Hamiltonians having exponential or power-law...

By Hamiltonian path-integration a purely-quantum, self-consistent, spin-wave approximation can be developed for spin models on a lattice, that finally allows to map the original quantum problem to a classical one ruled by an effective classical spin Hamiltonian. Such approach has revealed especially valuable to investigate systems with S > 1/2 whic...

The two-dimensional Heisenberg antiferromagnet experiences an effective easy-plane anisotropy when a magnetic field is applied, giving rise to Berezinskii-Kosterlitz-Thouless (BKT) critical behavior. Remarkably, the strength of the effective anisotropy, and consequently the critical BKT temperature, can be tuned by varying the field. By means of th...