arXiv subjects

Gabriele Spada

Publications and source records attributed to Gabriele Spada.

14 recordsLinked to original sources

arXiv2026

Quantum Impurities as Probes of Finite-Temperature Fluctuations in Two-Dimensional Bose Gases

Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.

cond-mat.quant-gas↗

arXiv2025

Supersolid phase in two-dimensional soft-core bosons at finite temperature

The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasi-crystal phase. Additionally, a potential intermediate hexatic phase with quasi long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.

cond-mat.quant-gas↗

arXiv2024

Quantum droplets in two-dimensional Bose mixtures at finite temperature

We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures subject to a strong transverse harmonic confinement. By means of exact path-integral Monte Carlo methods we determine the equilibrium density of the gas and the liquid as well as the pressure vs. volume dependence along isothermal curves. Results for the equation of state and for the gas-liquid coexistence region in quasi-2D configurations are compared with calculations in strictly two dimensions, finding excellent agreement. Within the pure 2D model we explore the relevance of the quantum scale anomaly and we determine the critical interaction strength for the occurrence of the first-order gas to liquid transition. Furthermore, we find that the superfluid response develops suddenly, following the density jump from the gas to the liquid state.

cond-mat.quant-gas↗

arXiv2023

Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories

Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B. Nickel, D. Meiron, and G. Baker Jr, Compilation of 2-pt and 4-pt graphs for continuous spin model, University of Guelph report (1977)], unfortunately left unpublished. We independently verify the results of Nickel et al., and we extend the computation to the eighth order in the coupling constant. The results of our calculations, together with the tools developed, are made available in Phi4tools, a user-friendly package that allows displaying the information about the individual Feynman diagrams, including the numerical values for the diagrams for zero, two, and four-point functions. We also provide the perturbative series up to order eight for the renormalization-group functions for the $O(N)$ and cubic anisotropic models.

hep-th↗

arXiv2023

Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point

We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte-Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.

cond-mat.quant-gas↗

arXiv2023

Thermal-induced Local Imbalance in Repulsive Binary Bose Mixtures

We study repulsive two-component Bose mixtures with equal populations and confined in a finite-size box through path-integral Monte Carlo simulations. For different values of the $s$-wave scattering length of the interspecies potential, we calculate the local population imbalance in a region of fixed volume inside the box at different temperatures. We find two different behaviors: for phase-separated states at $T=0$, thermal effects induce a diffusion process which reduces the local imbalance whereas, for miscible states at $T=0$, a maximum in the local population imbalance appears at a certain temperature, below the critical one. We show that this intriguing behavior is strongly related to the bunching effect associated with the Bose-Einstein statistics of the particles in the mixture and to an unexpected behavior of the cross pair distribution function not reported before.

cond-mat.quant-gas↗

arXiv2021

Thermodynamics of a dilute Bose gas: A path-integral Monte Carlo study

We present precise path-integral Monte-Carlo results for the thermodynamics of a homogeneous dilute Bose gas. Pressure and energy are calculated as a function of temperature both below and above the Bose-Einstein transition. Specifically, we address interaction effects, focusing on deviations from the ideal gas law in the thermodynamic limit. We also calculate the isothermal compressibility and the contact parameter, which provide a clear signature of the role played by interactions. In particular, we show that the compressibility exhibits a discontinuity at the transition point. To gain physical insight, numerical results are systematically compared with the predictions of first-order Hartree-Fock and second-order Popov theories, both giving an approximate description of the gas thermodynamics. The comparison shows the extension of the critical region around the transition point, where the inaccuracies of the perturbative expansions are more pronounced.

cond-mat.quant-gas↗

arXiv2020

Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models

In the classically unbroken phase, 3d $O(N)$ symmetric $\phi^4$ vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by $\kappa$) and for any $N$. It is shown that for $\kappa=\kappa_*$ the two fixed points merge and then, for $\kappa<\kappa_*$, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the $N=1$ $\phi^4$ theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d $O(N)$ models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large $N$ in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.

hep-th↗

arXiv2019

Renormalization Scheme Dependence, RG Flow and Borel Summability in $ϕ^4$ Theories in $d<4$

