Turin Lattice Meeting 2025
Aula C
Dipartimento di Fisica
A meeting of current and former members of the Torino Lattice Group with contributions on QCD phenomenology, machine learning, tensor networks, quantum computing, algorithms and more.
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Welcome and Introduction
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Talks
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1
Finite density QCD phase structure from lattice simulations: some recent results
First principle investigations are of fundamental interest for the study of QCD thermodynamics, both in their own right and in light of experimental measurements, from heavy-ion collisions and future observations from gravitational waves. Though not much is known quantitatively about the phase structure of QCD, a lot of progress has been made in the exploration of QCD thermodynamics. I will discuss our knowledge of the QCD phase diagram and present recent lattice results at finite density.
Speaker: Paolo Parotto (Istituto Nazionale di Fisica Nucleare) -
2
Analytic continuation from imaginary chemical potential as an inverse problem
Because of the sign problem, simulations of lattice QCD at finite density are often carried out using imaginary baryon chemical potentials. This creates the challenge of analytically continuing those results to physically relevant real values.
Our group recently proposed a technique for performing this continuation by employing the Cauchy integral formula to reframe it as an inverse problem: we demonstrate that this approach can be implemented effectively, using the computation of the number density as an example. As a check, we also extract derivatives of the number density, corresponding to higher-order moments, and find them to be in full agreement with values reported in literature.
Moreover, we show that the method is more broadly applicable than it may first appear, offering insight into a wide range of related inverse problems.Speaker: Marco Aliberti (Università degli Studi di Parma and INFN) -
3
Constrained Symplectic Quantization: a new method for real-time dynamics
We introduce Symplectic Quantization, a novel functional approach to quantum field theory that makes it possible to sample quantum fluctuations directly in Minkowski space--time, thus bypassing the limitations of traditional importance-sampling methods restricted to imaginary time. The technique is based on a deterministic dynamics governed by Hamilton-like equations in an auxiliary time parameter, which generates a microcanonical ensemble of field configurations. We prove that microcanonical correlation functions obtained in this formulation are equivalent to those of a Minkowskian canonical theory, where quantum fluctuations are weighted by the oscillatory factor $e^{iS}$, with $S$ the original action. We test the method on two representative systems. For the quantum harmonic oscillator, we reconstruct the full real-time dynamics not only of the ground state but also of excited states and quantum superpositions, accurately reproducing expectation values and interference phenomena that are inaccessible to Euclidean approaches. For a free scalar field theory in $1+1$ dimensions, we recover the complete structure of real-time quantum field theory, including the Feynman propagator, the Schwinger--Dyson equations and their contact terms, thereby clarifying the role of the generalized Hamilton equations within this framework.
These results show that Symplectic Quantization reproduces the full real-time quantum dynamics of both quantum-mechanical and field-theoretical systems with high accuracy, providing a solid foundation for future applications to interacting quantum field theories.Speaker: Martina Giachello (Istituto Nazionale di Fisica Nucleare)
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1
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Break
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Talks
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4
Quantum gravity from the replica trick
Replicated geometries, both in the continuum and on the lattice, are used to study entanglement in quantum field theories. In this talk we show how to gauge the permutation symmetry of a replicated system on the lattice by introducing a background gauge field. After providing a local action for the gauge field, we discuss how this construction enables simulations of matter fields coupled to dynamical geometries, hinting at connections between entanglement and 2d quantum gravity.
Speaker: Andrea Bulgarelli (University of Bonn) -
5
How hard is it to simulate a quantum many-body system?
Classical simulations play a central role in many-body quantum physics, from lattice gauge theories to strongly correlated systems, yet their computational cost varies dramatically across different regimes. In this talk, I will discuss how the complexity of simulating quantum many-body systems can be understood in terms of physical resources carried by quantum states.
I will first review tensor network methods, focusing on matrix product states, and explain how entanglement entropy—via area laws—controls their efficiency in one dimension. I will then argue why entanglement alone is not sufficient to characterize classical simulability, highlighting the special role of stabilizer states and introducing stabilizer Rényi entropy as a measure of non-Clifford complexity.
