Complexity and Floquet dynamics: Nonequilibrium Ising phase transitions

Camilo, Giancarlo; Teixeira, Daniel

doi:10.1103/physrevb.102.174304

Cited by 9 publications

(14 citation statements)

References 46 publications

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“…In fact, the study of complexity in field theory is interesting in its own right, apart from the relation to black holes. Quantum Computational Complexity is expected to have purely condensed matter applications for the detection of phase transitions [29,30] and in the study of thermalization and chaos [31,32] as a natural extension of entanglement entropy.…”

Section: Introductionmentioning

confidence: 99%

Quantum computational complexity from quantum information to black holes and back

Chapman

Policastro

2022

Eur. Phys. J. C

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Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely different physical problem – that of information processing inside black holes. Quantum computational complexity was suggested as a new entry in the holographic dictionary, which extends the connection between geometry and information and resolves the puzzle of why black hole interiors keep growing for a very long time. In this pedagogical review, we present the geometric approach to complexity advocated by Nielsen and show how it can be used to define complexity for generic quantum systems; in particular, we focus on Gaussian states in QFT, both pure and mixed, and on certain classes of CFT states. We then present the conjectured relation to gravitational quantities within the holographic correspondence and discuss several examples in which different versions of the conjectures have been tested. We highlight the relation between complexity, chaos and scrambling in chaotic systems. We conclude with a discussion of open problems and future directions. This article was written for the special issue of EPJ-C Frontiers in Holographic Duality.

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Section: Introductionmentioning

confidence: 99%

Quantum computational complexity from quantum information to black holes and back

Chapman

Policastro

2022

Eur. Phys. J. C

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“…The study is supplied by some evidences regarding the use of circuit complexity to diagnose additional types of critical behavior, in particular dynamical quantum phase transitions. This chapter is based on [22].…”

Section: Organization Of the Thesismentioning

confidence: 99%

“…The CFTs equipped with RG can be faced under a radically distinct perspective: the scaling transformations allow one to picture a continuous family of effective QFTs at different length (therefore energy 22 ) scales, each providing a different canvas of the theory according to the degree of magnification. One can therefore merge those screens together into an additional dimension furnished by the RG energy scale r, which can be interpreted as a geometrization of the scaling transformations.…”

Section: Renormalization Group and The Anti-de Sitter Spacetimementioning

confidence: 99%

“…( 1.59) 22 The energy in the CFT can be defined as follows: consider the theory on a cylinder R ⇥ S d 1 , then its energy spectrum is given by the spectrum of the dilation operator on R d 1 (the operator that generates scaling transformations). 23 See Section 1.4.4 for a second approach with further determinations.…”

Section: Renormalization Group and The Anti-de Sitter Spacetimementioning

confidence: 99%

“…Complexity and non-equilibrium phase transitions "Todo dia ela faz tudo sempre igual Me sacode às seis horas da manhã Me sorri um sorriso pontual E me beija com a boca de hortelã." -Cotidiano, Chico Buarque This chapter was first presented as[22] under the title: "Complexity and Floquet dynamics: non-equilibrium Ising phase transitions".-Phys. Rev.…”

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confidence: 99%

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Aspects of entanglement, chaos and complexity: from many-body to high energy systems

Júnior¹

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The determination of structures that can emerge out of the interactions among the constituents of a quantum many-body system is a foundational task of condensed matter physics. One of the most advanced proposals within this paradigm is the holographic generation of spacetime in some strongly coupled chaotic systems with particular patterns of entanglement and quantum complexity, which is historically motivated by the holographic principle and by the AdS/CFT correspondence. As a part of this scenario, this thesis is dedicated to the analysis of some concepts that are relevant to such proposal, where they are separately applied to some lattice models. Concretely, the matter is divided into three main studies: first, the calculation of the time-dependent circuit complexity in the Ising model with a periodically driven transverse field, where we establish the effectiveness of this quantity for the detection of nonequilibrium quantum phase transitions. Our results provide hints for understanding how universal features out of equilibrium are captured by the complexity of quantum states. Second, the derivation of a bound on the maximal rate of entanglement entropy production for a class of one-dimensional quantum circuits with periodic dynamics. An example of a circuit that saturates the bound is composed by parallel SWAP gates acting on entangled pairs. Out of inequalities obeyed by the entropy, in addition to considerations on multipartite entanglement, we indicate that the effect of a chaotic dynamics cannot result in the increase on the rate of entanglement production. Third, the construction of a class of supersymmetric many-body systems using symmetric inverse semigroups. For particular toy models built out of this structure, we study some questions regarding supersymmetric phases, integrability, disorder, spreading of quantum information and many-body localization. Finally, besides those three works, we include an essay addressing the problem of emergent holographic spaces out of two-dimensional conformal field theories, where the mediation between the two parts is performed by means of a Riemannian structure defined in the Hilbert space of the field theory.

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Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity

Bai

2022

J. High Energ. Phys.

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The Jarzynski identity can describe small-scale nonequilibrium systems through stochastic thermodynamics. The identity considers fluctuating trajectories in a phase space. The complexity geometry frames the discussions on quantum computational complexity using the method of Riemannian geometry, which builds a bridge between optimal quantum circuits and classical geodesics in the space of unitary operators. Complexity geometry enables the application of the methods of classical physics to deal with pure quantum problems. By combining the two frameworks, i.e., the Jarzynski identity and complexity geometry, we derived a complexity analog of the Jarzynski identity using the complexity geometry. We considered a set of geodesics in the space of unitary operators instead of the trajectories in a phase space. The obtained complexity version of the Jarzynski identity strengthened the evidence for the existence of a well-defined resource theory of uncomplexity and presented an extensive discussion on the second law of complexity. Furthermore, analogous to the thermodynamic fluctuation-dissipation theorem, we proposed a version of the fluctuation-dissipation theorem for the complexity. Although this study does not focus on holographic fluctuations, we found that the results are surprisingly suitable for capturing their information. The results obtained using nonequilibrium methods may contribute to understand the nature of the complexity and study the features of the holographic fluctuations.

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Complexity and Floquet dynamics: Nonequilibrium Ising phase transitions

Cited by 9 publications

References 46 publications

Quantum computational complexity from quantum information to black holes and back

Quantum computational complexity from quantum information to black holes and back

Aspects of entanglement, chaos and complexity: from many-body to high energy systems

Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity

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