Renormalization group (RG) and resummation techniques have been used in $N$-component $ϕ^4$ theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical properties. Since the coupling constant is relevant in $d<4$ dimensions, the RG is entirely governed by renormalization scheme-dependent terms. We show that the known proofs of the Borel summability of observables depend on the renormalization scheme and apply only in "minimal" ones, equivalent in $d=2$ to an operatorial normal ordering prescription, where the $β$-function is trivial to all orders in perturbation theory. The presence of a non-trivial fixed point can be unambiguously established by considering a physical observable, like the mass gap, with no need of RG techniques. Focusing on the $N=1$, $d=2$ $ϕ^4$ theory, we define a one-parameter family of renormalization schemes where Borel summability is guaranteed and study the accuracy on the determination of the critical exponent $ν$ as the scheme is varied. While the critical coupling shows a significant sensitivity on the scheme, the accuracy in $ν$ is essentially constant. As by-product of our analysis, we improve the determination of $ν$ obtained with RG methods by computing three more orders in perturbation theory.

hep-th↗

arXiv2019

$λϕ^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO

We extend the study of the two-dimensional euclidean $ϕ^4$ theory initiated in ref. [1] to the $\mathbb Z_2$ broken phase. In particular, we compute in perturbation theory up to N$^4$LO in the quartic coupling the vacuum energy, the vacuum expectation value of $ϕ$ and the mass gap of the theory. We determine the large order behavior of the perturbative series by finding the leading order finite action complex instanton configuration in the $\mathbb Z_2$ broken phase. Using an appropriate conformal mapping, we then Borel resum the perturbative series. Interestingly enough, the truncated perturbative series for the vacuum energy and the vacuum expectation value of the field is reliable up to the critical coupling where a second order phase transition occurs, and breaks down around the transition for the mass gap. We compute the vacuum energy using also an alternative perturbative series, dubbed exact perturbation theory, that allows us to effectively reach N$^8$LO in the quartic coupling. In this way we can access the strong coupling region of the $\mathbb Z_2$ broken phase and test Chang duality by comparing the vacuum energies computed in three different descriptions of the same physical system. This result can also be considered as a confirmation of the Borel summability of the theory. Our results are in very good agreement (and with comparable or better precision) with those obtained by Hamiltonian truncation methods. We also discuss some subtleties related to the physical interpretation of the mass gap and provide evidence that the kink mass can be obtained by analytic continuation from the unbroken to the broken phase.

hep-th↗

arXiv2018

$λϕ^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO

Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $λϕ^4$ theory in two dimensions in the $Z_2$ symmetric phase. We extend the results for the perturbative expansion of several quantities up to N$^8$LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods.

hep-th↗

arXiv2018

The Power of Perturbation Theory

We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.

hep-th↗

arXiv2018

Instantons from Perturbation Theory

In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative results can be encoded in a suitable modified perturbative series in a class of quantum mechanical problems. We illustrate this explicitly in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.

hep-th↗

arXiv2015

CP Violation Tests of Alignment Models at LHCII

We analyse the low-energy phenomenology of alignment models both model-independently and within supersymmetric (SUSY) scenarios focusing on their CP violation tests at LHCII. Assuming that New Physics (NP) contributes to K-Kbar and D-Dbar mixings only through non-renormalizable operators involving SU(2)_L quark-doublets, we derive model-independent correlations among CP violating observables of the two systems. Due to universality of CP violation in Delta F=1 processes the bound on CP violation in Kaon mixing generically leads to an upper bound on the size of CP violation in D mixing. Interestingly, this bound is similar in magnitude to the current sensitivity reached by the LHCb experiment which is starting now to probe the natural predictions of alignment models. Within SUSY, we perform an exact analytical computation of the full set of contributions for the D-Dbar mixing amplitude. We point out that chargino effects are comparable and often dominant with respect to gluino contributions making their inclusion in phenomenological analyses essential. As a byproduct, we clarify the limit of applicability of the commonly used mass insertion approximation in scenarios with quasi-degenerate and split squarks.

hep-ph↗