Finally, I will present recent results on fermionic many-body systems, where highly entangled Gaussian states remain efficiently simulable. I will show how fermionic non-Gaussianity, quantified by fermionic antiflatness, emerges as a key resource governing the classical complexity of fermionic simulations.Speaker: paolo stornati (ICFO) -
6
Space time tensor networks and temporal entropies
I will review how spatio-temporal tensor networks naturally arise in the computation of expectation values following quantum quenches [1], and how they encode the dynamical properties of many-body quantum systems. Particular emphasis will be given to the concept of generalized temporal entanglement [2], a quantity that captures the entanglement structure across time, provides insight into the complexity of contracting such networks and can be measured experimentally [3].
This motivates the use of generalized temporal entanglement as a diagnostic tool for understanding the computational cost of simulating out-of-equilibrium quantum dynamics. I will present analytical results for its scaling in critical Hamiltonians [4], highlighting a universal structure that allows us to identify and characterize emergent dynamical critical points [5].
Finally, I will introduce a new tensor network algorithm that exploits these insights to efficiently predict the evolution of local observables using only polynomial resources [5].
References:
[1] Spatio-temporal tensor-network approaches to out-of-equilibrium dynamics bridging open and closed systems
S Cerezo-Roquebrún, A Bou-Comas, JT Schneider, E López, Luca Tagliacozzo, Stefano Carignano,
Frontiers in Quantum Science and Technology 4, 1568471.[2] Temporal entropy and the complexity of computing the expectation value of local operators after a quench
S Carignano, CR Marimón, L Tagliacozzo
Physical Review Research 6 (3), 033021.[3] Measuring temporal entanglement in experiments as a hallmark for integrability
A Bou-Comas, CR Marimón, JT Schneider, S Carignano, L Tagliacozzo
arXiv preprint arXiv:2409.05517.[4] Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
S Carignano, L Tagliacozzo
arXiv preprint arXiv:2405.14706[5] Overcoming the entanglement barrier with sampled tensor networks
S Carignano, G Lami, J De Nardis, L Tagliacozzo
arXiv preprint arXiv:2505.09714Speaker: Luca Tagliacozzo (IFF-CSIC)
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4
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Break
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Talks
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7
Study of the continuum limit of the lattice step scaling function in (2+1)D U(1) Yang-Mills on the lattice
We study the continuum limit of the lattice step scaling function in a $U(1)$ lattice gauge theory in the Hamiltonian formalism. We study a system with static charges in the small coupling region and provide a new finite volume scheme to take the continuum limit, given a definition of the running coupling using the inter-quark force. We are able to reach small coupling thanks to a duality transformation and the plaquette state basis recently introduced.
Speaker: Alessio Negro (HISKP, Bonn) -
8
Out-of-equilibrium entanglement growth in integrable field theories
Entanglement is a key quantity in quantum mechanics and it has recently been central in the development of efficient tensor-network-based numerical methods, as density matrix renormalization group. They are crucial in investigating strongly interacting systems that cannot be tackled by analytical or Monte Carlo methods. However, keeping the entropy related to entanglement under control is a major imperative in order to maintain the efficiency of the method. During the out-of-equilibrium dynamics after the switch of a coupling constant of the system (i.e., a global quench), this is not possible. In this talk, we compute the linear growth of entanglement entropy during relaxation after a global quantum quench in (1+1)D integrable field theories, where exact methods are available.
Speaker: Dr Emanuele Di Salvo (Karlsruhe Institute of Technology) -
9
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 $\varphi^4$ 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 $\varphi^4$ 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.
Speaker: Mr Andrea Stampiggi (SISSA, INFN Sezione Trieste)
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7
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Talks
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10
Learning how to solve the signal-to-noise ratio problem
Monte Carlo simulations provide a systematically improvable framework for computing Euclidean correlation functions with high precision. However, their effectiveness is fundamentally constrained by the exponential decay of the signal-to-noise ratio at large Euclidean time separations. By expressing correlators as derivatives of one-point functions with respect to sources in the action, the signal-to-noise problem can be reformulated as an overlap problem within a reweighting procedure. Recent work has demonstrated that combining automatic differentiation with Hamiltonian Monte Carlo can exactly resolve this overlap problem in simple scalar theories, offering a constructive blueprint for more complex scenarios where an exact solution is unlikely to be accessible.
