Entanglement area law in interacting bosons: from Bose-Hubbard, $φ$4, and beyond

• URL: http://arxiv.org/abs/2411.02157v1
• Date: Mon, 04 Nov 2024 15:16:44 GMT
• Title: Entanglement area law in interacting bosons: from Bose-Hubbard, $φ$4, and beyond
• Authors: Donghoon Kim, Tomotaka Kuwahara,
• Abstract summary: The entanglement area law characterizes the information structure in quantum many-body systems. We prove the area law for one-dimensional interacting boson systems including the long-range interactions.
• Score: 0.276240219662896
• License:
• Abstract: The entanglement area law is a universal principle that characterizes the information structure in quantum many-body systems and serves as the foundation for modern algorithms based on tensor network representations. Historically, the area law has been well understood under two critical assumptions: short-range interactions and bounded local energy. However, extending the area law beyond these assumptions has been a long-sought goal in quantum many-body theory. This challenge is especially pronounced in interacting boson systems, where the breakdown of the bounded energy assumption is universal and poses significant difficulties. In this work, we prove the area law for one-dimensional interacting boson systems including the long-range interactions. Our model encompasses the Bose-Hubbard class and the $\phi4$ class, two of the most fundamental models in quantum condensed matter physics, statistical mechanics, and high-energy physics. This result achieves the resolution of the area law that incorporates both the challenges of unbounded local energy and long-range interactions in a unified manner. Additionally, we establish an efficiency-guaranteed approximation of the quantum ground states using Matrix Product States (MPS). These results significantly advance our understanding of quantum complexity by offering new insights into how bosonic parameters and interaction decay rates influence entanglement. Our findings provide crucial theoretical foundations for simulating long-range interacting cold atomic systems, which are central to modern quantum technologies, and pave the way for more efficient simulation techniques in future quantum applications.

Related papers

• Entanglement scaling and criticality of quantum many-body systems in canonical quantization picture using tensor network [0.0]
  This work investigates the quantum entanglement and criticality of the ground-state wave-functions of infinitely-many coupled quantum oscillators (iCQOs) By extending the imaginary-time evolution algorithm with translationally-invariant functional tensor network, we simulate the ground state of iCQOs with the presence of two- and three-body couplings. We reveal the logarithmic scaling law of entanglement entropy (EE) and the scaling law of correlation length against the virtual bond $chi$ at the dividing point of physical and non-physical regions.
  arXiv  Detail & Related papers  (2024-10-31T04:20:49Z)
• Probing critical phenomena in open quantum systems using atom arrays [3.365378662696971]
  At quantum critical points, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions. Here, we employ a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice. By accounting for and tuning the openness of our quantum system, we are able to directly observe power-law correlations and extract the corresponding scaling dimensions.
  arXiv  Detail & Related papers  (2024-02-23T15:21:38Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Interaction-induced topological pumping in a solid-state quantum system [18.7657779101508]
  Inter-particle interaction can profoundly alter the band structure of quantum many-body systems. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits.
  arXiv  Detail & Related papers  (2023-03-08T13:57:13Z)
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory [0.9208007322096533]
  Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. We introduce neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories.
  arXiv  Detail & Related papers  (2022-12-01T18:58:40Z)
• From Goldilocks to Twin Peaks: multiple optimal regimes for quantum transport in disordered networks [68.8204255655161]
  Open quantum systems theory has been successfully applied to predict the existence of environmental noise-assisted quantum transport. This paper shows that a consistent subset of physically modelled transport networks can have at least two ENAQT peaks in their steady state transport efficiency.
  arXiv  Detail & Related papers  (2022-10-21T10:57:16Z)
• Quantum Davidson Algorithm for Excited States [42.666709382892265]
  We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states. By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
  arXiv  Detail & Related papers  (2022-04-22T15:03:03Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Entanglement of Classical and Quantum Short-Range Dynamics in Mean-Field Systems [0.0]
  We show the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions. This leads to a theoretical framework in which the classical and quantum worlds are entangled.
  arXiv  Detail & Related papers  (2021-03-11T15:23:59Z)
• Quantum chaos driven by long-range waveguide-mediated interactions [125.99533416395765]
  We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave-function in real space.
  arXiv  Detail & Related papers  (2020-11-24T07:06:36Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)

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.