Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings

Sahu, Subhayan; Jian, Shao-Kai; Bentsen, Gregory; Swingle, Brian

doi:10.48550/arxiv.2109.00013

“…[51], where a similar but different long-range protocol is considered, suggesting these models critical point belong to the same α-dependent universality classes. Another recent article [87] considering tractable large-N models also investigated the effects of power-law long-range couplings on measurement induced phase transitions to analytically derive the phase diagram and probe the critical exponents. Some of the critical features we discussed are present in their treatment as well, further suggesting the generic features of those.…”

Section: Discussionmentioning

confidence: 99%

Measurement-induced criticality in extended and long-range unitary circuits

Sharma

¹

,

Turkeshi

²

,

Fazio

³

et al. 2022

View full text Add to dashboard Cite

We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.

show abstract

“…Since SYK-like models are solvable, they are ideal platforms for understanding the entanglement phase transitions [92][93][94][95][96][97][98]. In this section, we review the studies of non-unitary SYK models, focusing on continuous forced measurements which are equivalent to non-Hermitian Hamiltonian dynamics.…”

Section: Entanglement In Non-unitary Syk Modelsmentioning

confidence: 99%

“…Main previous studies focus on n = 2 [92][93][94][95][96][97]. The von Neumann entropy limit n → 1 has been studied in [98] with further assumptions.…”

Section: Entanglement In Non-unitary Syk Modelsmentioning

confidence: 99%

“…We focus on the non-interacting case studied in [95]. The effect of long-range couplings in interacting SYK-like models has been studied in [96].…”

Section: Effects Of Long-range Couplingsmentioning

confidence: 99%

“…This mechanism works for either projective or general measurements, regardless of whether the outcome is post-selected or not. SYK-like models are ideal platforms for revealing the underlying mechanism of these transitions [92][93][94][95][96][97][98]. In the last part of this review, we summarize recent progress in understanding the steady-state entanglement entropy of non-unitary SYK models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations

Zhang

¹

2022

View full text Add to dashboard Cite

Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-N solvable models: the Sachdev-Ye-Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK Model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition. CONTENTSI. Introduction 1 II. The SYK model and its generalizations 2 A. Large-N expansion 2 B. Low-energy limit and holography 3 C. Generalizations of the SYK model 4 III. Entanglement in the SYK model 5 A. The exact diagonalization 5 B. The eigenstate thermalization hypothesis 6 C. The path-integral approach 7 D. Exact results for SYK 2 9 IV. Entanglement in coupled SYK models 9 A. The set-up and G-Σ action 10 B. Early-time linear growth 11 C. Geometric interpretation for N 2 = N 1 12 D. Thermalization and replica wormholes 13 E. Entanglement dynamics of SYK chains 14 V. Entanglement in non-unitary SYK models 14 A. Emergent replica conformal symmetry 15 B. Entanglement phase transitions 16 C. Effects of long-range couplings 17 VI. Outlook 17 References 18

show abstract

Quantum Entanglement in the Sachdev-Ye-Kitaev Model and its Generalizations

Zhang¹

2022

Preprint

0

View full text Add to dashboard Cite

Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-N solvable models: the Sachdev-Ye-Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK Model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition. CONTENTSI. Introduction 1 II. The SYK model and its generalizations 2 A. Large-N expansion 2 B. Low-energy limit and holography 3 C. Generalizations of the SYK model 4 III. Entanglement in the SYK model 5 A. The exact diagonalization 5 B. The eigenstate thermalization hypothesis 6 C. The path-integral approach 7 D. Exact results for SYK 2 9 IV. Entanglement in coupled SYK models 9 A. The set-up and G-Σ action 10 B. Early-time linear growth 11 C. Geometric interpretation for N 2 = N 1 12 D. Thermalization and replica wormholes 13 E. Entanglement dynamics of SYK chains 14 V. Entanglement in non-unitary SYK models 14 A. Emergent replica conformal symmetry 15 B. Entanglement phase transitions 16 C. Effects of long-range couplings 17 VI. Outlook 17 References 18

show abstract

Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings

Cited by 3 publications

References 50 publications

Measurement-induced criticality in extended and long-range unitary circuits

Measurement-induced criticality in extended and long-range unitary circuits

Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations

Quantum Entanglement in the Sachdev-Ye-Kitaev Model and its Generalizations

Contact Info

Product

Resources

About