Non-analyticity in holographic complexity near critical points

Journal Article · Thu Jan 26 23:00:00 EST 2023 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/acb181· OSTI ID:2419759

Sood, Uday ^[1]; Kruczenski, Martin

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1. OSTI

Abstract

The region near a critical point is studied using holographic models of second-order phase transitions. In a previous paper, we argued that the quantum circuit complexity of the vacuum (C₀) is the largest at the critical point. When deforming away from the critical point by a termthe complexity $C\left(\tau \right)$ has a piece non-analytic inτ, namely $C_0-C\left(\tau \right)\sim |\tau -{\tau }_c{|}^{\nu (d-1)}+\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{t}\mathrm{i}\mathrm{c}$ . Here, as usual, $\nu =\frac{1}{d-\mathrm{\Delta }}$ andξis the correlation length $\xi \sim |\tau -{\tau }_c{|}^{-\nu }$ and there are possible logarithmic corrections to this expression. That was derived using numerical results for the Bose–Hubbard model and general scaling considerations. In this paper, we show that the same is valid in the case of holographic complexity providing evidence that the results are universal, and at the same time providing evidence for holographic computations of complexity.

• Research Organization: Purdue Univ., West Lafayette, IN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: SC0007884
• OSTI ID: 2419759
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 4 Vol. 56; ISSN 1751-8113
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

Physics