Entanglement and Conservation Laws in Many-Body Systems

Marko Žnidarič

Abstract Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Rényi entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q, and is in generic case first linear in time, similarly as for systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto ~ 105 qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems.

Frank Verstraete

J. W. Clark, Hessam Habibian, Aikaterini Mandilara +1 more

Asmi Haldar, Das, Anirban, Chaudhuri, Sagnik +5 more

The ergodicity postulate, a foundational pillar of Gibbsian statistical mechanics predicts that a periodically driven (Floquet) system in the absence of any conservation law heats to a featureless `infinite temperature' state. Here, we find--for a clean and interacting generic spin chain subject to a {\it strong} driving field--that this can be prevented by the emergence of {\it approximate but stable} conservation-laws not present in the undriven system. We identify their origin: they do not necessarily owe their stability to familiar protections by symmetry, topology, disorder, or even high energy costs. We show numerically, {\it in the thermodynamic limit,} that when required by these emergent conservation-laws, the entanglement-entropy density of an infinite subsystem remains zero over our entire simulation time of several decades in natural units. We further provide a recipe for designing such conservation laws with high accuracy. Finally, we present an ensemble description, which we call the strongly driven ensemble incorporating these constraints. This provides a way to control many-body chaos through stable Floquet-engineering. Strong signatures of these conservation-laws should be experimentally accessible since they manifest in all length and time scales. Variants of the spin model we have used, have already been realized using Rydberg-dressed atoms.

Ugo Marzolino

X. Zotos, Félix Naef, Peter Prelovšek

We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.