Quantum Energy Teleportation Across Lattice and Continuum

TL;DR

This paper investigates quantum energy teleportation in the massive Thirring model, connecting lattice and continuum descriptions by analyzing neutral and charged sectors through novel measurement protocols.

Contribution

It introduces a lattice neutral current protocol that aligns with continuum behavior, clarifying the relation between lattice and continuum QET models.

Findings

The continuum measurement is a weak binary POVM linked to a conserved-current correlator.

Lattice protocols typically access charged sectors, missing the neutral current contribution.

A new lattice protocol captures the neutral current sector, with energy scaling quadratically with measurement strength.

Abstract

Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine--Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice $U(1)$ selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.