Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits

• URL: http://arxiv.org/abs/2304.06744v2
• Date: Tue, 8 Aug 2023 10:24:00 GMT
• Title: Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Authors: Patrick Emonts, Erez Zohar
• Abstract summary: Fermionic tensor network state constructions describe the physics of ground states of non-interacting fermionic Hamiltonians. We show how to generalize such states from two to three spatial dimensions, focusing on spin representations and requirements of lattice rotations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fermionic Gaussian Projected Entangled Pair States are fermionic tensor network state constructions which describe the physics of ground states of non-interacting fermionic Hamiltonians. As non-interacting states, one may study and analyze them very efficiently, in both analytical and numerical means. Recently it was shown that they may be used as the starting point - after applying so-called PEPS gauging mechanisms - for variational study of lattice gauge theories. This is done using sign-problem free variational Monte-Carlo. In this work we show how to generalize such states from two to three spatial dimensions, focusing on spin representations and requirements of lattice rotations. We present constructions which are crucial for the application of the above mentioned variational Monte-Carlo techniques for studying non-perturbative lattice gauge theory physics, with fermionic matter, in $2+1$-d and $3+1$-d models. Thus, the constructions presented here are crucial for the study of non-trivial lattice gauge theories with fermionic tensor network states.

Related papers

• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories [0.0]
  Gauge theories form the basis of our understanding of modern physics. In the non-perturbative regime, gauge theories are treated discretely as lattice gauge theories. We present a unified and comprehensive framework for gauged Gaussian Projected Entangled Pair States (PEPS)
  arXiv  Detail & Related papers  (2024-04-19T18:14:43Z)
• 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)
• $\mathbb{Z}_N$ lattice gauge theories with matter fields [0.0]
  We study fermions and bosons in $mathbb Z_N$ lattice gauge theories. We present analytical arguments for the most important phases and estimates for phase boundaries of the model.
  arXiv  Detail & Related papers  (2023-08-24T21:05:15Z)
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density [0.7734726150561088]
  We present a variational, sign-problem-free Monte Carlo method for lattice gauge theories with continuous gauge groups. We apply it to (2+1)-dimensional compact QED with dynamical fermions at finite density.
  arXiv  Detail & Related papers  (2023-04-12T15:35:57Z)
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration [0.0]
  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.
  arXiv  Detail & Related papers  (2022-10-31T18:00:02Z)
• 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)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d [0.688204255655161]
  Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. It is possible to efficiently compute physical observables using a variational Monte Carlo procedure. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters.
  arXiv  Detail & Related papers  (2020-08-03T13:59:42Z)

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.