The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.

International Symposium on Lattice Field Theory (LATTICE)Nov 7, 20229 citations

Duality transformations and the entanglement entropy of gauge theories

Andrea Bulgarelli, Marco Panero C

A bstract The study of entanglement in gauge theories is expected to provide insights into many fundamental phenomena, including confinement. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. In this work we study lattice gauge theories that admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In the first part of this work, we explicitly perform the duality transformation in a replica geometry, deriving the structure of a replica space for a gauge theory. Then, in the second part, we calculate, by means of Monte Carlo simulations, the entropic c-function of the ℤ 2 gauge theory in three spacetime dimensions, exploiting its dual description in terms of the three-dimensional Ising model.A bstract The study of entanglement in gauge theories is expected to provide insights into many fundamental phenomena, including confinement. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. In this work we study lattice gauge theories that admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In the first part of this work, we explicitly perform the duality transformation in a replica geometry, deriving the structure of a replica space for a gauge theory. Then, in the second part, we calculate, by means of Monte Carlo simulations, the entropic c-function of the ℤ 2 gauge theory in three spacetime dimensions, exploiting its dual description in terms of the three-dimensional Ising model.

arXiv:2404.01987Journal of High Energy PhysicsJun 7, 202412 citations

Computing quantum entanglement with machine learning

Andrea Bulgarelli, Elia Cellini, Karl Jansen +5 more

Entanglement calculations in quantum field theories are extremely challenging and typically rely on the replica trick, where the problem is rephrased in a study of defects. We demonstrate that the use of deep generative models drastically outperforms standard Monte Carlo algorithms. Remarkably, such a machine-learning method enables high-precision estimates of Rényi entropies in three dimensions for very large lattices. Moreover, we propose a new paradigm for studying lattice defects with flow-based sampling.Entanglement calculations in quantum field theories are extremely challenging and typically rely on the replica trick, where the problem is rephrased in a study of defects. We demonstrate that the use of deep generative models drastically outperforms standard Monte Carlo algorithms. Remarkably, such a machine-learning method enables high-precision estimates of Rényi entropies in three dimensions for very large lattices. Moreover, we propose a new paradigm for studying lattice defects with flow-based sampling.

International Symposium on Lattice Field Theory (LATTICE)Jul 5, 20260 citations

Computing quantum entanglement with machine learning

Bulgarelli, Andrea, Cellini, Elia, Jansen, Karl +5 more

arXiv:2512.11389Dec 12, 20250 citations

Duality and entanglement in lattice gauge theories

Andrea Bulgarelli, Marco Panero C

The study of entanglement in quantum field theories provides insight into universal properties which are typically challenging to extract by means of local observables. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. On the other hand, (2+1)-dimensional lattice gauge theories are known to admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In this contribution, we exploit Kramers-Wannier duality to perform a numerical study of the entropic c-function of the (2+1)-dimensional $\mathbb{Z}_2$ gauge theory in the continuum limit. Our results are compared with analytical predictions from holographic models.The study of entanglement in quantum field theories provides insight into universal properties which are typically challenging to extract by means of local observables. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities that stem from the non-factorizability of the Hilbert space. On the other hand, (2+1)-dimensional lattice gauge theories are known to admit a dual description in terms of spin models, for which the replica trick and Rényi entropies are well defined. In this contribution, we exploit Kramers-Wannier duality to perform a numerical study of the entropic c-function of the (2+1)-dimensional $\mathbb{Z}_2$ gauge theory in the continuum limit. Our results are compared with analytical predictions from holographic models.

arXiv:2411.17231International Symposium on Lattice Field Theory (LATTICE)Dec 5, 20241 citation

Entanglement in four-dimensional SU(3) gauge theory

Etsuko Itou, Keitaro Nagata, Yoshiyuki Nakagawa +2 more

We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic | $c$ |-function (⁠| $C(l)$ |⁠) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For | $0 \leqslant l \leqslant 0.7$ | fm, where | $l$ | is the length of the subspace, the entropic | $c$ |-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20% discrepancy. When | $l$ | is close to the | $\Lambda _{{\rm QCD}}^{-1} \big (\sim T_c^{-1}\big )$ | scale, the entropic | $c$ |-function decreases smoothly, and it is consistent with zero within error bars at | $l \gtrsim 0.9$ | fm.We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic |$c$|-function (⁠|$C(l)$|⁠) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For |$0 \leqslant l \leqslant 0.7$| fm, where |$l$| is the length of the subspace, the entropic |$c$|-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20% discrepancy. When |$l$| is close to the |$\Lambda _{{\rm QCD}}^{-1} \big (\sim T_c^{-1}\big )$| scale, the entropic |$c$|-function decreases smoothly, and it is consistent with zero within error bars at |$l \gtrsim 0.9$| fm.

Jan 1, 201634 citations

\mathbb{Z}_2

gauge theory in the continuum limit. Our results are compared with analytical predictions from holographic models.

We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic |

c

|-function (⁠|

C(l)

|⁠) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For |

0 \leqslant l \leqslant 0.7

| fm, where |

l

| is the length of the subspace, the entropic |

c

|-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20% discrepancy. When |

l

| is close to the |

\Lambda _{{\rm QCD}}^{-1} \big (\sim T_c^{-1}\big )

| scale, the entropic |

c

|-function decreases smoothly, and it is consistent with zero within error bars at |

l \gtrsim 0.9

| fm.