Measuring Renyi Entropy in Neural Network Quantum States

• URL: http://arxiv.org/abs/2308.05513v2
• Date: Thu, 14 Mar 2024 07:42:45 GMT
• Title: Measuring Renyi Entropy in Neural Network Quantum States
• Authors: Han-Qing Shi, Hai-Qing Zhang,
• Abstract summary: We compute the Renyi entropy in a one-dimensional transverse-field quantum Ising model. In the static ground state, Renyi entropy can uncover the critical point of the quantum phase transition from paramagnetic to ferromagnetic. In the dynamical case, we find coherent oscillations of the Renyi entropy after the end of the linear quench.
• Score: 1.3658544194443192
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We compute the Renyi entropy in a one-dimensional transverse-field quantum Ising model by employing a swapping operator acting on the states which are prepared from the neural network methods. In the static ground state, Renyi entropy can uncover the critical point of the quantum phase transition from paramagnetic to ferromagnetic. At the critical point, the relation between the Renyi entropy and the subsystem size satisfies the predictions from conformal field theory. In the dynamical case, we find coherent oscillations of the Renyi entropy after the end of the linear quench. These oscillations have universal frequencies which may come from the superpositions of excited states. The asymptotic form of the Renyi entropy implies a new length scale away from the critical point. This length scale is also verified by the overlap of the reduced Renyi entropy against the dimensionless subsystem size.

Related papers

• Quantum amplification, relic gravitons and Landauer's conjecture [0.0]
  We show that during quantum amplification the heat flow does restrict the increase of the Von Neumann entropy. The bounds obtained here set a limit on initial thermal gravitons and on the total duration of inflation.
  arXiv  Detail & Related papers  (2024-09-30T15:42:08Z)
• Logarithmic singularities of Renyi entropy as a sign of chaos? [0.0]
  We analyze the logarithmic singularities of the Renyi entropy in various two-dimensional conformal field theories. We show that there are always logarithmic singularities of the Renyi entropy in holographic CFTs, but no such singularities in free and rational CFTs.
  arXiv  Detail & Related papers  (2024-04-07T04:14:55Z)
• Entanglement phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
  EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
  arXiv  Detail & Related papers  (2023-08-28T14:28:59Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Observational entropic study of Anderson localization [0.0]
  We study the behaviour of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-Andr'e model. For a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase of the observational entropy followed by the quantum quench, is logarithmic in time in the delocalized phase as well as at the transition point, while in the localized phase it oscillates.
  arXiv  Detail & Related papers  (2022-09-21T11:26:43Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• R\'{e}nyi entanglement entropy after a quantum quench starting from insulating states in a free boson system [0.0]
  We investigate the time-dependent R'enyi entanglement entropy after a quantum quench. We calculate the time evolution of the R'enyi entanglement entropy in unprecedentedly large systems. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.
  arXiv  Detail & Related papers  (2022-07-18T02:36:14Z)
• Subregion Spectrum Form Factor via Pseudo Entropy [0.0]
  We consider a transition matrix between the thermofield double state and its time-evolved state in two-dimensional field theories. We show that the real part of the pseudo entropy behaves similarly to the spectral form factor.
  arXiv  Detail & Related papers  (2021-09-01T13:17:19Z)
• Taking the temperature of a pure quantum state [55.41644538483948]
  Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. We propose a scheme to measure the temperature of such pure states through quantum interference.
  arXiv  Detail & Related papers  (2021-03-30T18:18:37Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• 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.