Entanglement phases, localization and multifractality of monitored free fermions in two dimensions

• URL: http://arxiv.org/abs/2309.12391v4
• Date: Mon, 12 Aug 2024 13:22:49 GMT
• Title: Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Authors: K. Chahine, M. Buchhold,
• Abstract summary: We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U$(1)$-symmetry in two spatial dimensions (2D) By deriving the exact fermion replica-quantum master equation, we line out two approaches: (i) a nonlinear sigma model analogous to disordered free fermions, resulting in an SU$(R)$-symmetric field theory of symmetry class AIII in (2+1) space-time dimensions, or (ii) for bipartite lattices, third quantization leading to a non-Hermitian SU$ (2R)$-symmetric Hubbard model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with U$(1)$-symmetry in two spatial dimensions (2D). By deriving the exact fermion replica-quantum master equation, we line out two approaches: (i) a nonlinear sigma model analogous to disordered free fermions, resulting in an SU$(R)$-symmetric field theory of symmetry class AIII in (2+1) space-time dimensions, or (ii) for bipartite lattices, third quantization leading to a non-Hermitian SU$(2R)$-symmetric Hubbard model. Using exact numerical simulations, we explore the phenomenology of the entanglement transition in 2D monitored fermions, examining entanglement entropy and wave function inverse participation ratio. At weak monitoring, we observe characteristic $L\log L$ entanglement growth and multifractal dimension $D_q=2$, resembling a metallic Fermi liquid. Under strong monitoring, wave functions localize and the entanglement saturates towards an area law. Between these regimes, we identify a high-symmetry point exhibiting both entanglement growth indicative of emergent conformal invariance and maximal multifractal behavior. While this multifractal behavior aligns with the nonlinear sigma model of the Anderson transition, the emergent conformal invariance is an unexpected feature not typically associated with Anderson localization. These discoveries add a new dimension to the study of 2D monitored fermions and underscore the need to further explore the connection between non-unitary quantum dynamics in $D$ dimensions and quantum statistical mechanics in $D+1$ dimensions.

Related papers

• Entanglement Transition due to particle losses in a monitored fermionic chain [0.0]
  We study the dynamics of the entanglement entropy under quantum jumps that induce local particle losses in a model of free fermions hopping. We show that by tuning the system parameters, a measurement-induced entanglement transition occurs where the entanglement entropy scaling changes from logarithmic to area-law.
  arXiv  Detail & Related papers  (2024-08-07T11:30:09Z)
• A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge [0.0]
  We study measurement-induced phases of free fermion systems with U(1) symmetry. We derive a field theory description for the purity and bipartite entanglement at large space and time scales.
  arXiv  Detail & Related papers  (2024-07-10T20:53:47Z)
• Anomaly inflow for dipole symmetry and higher form foliated field theories [0.0]
  We introduce a series of $(d+1)$-dimensional BF theories with $p$-form gauge fields. We show that gauge invariant loops have unusual form, containing linear function of the spatial coordinate. We also show that the theories exhibit a mixed 't Hooft anomaly between $p$-form and $(d-p)$-form dipole symmetries.
  arXiv  Detail & Related papers  (2024-06-07T13:22:40Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Nonlinear sigma models for monitored dynamics of free fermions [0.0]
  We derive descriptions for measurement-induced phase transitions in free fermion systems. We use the replica trick to map the dynamics to the imaginary time evolution of an effective spin chain. This is a nonlinear sigma model for an $Ntimes N$ matrix, in the replica limit $Nto 1$.
  arXiv  Detail & Related papers  (2023-02-24T18:56:37Z)
• Spectral crossover in non-hermitian spin chains: comparison with random matrix theory [1.0793830805346494]
  We study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. The presence of a random field along the $x$-direction together with the one along $z$ facilitates integrability and $mathcalRT$-symmetry breaking.
  arXiv  Detail & Related papers  (2023-02-02T21:26:44Z)
• Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials [77.34726150561087]
  We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times. In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
  arXiv  Detail & Related papers  (2022-10-03T16:51:25Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)

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.