Localization in Fractonic Random Circuits

By S. Pai, M. Pretko, R. Nandkishore. Physical Review X, 2018

160 citations recorded by the source corpus.

We study the spreading of initially-local operators under unitary time evolution in a 1d random quantum circuit model which is constrained to conserve a $U(1)$ charge and its dipole moment, motivated by the quantum dynamics of fracton phases. We discover that charge remains localized at its initial position, providing a crisp example of a non-ergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well-described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions in good agreement with numerics. Importantly, these equations also predict localization in 2d fractonic circuits. Immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct to non-fractonic circuits. Fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum follows semi-Poisson statistics, similar to eigenstates of MBL systems. The non-ergodic phenomenology persists to initial conditions containing non-zero density of dipolar or fractonic charge. Our work implies that low-dimensional fracton systems preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that 1d and 2d fracton systems should realize true MBL under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in d>1 being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new non-ergodic phases in high dimensions.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6202a42d89af233165d4e18744d5266c4bb75d96

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Citations in the corpus

Random Quantum Circuits (2022, background): “A separate line of work studied “fractonic” circuits which conserve both a U(1) charge, Q = ∑ x qx and its dipole moment, P = ∑ x xqx (190, 191, 192, 193).”
Statistical localization: From strong fragmentation to strong edge modes (2019, background): “Such dipoleconserving Hamiltonians appear as effective descriptions in a variety of settings, such as fracton systems [49, 95], the quantum Hall effect [47, 96–99], and for charged particles in a strong electric field [32, 100].”
Fracton phases of matter (2020, background): “(Figure taken from Reference [13].”
Fracton hydrodynamics (2020, background): “edu While local mobility constraints can lead to very long relaxation times for equilibration [46] and can even produce localization in certain subspaces [47–49], typical initial states in most fracton systems can reach local equilibrium.”
Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “There are also generalizations of the random unitary circuit to respect charge conservation [74, 75], dipolar conservation [76] or other kinetic constraints, which are important for studying the interplay between transport phenomena and scrambling.”
Localization from Hilbert space shattering: From theory to physical realizations (2020, methodology): “Figure taken from [35].”
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[71] Shriya Pai, Michael Pretko, and Rahul M.”