Abstract
Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to non-unitary evolution, e.g., via projective measurements. Here we employ the idea of space-time rotation of a circuit to explore the relation between systems that fall into these two classes. In particular, by space-time rotating unitary Floquet circuits that display a localization transition, we construct non-unitary circuits that display a rich variety of entanglement scaling and phase transitions. One outcome of our approach is a non-unitary circuit for free fermions in 1d that exhibits an entanglement transition from logarithmic scaling to volume-law scaling. This transition is accompanied by a 'purification transition' analogous to that seen in hybrid projective-unitary circuits. We follow a similar strategy to construct a non-unitary 2d Clifford circuit that shows a transition from area to volume-law entanglement scaling. Similarly, we space-time rotate a 1d spin chain that hosts many-body localization to obtain a non-unitary circuit that exhibits an entanglement transition. Finally, we introduce an unconventional correlator and argue that if a unitary circuit hosts a many-body localization transition, then the correlator is expected to be singular in its non-unitary counterpart as well.
Highlights
Generic isolated quantum systems typically thermalize via the interaction between their constituents [1,2,3,4,5]
We employ the idea of the spacetime rotation of unitary circuits to construct nonunitary circuits that display entanglement phase transitions
We focus on specific Floquet unitary circuits that display localizationdelocalization transitions of various kinds
Summary
Generic isolated quantum systems typically thermalize via the interaction between their constituents [1,2,3,4,5]. The first example we study corresponds to a Floquet circuit that displays an Anderson localization transition due to quasiperiodic disorder Rotating this circuit results in a one-dimensional (1D) free-fermion nonunitary circuit that exhibits a transition from a volume-law entanglement regime, S ∼ L (L is the spatial size), to a regime with entanglement characteristic of critical ground states: S ∼ log(L). We construct a 2D model where the unitary corresponds to a Floquet Clifford circuit and which displays a localization transition Spacetime rotating this circuit results in a nonunitary circuit consisting of only unitaries and “forced” projective measurements. A two-dimensional Clifford Floquet circuit that displays a localization-delocalization transition, and study its spacetime-rotated version that turns out to be a hybrid circuit consisting of only unitaries and forced projective measurements.
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