Non-Gaussian Entanglement Renormalization for Quantum Fields

• URL: http://arxiv.org/abs/2003.08438v2
• Date: Mon, 22 Jun 2020 11:18:57 GMT
• Title: Non-Gaussian Entanglement Renormalization for Quantum Fields
• Authors: Jose J. Fernandez-Melgarejo and Javier Molina-Vilaplana
• Abstract summary: The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory. We show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) is presented. This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit. Here we present these transformations for the case of self-interacting scalar and fermionic field theories. Finally, the icMERA tensor network is fully optimized for the $\lambda \phi^4$ theory in $(1+1)$ dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories.

Related papers

• Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms [0.0]
  We propose an adaptation of Entanglement Renormalization for quantum field theories using discrete wavelet transforms. We describe two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions.
  arXiv  Detail & Related papers  (2024-04-17T20:01:51Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Renormalization group for measurement and entanglement phase transitions [0.0]
  We analyze the renormalization-group (RG) flows of two effective Lagrangians. We show that the theory for the random tensor network formally possesses a dimensional reduction property analogous to that of the random-field Ising model.
  arXiv  Detail & Related papers  (2023-03-14T12:40:03Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Exact Renormalization of Wave Functionals yields Continuous MERA [0.8778115505805627]
  We show that cMERA can be derived from a more fundamental "microscopic" principle, suitably adapted to quantum states of the field theory. The establishment of such a principle may provide a path forward for exploring cMERA beyond the free field regime.
  arXiv  Detail & Related papers  (2023-01-23T19:11:25Z)
• Spin Current Density Functional Theory of the Quantum Spin-Hall Phase [59.50307752165016]
  We apply the spin current density functional theory to the quantum spin-Hall phase. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone.
  arXiv  Detail & Related papers  (2022-08-29T20:46:26Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Perturbation theory without power series: iterative construction of non-analytic operator spectra [0.0]
  It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place.
  arXiv  Detail & Related papers  (2021-05-11T12:21:18Z)
• 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)
• Unitary, continuum, stationary perturbation theory for the radial Schr\"odinger equation [0.0]
  We test the concept of unitary transformations of generators in the nonrelativistic case. A stationary perturbation theory can be constructed to find approximate solutions of the radial Schr"odinger equation.
  arXiv  Detail & Related papers  (2020-07-31T01:41:12Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

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.