Realizing the entanglement Hamiltonian of a topological quantum Hall system

• URL: http://arxiv.org/abs/2307.06251v1
• Date: Wed, 12 Jul 2023 15:40:06 GMT
• Title: Realizing the entanglement Hamiltonian of a topological quantum Hall system
• Authors: Quentin Redon, Qi Liu, Jean-Baptiste Bouhiron, Nehal Mittal, Aur\'elien Fabre, Raphael Lopes, Sylvain Nascimbene
• Abstract summary: Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally quantifies entanglement, has been proposed as a first signature of topological order. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed Hall systems.
• Score: 10.092164351939825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally quantifies entanglement, has been proposed as a first signature of topological order. Conversely, the full description of entanglement relies on the entanglement Hamiltonian, a more complex object originally introduced to formulate quantum entanglement in curved spacetime. As conjectured by Li and Haldane, the entanglement Hamiltonian of a many-body system appears to be directly linked to its boundary properties, making it particularly useful for characterizing topological systems. While the entanglement spectrum is commonly used to identify complex phases arising in numerical simulations, its measurement remains an outstanding challenge. Here, we perform a variational approach to realize experimentally, as a genuine Hamiltonian, the entanglement Hamiltonian of a synthetic quantum Hall system. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed Hall systems, as suggested by the Bisognano-Wichmann prediction. The spectrum of the optimal variational Hamiltonian exhibits a chiral dispersion akin to a topological edge mode, revealing the fundamental link between entanglement and boundary physics. Our variational procedure can be easily generalized to interacting many-body systems on various platforms, marking an important step towards the exploration of exotic quantum systems with long-range correlations, such as fractional Hall states, chiral spin liquids and critical systems.

Related papers

• 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)
• Exploring Large-Scale Entanglement in Quantum Simulation [0.0]
  Entanglement is a distinguishing feature of quantum many-body systems. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian.
  arXiv  Detail & Related papers  (2023-05-31T18:00:01Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter [0.0]
  Topological phases are characterized by their entanglement properties. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian.
  arXiv  Detail & Related papers  (2021-10-08T06:13:51Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Quantum Variational Learning of the Entanglement Hamiltonian [0.0]
  Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions.
  arXiv  Detail & Related papers  (2021-05-10T12:54:50Z)
• Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
  We propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
  arXiv  Detail & Related papers  (2021-04-13T17:24:08Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps [0.0]
  We propose the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. We focus on reproducing the universal ratios of the entanglement spectrum for systems in two different geometries. Our results demonstrate the possibility of measuring the entanglement spectra of the Heisenberg and XX models in a realistic cold-atom experimental setting.
  arXiv  Detail & Related papers  (2020-07-10T08:33:00Z)
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
  Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
  arXiv  Detail & Related papers  (2020-04-07T15:00:41Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.