arXiv subjects

Andrea Stampiggi

Publications and source records attributed to Andrea Stampiggi.

6 recordsLinked to original sources

arXiv2026

Variational Method in Quantum Field Theory

We develop a variational framework for addressing two-dimensional non-integrable quantum field theories through the exact structure of their integrable counterparts. Concentrating on the $φ^4$ Landau-Ginzburg model, we use the analytical Vacuum Expectation Values and Form Factors of local operators in the sinh-Gordon theory as the foundation of a variational ansatz. In this way, we obtain controlled estimates of central physical quantities of the $φ^4$ theory - such as the finite-volume ground-state energy and the physical mass as a function of the coupling constant. The strengths of the variational methods are leveraged in combination with the Hamiltonian truncation techniques and the LeClair-Mussardo formula, which also allow to probe the accuracy of the variational approximation varying the system size. Within the weak-coupling regime, a detailed numerical analysis reveals the behaviour of the finite-volume spectrum, the ground-state energy, and the elastic part of the scattering matrix, showing how the rigorous machinery of integrable models can serve as a guiding light into the complex landscape of non-integrable quantum field dynamics.

hep-th↗

arXiv2026

Spectral Decimation of Quantum Many-Body Hamiltonians

We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of statistical mixtures, we derive an explicit expression for the size of a characteristic symmetry sector (CSS), defined as the largest subsequence of levels exhibiting non-Poissonian correlations. The CSS dimension is shown to be the size-biased average of the underlying symmetry sectors, establishing a direct link between spectral statistics and Hilbert-space structure. We apply this framework to two paradigmatic settings: Hilbert-space fragmentation and disorder-induced many-body localization (MBL). In fragmented systems, the CSS reproduces the mixture prediction and isolates correlated subsectors even when the full spectrum appears nearly Poissonian. In the disordered Heisenberg chain, spectral decimation reveals the gradual emergence of integrability through a shrinking CSS, whose statistics exhibit signatures consistent with local integrals of motion. We introduce a characteristic symmetry entropy (CSE) as a finite-size scaling observable and extract, within accessible system sizes, the crossover exponents. Our results establish spectral decimation as a controlled, unbiased and computationally inexpensive diagnostic of hidden structure in many-body spectra, capable of distinguishing between chaotic dynamics, statistical mixtures, and emergent integrability.

cond-mat.stat-mech↗

arXiv2025

Statistical Signatures of Integrable and Non-Integrable Quantum Hamiltonians

Integrability is a cornerstone of classical mechanics, where it has a precise meaning. Extending this notion to quantum systems, however, remains subtle and unresolved. In particular, deciding whether a quantum Hamiltonian - viewed simply as a matrix - defines an integrable system is far from obvious, yet crucial for understanding non-equilibrium dynamics, spectral correlations, and correlation functions in many-body physics. We develop a statistical framework that approaches quantum integrability from a probabilistic standpoint. A key observation is that integrability requires a finite probability of vanishing energy gaps. Building on this, we propose a two-step protocol to distinguish integrable from non-integrable Hamiltonians. First, we apply a systematic Monte Carlo decimation of the spectrum, which exponentially compresses the Hilbert space and reveals whether level spacings approach Poisson statistics or remain mixed. The termination point of this decimation indicates the statistical character of the spectrum. Second, we analyze $k$-step gap distributions, which sharpen the distinction between Poisson and mixed statistics. Our procedure applies to Hamiltonians of any finite size, independent of whether their structure involves a few blocks or an exponentially fragmented Hilbert space. As a benchmark, we implement the protocol on quantum Hamiltonians built from the permutation group $\mathcal{S}_N$, demonstrating both its effectiveness and generality.

cond-mat.stat-mech↗

arXiv2025

Discrete-to-Continuum Approach for the Analytic Continuation of One-Particle Propagator on the Circle

Despite the simplicity of one-particle dynamics, explicit expressions for the one-dimensional propagator on a circle suitable to numerical evaluation are surprisingly lacking -- not only in the presence of potentials but even in the free case. Using a lattice regularization of the circle, we derive finite expressions for the free discrete propagator through an algebraic approach, aiming to provide physical insight into the readout of a digital quantum simulation. Moreover, these expressions allow for the reconstruction of the propagator in the continuous circle limit, which exhibits in the free case a peculiar non-analytic behavior in its transition between irrational and rational times. The latter propagator yields a finite analytic continuation of the corresponding elliptic theta function at the locus of essential singularities for real times, achieved through the introduction of a $σ$ distribution -- the ``square-root'' of the Dirac delta. We also show that the well-known infinite line limit is consistently recovered within this approach. In addition, we apply these results by studying numerically the dynamics of wave packets in cosine and random potentials. At early simulation times, we observe evidence of the semi-classical limit, where the probability density maximum follows the minimum of the propagator phase.

quant-ph↗

arXiv2024

Reflection and Transmission Amplitudes in a Digital Quantum Simulation

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed.

quant-ph↗

arXiv2024

Form Factors of the Tricritical Three-state Potts Model in its Scaling Limit

We compute the form factors of the order and disorder operators, together with those of the stress-energy tensor, of the two-dimensional three-state Potts model with vacancies along its thermal deformation of the critical point. At criticality the model is described by the non-diagonal partition function of the unitary minimal model $\mathcal{M}_{6,7}$ of conformal field theories and is accompanied by an internal $S_3$ symmetry. Its off-critical thermal deformation is an integrable massive theory which is still invariant under $S_3$. The presence of infinitely many conserved quantities, whose spin spectrum is related to the exceptional Lie algebra $E_6$, allows us to determine the analytic $S$-matrix, the exact mass spectrum and the matrix elements of local operators of this model in an exact non-perturbative way. We use the spectral representation series of the correlators and the fast convergence of these series to compute several universal ratios of the renormalization group.

hep-th↗