In this talk, I will review this approach and discuss how neural networks naturally extend this program. In particular, I will show that linearised (normalising) flows naturally emerge as potential candidates to address this overlap problem in practice and may even offer a deeper geometrical understanding of the underlying minimisation problem.
Speaker: Dr Pietro Butti (QTC - University of Southern Denmark) -
11
A scalable flow-based approach to mitigate topological freezing
In recent years, flow-based samplers have emerged as a promising alternative to traditional sampling methods in lattice gauge theory. In this talk, we will introduce a class of flow-based samplers known as Stochastic Normalizing Flows (SNFs), which combine neural networks with non-equilibrium Monte Carlo algorithms. We will show that SNFs exhibit excellent scaling with the volume in lattice $\textrm{SU}(3)$ gauge theory. Then, we will present an application to $\textrm{SU}(3)$ gauge theory with open boundary conditions, demonstrating how this approach represents an efficient strategy for the sampling of topological observables at fine lattice spacings.
Speaker: Elia Cellini (University of Edinburgh) -
12
Interfaces Free energy in the phi^4 theory
In the magnetized phase of the phi^4 theory interfaces can form between two magnetization domains each in a different spontaneously broken vacuum. When we impose anti-periodic boundary conditions in one of the directions an interface necessarily forms somewhere in the bulk.
We compute the free energy associated to these interfaces with the Jarzynski equality. And study its behavior changing the geometry of the lattice and the coupling of the theory, testing an Effective String Theory model.
Particularly interesting is the region in the phase diagram of the theory where the attraction to the Gaussian fixed point allows the string tension to be small with respect to the mass of the bulk particle. This leads to a different phenomenology in the effective string theory that we analyze.
Speaker: Lorenzo Verzichelli (Universita` di Torino)
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10
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Break
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Talks
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13
Ground-State Extraction of Heavy-Light-Meson Semileptonic Decay Form Factors
We discuss the extraction of form factors for heavy-light
pseudo-scalar to light pseudo-scalar decay form factors from finite time
correlation functions. Particular emphasis is placed on controlling the
contamination from excited-states using also the information from chiral
perturbation theory to isolate the ground-state contribution. The analysis is
performed on CLS ensembles with $N_f = 2+1$ flavours of
$\mbox{O}(a)$-improved Wilson fermions (presently) at the
$\mathrm{SU}(3)$-symmetric point with relativistic heavy-quark masses in the
charm region and above. Our form factors will be used in a computation of
the $B \to \pi$ form factors combining the continuum-limit relativistic
results with static-limit calculations.Speaker: Antonino D'Anna (IFT UAM-CSIC) -
14
Studying the effective restoration of the $U(1)_A$ symmetry on the lattice with Wilson fermions
It has been argued in the literature that an effective restoration of the $U(1)_A$ symmetry can be probed by examining the degeneracy of flavour non-singlet pseudoscalar and scalar correlation functions. In this talk, I will present a method to investigate the onset of such degeneracies using correlators computed on anisotropic lattice ensembles generated by the FASTSUM collaboration with unphysical pion masses and $N_f=2+1$ flavours of sea quarks. As a first validation step, the method is applied to the vector and axial–vector channels, which are sensitive to the restoration of $SU(2)_L\times SU(2)_R$ chiral symmetry. The resulting pseudo-critical temperature is in agreement with that obtained from the renormalised chiral condensate on the same ensambles. Applying the method with scalar and pseudoscalar correlators we observe indications of effective $U(1)_A$ symmetry restoration in the temperature range $T_c < T_{U(1)_A} < 2T_c$.
Speaker: Antonio Smecca (Istituto Nazionale di Fisica Nucleare)
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13
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