SciPost Physics

SciPost Phys. 12, 007 (2022) · published 6 January 2022

• doi: 10.21468/SciPostPhys.12.1.007
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

• Bidzhiev et al., Macroscopic Effects of Localized Measurements in Jammed States of Quantum Spin Chains
  Phys. Rev. Lett. 128, 130603 (2022) [Crossref]
• Vernier et al., Strong Zero Modes in Integrable Quantum Circuits
  Phys. Rev. Lett. 133, 050606 (2024) [Crossref]
• Su et al., Integrable nonunitary quantum circuits
  Phys. Rev. B 106, 134312 (2022) [Crossref]
• Biagetti et al., Bound-state confinement after trap-expansion dynamics in integrable systems
  J. Stat. Mech. 2024, 093103 (2024) [Crossref]
• Fritzsch et al., Boundary chaos
  Phys. Rev. E 106, 014210 (2022) [Crossref]
• Žnidarič, Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums
  Phys. Rev. Research 5, 033145 (2023) [Crossref]
• Bertini et al., Dynamics of charge fluctuations from asymmetric initial states
  Phys. Rev. B 109, 184312 (2024) [Crossref]
• Hudomal et al., Integrability Breaking and Bound States in Google’s Decorated XXZ Circuits
  PRX Quantum 5, 010316 (2024) [Crossref]
• Claeys et al., Absence of Superdiffusion in Certain Random Spin Models
  Phys. Rev. Lett. 128, 246603 (2022) [Crossref]
• Lee et al., Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
  Phys. Rev. B 108, 064311 (2023) [Crossref]
• Sopena et al., Algebraic Bethe Circuits
  Quantum 6, 796 796 (2022) [Crossref]
• Bensa et al., Purity decay rate in random circuits with different configurations of gates
  Phys. Rev. A 107, 022604 (2023) [Crossref]
• Rampp et al., Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
  Quantum 8, 1434 1434 (2024) [Crossref]
• Miao et al., The Floquet Baxterisation
  SciPost Phys. 16, 078 (2024) [Crossref]
• Borsi et al., Construction and the ergodicity properties of dual unitary quantum circuits
  Phys. Rev. B 106, 014302 (2022) [Crossref]
• Zhang et al., Geometric representations of braid and Yang–Baxter gates
  J. Phys. A: Math. Theor. 57, 445303 (2024) [Crossref]
• Vernier et al., Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions
  Phys. Rev. Lett. 130, 260401 (2023) [Crossref]
• Bennett et al., Occupancy probabilities in superintegrable bosonic networks
  Nuclear Physics B 998, 116406 116406 (2024) [Crossref]
• Morvan et al., Formation of robust bound states of interacting microwave photons
  Nature 612, 240 (2022) [Crossref]
• Giudice et al., Temporal Entanglement, Quasiparticles, and the Role of Interactions
  Phys. Rev. Lett. 128, 220401 (2022) [Crossref]
• Duh et al., Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution
  Phys. Rev. Research 6, 023068 (2024) [Crossref]
• Bensa et al., Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
  Phys. Rev. Research 4, 013228 (2022) [Crossref]
• Zadnik et al., Quantum Many-Body Spin Ratchets
  PRX Quantum 5, 030356 (2024) [Crossref]
• Rosenberg et al., Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
  Science 384, 48 (2024) [Crossref]
• Zhang et al., Optimal Realization of Yang–Baxter Gate on Quantum Computers
  Adv Quantum Tech 7, 2300345 (2024) [Crossref]