Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality

• URL: http://arxiv.org/abs/2212.06188v3
• Date: Mon, 18 Sep 2023 11:22:59 GMT
• Title: Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Authors: Bruno Bertini, Pasquale Calabrese, Mario Collura, Katja Klobas, Colin Rylands
• Abstract summary: We consider the evolution of the full counting statistics (FCS) and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. We show that whenever the initial state is also U(1), the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Due to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution - or its Fourier transform known as full counting statistics (FCS) - contains much more information than say the mean value of the measured observable and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables - the charged moments - that characterise how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry. Here we consider the evolution of the FCS and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. For large scales these quantities take a simple large-deviation form, showing two different regimes as functions of time: while for times much larger than the size of the region they approach a stationary value set by the local equilibrium state, for times shorter than region size they show a non-trivial dependence on time. We show that, whenever the initial state is also U(1) symmetric, the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality. Namely, it coincides with the stationary value in the system where the roles of time and space are exchanged. We use this observation to find some general properties of FCS and charged moments out-of-equilibrium, and to derive an exact expression for these quantities in interacting integrable models. We test this expression against exact results in the Rule 54 quantum cellular automaton and exact numerics in the XXZ spin-1/2 chain.

Related papers

• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Quantum many-body spin ratchets [0.0]
  We show that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. We also show that the scaled cumulant generating function of the time-integrated current instead obeys a generalized fluctuation relation.
  arXiv  Detail & Related papers  (2024-06-03T17:51:36Z)
• Signatures of quantum phases in a dissipative system [13.23575512928342]
  Lindbladian formalism has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model.
  arXiv  Detail & Related papers  (2023-12-28T17:53:26Z)
• Full Counting Statistics of Charge in Quenched Quantum Gases [0.0]
  We study the full counting statistics of particle number in one dimensional interacting Bose and Fermi gases. We show that the scaled cumulants of the charge in the initial state and at long times are simply related.
  arXiv  Detail & Related papers  (2023-12-05T18:00:36Z)
• Timescales of quantum and classical chaotic spin models evolving toward equilibrium [0.0]
  We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Numerical simulations, supported by semi-analytical analysis, reveal that the relaxation of single-particle energies (global quantity) and on-site magnetization (local observable) occurs on a timescale independent of the system size $L$.
  arXiv  Detail & Related papers  (2023-07-11T18:00:04Z)
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain [62.997667081978825]
  We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization. In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
  arXiv  Detail & Related papers  (2022-12-19T12:34:37Z)
• 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)
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields [0.0]
  In time-independent quantum systems, entanglement entropy possesses an inherent scaling symmetry that the energy of the system does not have. We show that such systems have dynamical scaling symmetry that leaves the evolution of various measures of quantum correlations invariant.
  arXiv  Detail & Related papers  (2022-05-26T13:20:46Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.