Hamiltonian truncation tensor networks for quantum field theories

• URL: http://arxiv.org/abs/2312.12506v1
• Date: Tue, 19 Dec 2023 19:00:02 GMT
• Title: Hamiltonian truncation tensor networks for quantum field theories
• Authors: Philipp Schmoll, Jan Naumann, Alexander Nietner, Jens Eisert, Spyros Sotiriadis
• Abstract summary: 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.
• Score: 42.2225785045544
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly challenging. In this work, we introduce a tensor network method for the classical simulation of continuous quantum field theories that is suitable for the study of low-energy eigenstates and out-of-equilibrium time evolution. The method is built on Hamiltonian truncation and tensor network techniques, bridging the gap between two successful approaches. One of the key developments is the exact construction of matrix product state representations of global projectors, crucial for the implementation of interacting theories. Despite featuring a relatively high computational effort, our method dramatically improves predictive precision compared to exact diagonalisation-based Hamiltonian truncation, allowing the study of so far unexplored parameter regimes and dynamical effects. We corroborate trust in the accuracy of the method by comparing it with exact theoretical results for ground state properties of the sine-Gordon model. We then proceed with discussing $(1+1)$-dimensional quantum electrodynamics, the massive Schwinger model, for which we accurately locate its critical point and study the growth and saturation of momentum-space entanglement in sudden quenches.

Related papers

• Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach [0.0]
  We employ the recently-developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings. We show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings.
  arXiv  Detail & Related papers  (2024-03-06T00:47:38Z)
• Quantum Simulation of Boson-Related Hamiltonians: Techniques, Effective Hamiltonian Construction, and Error Analysis [6.8063130539569]
  We discuss the incorporation of bosonic degrees of freedom into optimized fermion algorithms for near-future quantum simulations. troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes.
  arXiv  Detail & Related papers  (2023-07-13T06:46:25Z)
• Robust Hamiltonian Engineering for Interacting Qudit Systems [50.591267188664666]
  We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. We experimentally demonstrate these techniques in a strongly-interacting, disordered ensemble of spin-1 nitrogen-vacancy centers.
  arXiv  Detail & Related papers  (2023-05-16T19:12:41Z)
• Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory [0.0]
  Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe. We compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory. Results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer.
  arXiv  Detail & Related papers  (2022-10-06T17:47:33Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
  We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
  arXiv  Detail & Related papers  (2022-07-14T10:05:20Z)
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation [0.0]
  Entanglement is the fundamental difference between classical and quantum systems. We present the first method for the explicit computation of reduced density matrices of interacting quantum field theories.
  arXiv  Detail & Related papers  (2022-02-22T19:00:05Z)
• Quantum Simulation of Conformal Field Theory [77.34726150561087]
  We describe a quantum algorithm to simulate the dynamics of conformal field theories. A full analysis of the approximation errors suggests near-term applicability.
  arXiv  Detail & Related papers  (2021-09-29T06:44:33Z)
• Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
  This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime. The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations. Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
  arXiv  Detail & Related papers  (2020-01-23T18:09:10Z)

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.