Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality

Abstract

In recent years entanglement measures, such as the von Neumann and the Rényi entropies, provided a unique opportunity to access elusive features of quantum many-body systems. However, extracting entanglement properties analytically, experimentally, or in numerical simulations can be a formidable task. Here, by combining the replica trick and the Jarzynski equality we devise an alternative effective out-of-equilibrium protocol for measuring the equilibrium Rényi entropies. The key idea is to perform a quench in the geometry of the replicas. The Rényi entropies are obtained as the exponential average of the work performed during the quench. We illustrate an application of the method in classical Monte Carlo simulations, although it could be useful in different contexts, such as in quantum Monte Carlo, or experimentally in cold-atom systems. The method is most effective in the quasistatic regime, i.e., for a slow quench. As a benchmark, we compute the Rényi entropies in the Ising universality class in 1+1 dimensions. We find perfect agreement with the well-known conformal field theory predictions.

Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap

“…In this work, we revisit this question in the context of recent progress in measuring the second Renyi entanglement entropy with ultracold atoms in optical lattices [29,30]. This has opened a new window for the exploration of many-body physics and quantum phase transitions [31][32][33] at the interface with quantum information theory [34][35][36][37][38][39][40][41][42][43].…”

Entanglement Entropy from Nonequilibrium Work

“…At the same time, the ability to view the Rényi entanglement entropy as a difference of free energies begs the question of whether one can apply nonequilibrium work relations [25,26] that have been widely used in the molecular dynamics community [27]. Indeed, this idea was recently explored in the context of classical path integral Monte Carlo [28], paving the way for the extension to QMC that we present here.…”

Measuring von Neumann entanglement entropies without wave functions

“…Examples of its relevance include the existence of area laws bounding entanglement in ground state of local Hamiltonians [3], the sharp characterization of conformal field theories (CFTs) in one-dimension (1D) [5][6][7], topological order [8,9] and spontaneous symmetry breaking [10], and its importance in understanding the complexity of classical simulations [11]. However, differently from remarkable theoretical [12][13][14][15][16] and experimental [17,18] studies aimed at measuring Renyi entropies, the VNE has so far eluded a direct experimental verification, as it requires tomographic access to the system wave function -which becomes quickly impractical beyond few spins. The same limitations affect numerical methods such as quantum Monte Carlo (QMC) [19], which typically cannot sample wave functions, and, thus, cannot compute the VNE.…”