Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods

• URL: http://arxiv.org/abs/2501.11115v1
• Date: Sun, 19 Jan 2025 17:09:57 GMT
• Title: Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods
• Authors: Giovanni Cataldi,
• Abstract summary: This thesis develops advanced Network (TN) methods to address Hamiltonian Lattice Theories (LGTs) A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields. These advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.
• Score: 0.0
• License:
• Abstract: This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.

Related papers

• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm [0.0]
  We leverage the interplay between gapped phases and dualities of symmetric one-dimensional quantum lattice models. For every phase in the phase diagram, the dual representation of the ground state that breaks all symmetries minimises both the entanglement entropy and the required number of variational parameters. Our work testifies to the usefulness of generalised non-invertible symmetries and their formal category theoretic description for the nuts and bolts simulation of strongly correlated systems.
  arXiv  Detail & Related papers  (2024-08-12T17:51:00Z)
• Hamiltonian truncation tensor networks for quantum field theories [42.2225785045544]
  We introduce a tensor network method for the classical simulation of continuous quantum field theories. The method is built on Hamiltonian truncation and tensor network techniques. One of the key developments is the exact construction of matrix product state representations of global projectors.
  arXiv  Detail & Related papers  (2023-12-19T19:00:02Z)
• A new basis for Hamiltonian SU(2) simulations [0.0]
  We develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. We show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved.
  arXiv  Detail & Related papers  (2023-07-21T18:03:26Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions [51.52945471576731]
  This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD.
  arXiv  Detail & Related papers  (2022-07-18T21:13:34Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Stochastic normalizing flows as non-equilibrium transformations [62.997667081978825]
  We show that normalizing flows provide a route to sample lattice field theories more efficiently than conventional MonteCarlo simulations. We lay out a strategy to optimize the efficiency of this extended class of generative models and present examples of applications.
  arXiv  Detail & Related papers  (2022-01-21T19:00:18Z)
• Cold Atom Quantum Simulator for String and Hadron Dynamics in Non-Abelian Lattice Gauge Theory [0.0]
  Scheme calls for the realization of a two-state ultracold fermionic system in a 1-dimensional bipartite lattice. Being based on novel loop string hadron formalism of SU(2) lattice gauge theory, this simulation technique is completely SU(2) invariant.
  arXiv  Detail & Related papers  (2020-09-29T12:39:14Z)
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories [0.0]
  Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation. It remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories. This paper is a first step toward addressing this question in the case of non-Abelian LGTs.
  arXiv  Detail & Related papers  (2020-09-24T16:44:39Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.