---

I will discuss the effects of local measurements on critical quantum ground states. These states are highly entangled and feature algebraic correlations between local observables. As a consequence, local measurements can have highly nonlocal effects. Our focus is on Tomonaga-Luttinger liquid (TLL) ground states, a continuous family of critical states in one dimension whose structure is parameterized by a Luttinger parameter K. We show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long-wavelength correlations. Conditioning first on a particular measurement outcome we show that there is a transition in the character of the resulting quantum state for K<1, and highlight a formal analogy with the effect of an impurity on transport. To study the full ensemble of measurement outcomes we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. We show how their behaviour can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for K<1/2. For K<1/2 there is a suppression of quantum fluctuations of measured observables which becomes more prominent at long wavelengths.

---

Samuel Garratt
Seminar Room 0.03, ETP
Contact: Michael Buchhold