arXiv subjects

Christian Apostoli

Publications and source records attributed to Christian Apostoli.

5 recordsLinked to original sources

arXiv2025

Unraveling Open Quantum Dynamics with Time-Dependent Variational Monte Carlo

We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (tVMC) with quantum trajectory techniques. Our approach unravels the Lindblad master equation into an ensemble of stochastic Schr\"{o}dinger equations for a variational ansatz, avoiding the exponential cost of density matrix evolution. The method is compatible with generic ans\"{a}tze, including expressive neural-network wavefunctions. We derive the nonlinear stochastic equations of motion for the variational parameters and employ suitable Stratonovich numerical solvers. To validate our approach, we simulate quenches in the locally dissipative long-range Ising model in a transverse field, accurately capturing non-equilibrium magnetization and spin squeezing dynamics relevant to trapped-ion and Rydberg atom experiments. The framework is computationally efficient, scalable on high-performance computing platforms, and can be readily integrated into existing tVMC implementations. This work enables large-scale simulations of complex, dissipative quantum systems in higher dimensions, with broad implications for quantum technology and fundamental science.

quant-ph↗

arXiv2025

Adaptive quantum dynamics with the time-dependent variational Monte Carlo method

We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is specifically designed to enhance numerical stability when overparameterized variational ans\"atze lead to ill-conditioned equations of motion. Building on the concept of the local-in-time error (LITE), a measure of the deviation between variational and exact evolution, we introduce a procedure to quantify each parameter's contribution to reducing the LITE, using only quantities already computed in standard tVMC simulations. These relevance estimates guide the selective evolution of only the most significant parameters at each time step, while maintaining a prescribed level of accuracy. We benchmark the algorithm on quantum quenches in the one-dimensional transverse-field Ising model using both spin-Jastrow and restricted Boltzmann machine wave functions, with an emphasis on overparameterized regimes. The adaptive scheme significantly improves numerical stability and reduces the need for strong regularization, enabling reliable simulations with highly expressive variational ans\"atze.

quant-ph↗

arXiv2024

Spectrum of density, spin and pairing fluctuations of an attractive two-dimensional Fermi gas

We leverage random phase approximation and unbiased auxiliary-field quantum Monte Carlo methods to compute dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the collective excitations of the system to generate robust benchmark results and to shed light into fermionic superfluidity in the strongly correlated regime. In particular we are motivated by a recent paper suggesting that the Higgs mode can be detected in the spectrum of spin fluctuations. Despite the fact that we are somewhat limited by finite-size effects, our study pinpoints indeed a clear peak in the spin channel at low momentum, but a detailed analysis suggests that such a peak, though certainly interesting, does not correspond to the Higgs mode. We propose a different explanation for the shape of the spin structure factor. On the other hand, our results clearly show that the Higgs mode can be detected in the density channel at very small wave vectors, although very good resolution is necessary.

cond-mat.quant-gas↗

arXiv2023

A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas

We show that a two-body Jastrow wave function is able to capture the ground-state properties of the $S=1$ antiferromagnetic Heisenberg chain with the single-ion anisotropy term, in both the topological and trivial phases. Here, the optimized Jastrow pseudo potential assumes a very simple form in Fourier space, i.e., $v_{q} \approx 1/q^2$, which is able to give rise to a finite string-order parameter in the topological regime. The results are analysed by using an exact mapping from the quantum expectation values over the variational state to the classical partition function of the one-dimensional Coulomb gas of particles with charge $q=\pm 1$. Here, two phases are present at low temperatures: the first one is a diluted gas of dipoles (bound states of particles with opposite charges), which are randomly oriented (describing the trivial phase); the other one is a dense liquid of dipoles, which are aligned thanks to the residual dipole-dipole interactions (describing the topological phase, with the finite string order being related to the dipole alignment). Our results provide an insightful interpretation of the ground-state nature of the spin-1 antiferromagnetic Heisenberg model.

cond-mat.str-el↗

arXiv2021

Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid

Repulsive soft-core atomic systems may undergo clustering if their density is high enough that core overlap is unavoidable. In one-dimensional quantum systems, it has been shown that this instability triggers a transition from a Luttinger liquid to various cluster Luttinger liquids. Here, we focus on the Luttinger liquid regime and theoretically study the evolution of key observables related to density fluctuations, that manifest a striking dependence on density. We tune the interaction so that the low-density regime corresponds to a Tonks-Girardeau gas, and show that as the density is increased the system departs more and more from Tonks-Girardeau behavior, displaying a much larger compressibility as well as rotonic excitations that finally drive the clustering transition. We compare various theoretical approaches, which are accurate in different regimes. Using quantum Monte Carlo methods and analytic continuation as a benchmark, we investigate the regime of validity of the mean-field Bogoliubov and the real-time multiconfiguration time-dependent Hartree-Fock approaches. Part of the behavior that we describe should be observable in ultracold Rydberg-dressed gases, provided that system losses are prevented.

cond-mat.quant-gas↗