Charge fluctuation and charge-resolved entanglement in monitored quantum circuit with $U(1)$ symmetry

• URL: http://arxiv.org/abs/2210.16009v2
• Date: Wed, 23 Nov 2022 04:55:10 GMT
• Title: Charge fluctuation and charge-resolved entanglement in monitored quantum circuit with $U(1)$ symmetry
• Authors: Hisanori Oshima and Yohei Fuji
• Abstract summary: We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements. We find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling behaviors akin to Tomonaga-Luttinger-liquid theory for equilibrium critical quantum systems with $U(1)$ symmetry, such as logarithmic scaling of bipartite charge fluctuation, power-law decay of charge correlation functions, and logarithmic scaling of charge-resolved entanglement whose coefficient becomes a universal quadratic function in a flux parameter. These critical features, however, do not persist below the transition in contrast to a recent prediction based on replica field theory and mapping to a classical statistical mechanical model.

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)
• 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)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems [0.0]
  We study fluctuations of the charge transferred across the central bond in typical circuits. We show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading $t-1/2$ quantum corrections.
  arXiv  Detail & Related papers  (2023-02-02T19:00:05Z)
• Field theory of charge sharpening in symmetric monitored quantum circuits [0.2936007114555107]
  Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations.
  arXiv  Detail & Related papers  (2021-11-17T19:00:28Z)
• Measurement-induced criticality in $\mathbb{Z}_2$-symmetric quantum automaton circuits [6.723539428281127]
  We study entanglement dynamics in hybrid $mathbbZ$-symmetric quantum automaton circuits. We show that there exists an entanglement phase transition from a volume law phase to a critical phase by varying the measurement rate $p$.
  arXiv  Detail & Related papers  (2021-10-20T18:52:14Z)
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits [1.1968749490556412]
  We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement. We find that while R'enyi entropies grow sub-ballistically as $sqrttt$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R'enyi entropies grow ballistically with time.
  arXiv  Detail & Related papers  (2021-07-21T18:00:13Z)
• SYK meets non-Hermiticity II: measurement-induced phase transition [16.533265279392772]
  We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.
  arXiv  Detail & Related papers  (2021-04-16T17:55:08Z)
• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{PT}$ symmetry to quantum fluctuations [0.0]
  We study a minimal model that has a driven-dissipative quantum phase transition. We analyze the critical phenomena in this system, showing which aspects can be captured by each approach. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
  arXiv  Detail & Related papers  (2020-07-02T22:39:35Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.