Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration

• URL: http://arxiv.org/abs/2211.00023v2
• Date: Wed, 11 Jan 2023 12:16:46 GMT
• Title: Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration
• Authors: Patrick Emonts, Ariel Kelman, Umberto Borla, Sergej Moroz, Snir Gazit, Erez Zohar
• Abstract summary: We use Gauged Gaussian Fermionic PEPS to find the ground state of $2+1d$ dimensional pure $mathbbZ$ lattice gauge theories. We do so by combining PEPS methods with Monte-Carlo computations, allowing for efficient contraction of the PEPS and computation of correlation functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure $\mathbb{Z}_2$ lattice gauge theories for a wide range of coupling constants. We do so by combining PEPS methods with Monte-Carlo computations, allowing for efficient contraction of the PEPS and computation of correlation functions. Previously, such numerical computations involved the calculation of the Pfaffian of a matrix scaling with the system size, forming a severe bottleneck; in this work we show how to overcome this problem. This paves the way for applying the method we propose and benchmark here to other gauge groups, higher dimensions, and models with fermionic matter, in an efficient, sign-problem-free way.

Related papers

• Superposing and gauging fermionic Gaussian projected entangled pair states to get lattice gauge theory groundstates [0.0]
  Gauged Gaussian fermionic projected entangled pair states (GGFPEPS) form a novel type of Ansatz state for the groundstate of lattice gauge theories. We will present a framework for the efficient computation of observables in the case where the non-Gaussianity of the PEPS follows from the superposition of (few) Gaussian PEPS.
  arXiv  Detail & Related papers  (2024-12-02T17:31:20Z)
• Projected Entangled Pair States with flexible geometry [0.0]
  Projected Entangled Pair States (PEPS) are a class of quantum many-body states that generalize Matrix Product States for one-dimensional systems to higher dimensions. PEPS have advanced understanding of strongly correlated systems, especially in two dimensions, e.g., quantum spin liquids. We present a PEPS algorithm to simulate low-energy states and dynamics defined on arbitrary, fluctuating, and densely connected graphs.
  arXiv  Detail & Related papers  (2024-07-30T19:03:52Z)
• Towards determining the (2+1)-dimensional Quantum Electrodynamics running coupling with Monte Carlo and quantum computing methods [0.0]
  We present a strategy for studying the running coupling and extracting the non-perturbative $Lambda$- parameter. We use Monte Carlo simulations and quantum computing to bridge results from small lattice spacings to large-scale lattice calculations. The procedure outlined in this work can be extended to Abelian and non-Abelian lattice gauge theories with matter fields.
  arXiv  Detail & Related papers  (2024-04-26T17:17:20Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Efficiently Escaping Saddle Points for Non-Convex Policy Optimization [40.0986936439803]
  Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. We propose a variance-reduced second-order method that uses second-order information in the form of Hessian vector products (HVP) and converges to an approximate second-order stationary point (SOSP) with sample complexity of $tildeO(epsilon-3)$.
  arXiv  Detail & Related papers  (2023-11-15T12:36:45Z)
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States [0.0]
  The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. Our analysis reveals that PEPS-METTS achieves accurate long-range correlations with significantly lower bond dimensions.
  arXiv  Detail & Related papers  (2023-10-12T17:23:55Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• Random insights into the complexity of two-dimensional tensor network calculations [0.27708222692419743]
  Projected entangled pair states offer memory-efficient representations of some quantum many-body states. Projected entangled pair states offer memory-efficient representations of some quantum many-body states that obey an entanglement area law.
  arXiv  Detail & Related papers  (2023-07-20T17:34:06Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Quantitative Propagation of Chaos for SGD in Wide Neural Networks [39.35545193410871]
  In this paper, we investigate the limiting behavior of a continuous-time counterpart of the Gradient Descent (SGD) We show 'propagation of chaos' for the particle system defined by this continuous-time dynamics under different scenarios. We identify two under which different mean-field limits are obtained, one of them corresponding to an implicitly regularized version of the minimization problem at hand.
  arXiv  Detail & Related papers  (2020-07-13T12:55:21Z)
• Targeted free energy estimation via learned mappings [66.20146549150475]
  Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences. FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase overlap.
  arXiv  Detail & Related papers  (2020-02-12T11:10:00Z)

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.