Entanglement entropy and its quench dynamics for pure states of the Sachdev-Ye-Kitaev model

Zhang, Pengfei

doi:10.1007/jhep06(2020)143

Cited by 30 publications

(33 citation statements)

References 52 publications

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“…Many variants of the SYK model have been constructed to study quantum chaos, quantum gravity and non-Fermi liquid analytically [22-25, 25, 26, 26-31]. In particular, there are studies on the entanglement entropy of the SYK model [32][33][34][35][36][37][38], where transitions to the replica wormhole [39,40] solution are found in the long time limit.…”

Section: Introductionmentioning

confidence: 99%

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

2021

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We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large N limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

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Section: Introductionmentioning

confidence: 99%

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

2021

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“…It is dual to a Jackiw-Teitelboim (JT) gravity [27,28] in AdS 2 spacetime [23,24]. Since the SYK model is solvable in large N limit, quite a few results for the SYK model's entropy dynamics are obtained for various SYK-like models [29][30][31][32][33][34][35][36][37] and for the Maldacena-Qi model [38] which is dual to a traversable wormhole. These entropy dynamics are also calculated on gravity side [39][40][41][42][43].…”

Section: Jhep04(2021)215mentioning

confidence: 99%

Entropy linear response theory with non-Markovian bath

Chen

2021

J. High Energ. Phys.

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We developed a perturbative calculation for entropy dynamics, which considers a sudden coupling between a system and a bath. The theory we developed can work in a general environment without Markovian approximation. A perturbative formula is given for bosonic environments and fermionic environments, respectively. We find the Rényi entropy response is only related to the spectral functions of the system and the environment, together with a statistical kernel distribution function. We find a t2 growth/decay in the short time limit and a linear t growth/decay in a longer time scale for the second Rényi entropy response. A non-monotonic behavior of Rényi entropy for fermionic systems is found to be quite general when the environmental temperature is the lower one. A Fourier’s law in heat transport is obtained when two systems’ temperatures are close to each other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free fermions, a Page curve alike dynamics is found in a process dual to black hole evaporation. An oscillation of Rényi entropy is found for an environment with a gapped spectrum.

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“…Remarkably, these models can be solved exactly in a suitable large-N limit, without resorting to any kind of perturbative treatment. As a result, the study of this family of large-N fermionic model has given insights into transport [32,[43][44][45][46][47], thermalization [54][55][56][57][58][59][60][61][62], many-body chaos [27,30,34], and entanglement [43,[63][64][65][66][67] in strongly interacting fermionic systems, as well as their intriguing connections with black holes [27,28,35]. Here we use the path-integral technique of Sec.…”

Section: Rényi Entropy For Syk and Related Modelsmentioning

confidence: 99%

“…III for all the models discussed in this section by numerically solving the saddlepoint equations, such as Eqs. (67) and (71), and using Eq. (69).…”

Section: Rényi Entropy In the Thermal Statementioning

confidence: 99%

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Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

Haldar

Bera

Banerjee

2020

Phys. Rev. Research

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We present a method for calculating Rényi entanglement entropies for fermionic field theories originating from microscopic Hamiltonians. The method builds on an operator identity, which leads to the representation of traces of operator products, and thus Rényi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out of equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well-known expressions for entanglement entropy in terms of the correlation matrix for noninteracting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Rényi entropy in a few zero-and higher dimensional large-N interacting models akin to the Sachdev-Ye-Kitaev (SYK) model and for the Hubbard model within the dynamical mean field theory (DMFT) approximation. We use the formulation to compute Rényi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-N models and compare the results successfully with those obtained via exact diagonalization for finite N. We elucidate the connection between Rényi entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

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Entanglement entropy and its quench dynamics for pure states of the Sachdev-Ye-Kitaev model

Cited by 30 publications

References 52 publications

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

Entropy linear response theory with non-Markovian bath

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

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