Measurement-induced entanglement transitions in quantum circuits of non-interacting fermions: Born-rule versus forced measurements

• URL: http://arxiv.org/abs/2302.09094v1
• Date: Fri, 17 Feb 2023 19:00:11 GMT
• Title: Measurement-induced entanglement transitions in quantum circuits of non-interacting fermions: Born-rule versus forced measurements
• Authors: Chao-Ming Jian, Hassan Shapourian, Bela Bauer, and Andreas W. W. Ludwig
• Abstract summary: We address entanglement transitions in monitored random quantum circuits of non-interacting fermions. For a generic circuit with no symmetry other than fermion parity, we numerically obtain several critical exponents. We show that the two transitions with Bornrule and forced measurements are in different universality classes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We address entanglement transitions in monitored random quantum circuits of non-interacting fermions, in particular, the question of whether Born-rule and forced measurements yield the same universality class. For a generic circuit with no symmetry other than fermion parity, acting on a one-dimensional Majorana chain, we numerically obtain several critical exponents, providing clear evidence that the two transitions with Born-rule and forced measurements are in different universality classes. We provide a theoretical understanding for our numerical results by identifying the underlying statistical mechanics model which follows from the general correspondence, established in Jian et al., Phys. Rev. B 106, 134206, between non-unitary circuits of non-interacting fermions and the ten-fold Altland-Zirnbauer (AZ) symmetry classes. The AZ class is the same for Born-rule and forced measurements of the circuits. For the circuit under consideration (in AZ class DIII), the statistical mechanics model describing the transition is the principal chiral non-linear sigma model whose field variable is an ${\rm SO}(n)$ matrix in the replica limits $n\to 0$ and $n\to 1$ for forced and Born-rule measurements, respectively. The former is in an Anderson localization universality class while we show that the latter is in a novel universality class beyond Anderson localization. Both entanglement transitions are driven by proliferation of $\mathbb{Z}_2$ topological defects. The different replica limits account for the difference in the universality classes. Furthermore, we provide numerical and symmetry-based arguments that the entanglement transition in the previously-studied monitored circuit of Majorana fermions based on the loop model with crossings, a highly fine-tuned circuit, belongs to a universality class different from both transitions in the generic circuits discussed in this paper.

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