A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars

Abstract

We propose a quantum model of fermions simulating the electrical breakdown process of dielectrics. The model consists of $M$ sites with $N$ fermion modes per site, and has a conserved charge $Q$. It has an on-site chemical potential $\mu$ with disorder $W$, and an interaction of strength $J$ restricting each fermion to excite two more fermions when moving forward by one site. We show the $N=3$ model with disorder $W=0$ show a Hilbert space fragmentation and is exactly solvable except for very few Krylov subspaces. The analytical solution shows that the $N=3$ model exhibits many-body localization (MBL) as $M\to \infty$, which is stable against $W>0$ as our exact diagonalization (ED) shows. At $N>3$, our ED suggests a MBL to quantum chaos crossover at small $W$ as $M/N$ decreases across $1$, and persistent MBL at large $W$. At $W=0$, an exactly solvable many-body scar flat band exists in many charge $Q$ sectors, which has a nonzero measure in the thermodynamic limit. We further calculate the time evolution of a fermion added to the particle vacuum, which shows a breakdown (dielectric) phase when $\mu /J<1/2$ ($\mu /J>1/2$) if $W\ll J$, and no breakdown if $W\gg J$.

arXiv comment21+8 pages, 17+5 figures

References in corpus (59)

• Chaos and Quantum Thermalization
• Probing many-body dynamics on a 51-atom quantum simulator
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Localization of interacting fermions at high temperature
• Comments on the Sachdev-Ye-Kitaev model
• The many-body localization phase transition
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum many-body scars
• Many body localization in Heisenberg XXZ magnet in a random field
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Integrals of motion in the Many-Body localized phase
• Localization from Hilbert space shattering: from theory to physical realizations
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Stability and instability towards delocalization in MBL systems
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Band touching from real space topology in frustrated hopping models
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Constructing local integrals of motion in the many-body localized phase
• Avalanches and many-body resonances in many-body localized systems
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Stark many-body localization
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Hilbert-Space Fragmentation from Strict Confinement
• How a small quantum bath can thermalize long localized chains
• Many-body delocalization as a quantum avalanche
• Notes on the complex Sachdev-Ye-Kitaev model
• Higher Dimensional Generalizations of the SYK Model
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Systematic construction of scarred many-body dynamics in 1D lattice models
• Quaternion, harmonic oscillator, and high-dimensional topological states
• Quantum Many-body Scars in a Landau Level on a Thin Torus
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Creating quantum many-body scars through topological pumping of a 1D dipolar gas
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Dielectric Breakdown in a Mott Insulator: Many-body Schwinger-Landau-Zener Mechanism studied with a Generalized Bethe Ansatz
• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Many-body localization in a fragmented Hilbert space
• Avalanche induced co-existing localised and thermal regions in disordered chains
• Are many-body localized systems stable in the presence of a small bath?
• The chiral SYK model
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Conserved Quantities from Entanglement Hamiltonian
• Integrability of the $\nu =4/3$ fractional quantum Hall edge states

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