Subsystem Rényi entropy of thermal ensembles for SYK-like models

Zhang, Pengfei; Liu, Chunxiao; Chen, Xiao

doi:10.21468/scipostphys.8.6.094

Cited by 46 publications

(69 citation statements)

References 62 publications

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“…where N is a normalization constant. This distribution defines the so-called β-Jacobi ensemble (with β = 2), and has been recently exploited for the computation of averaged subsystem entanglement in the context of random non-interacting fermionic ensembles [55][56][57][58]. Note that the distribution depends on both and M .…”

Section: Figmentioning

confidence: 99%

Open Quantum Symmetric Simple Exclusion Process

Bernard

Jin

2019

Phys. Rev. Lett.

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We present the solution to a model of fermions hopping between neighbouring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the symmetric simple exclusion process. However, the full distribution encodes for a richer behaviour entailing fluctuating quantum coherences which survive in the steady limit. We determine exactly the steady statistical distribution of the system state. We show that the out of equilibrium quantum coherence fluctuations satisfy a large deviation principle and we present a method to recursively compute exactly the large deviation function. As a byproduct, our approach gives a solution of the classical symmetric simple exclusion process based on fermion technology. Our results open the route towards the extension of the macroscopic fluctuation theory to many body quantum systems.Introduction.-Non-equilibrium phenomena are ubiquitous in Nature. Understanding the fluctuations of the flux of heat or particles through systems is a central question in non equilibrium statistical mechanics. Last decade has witnessed tremendous conceptual and technical progresses in this direction for classical systems, starting from the exact analysis of simple models [1-3], such as the Symmetric Simple Exclusion Process (SSEP) [4][5][6][7], via the understanding of fluctuation relations [8][9][10] and their interplay with time reversal [11,12], and culminating in the formulation of the macroscopic fluctuation theory (MFT) which is an effective theory adapted to describe transport and its fluctuations in diffusive classical systems [13]. Whether MFT may be extended to the quantum realm is yet unexplored.In parallel, the study of quantum systems out of equilibrium has received a large amount of attention in recent years [19][20][21][22]. Experimentally, unprecedented control of cold atom gases gave access to the observation of many body quantum systems in inhomogeneous and isolated setups [14][15][16][17][18]. Theoretically, results about closed, quantum systems have recently flourished, with a better perception of the roles of integrability, chaos or disorder [23][24][25][26][27][28][29][30][31][32][33][34]. In critical or integrable models, a good understanding has been obtained with a precise description of entanglement dynamics, quenched dynamics, as well as transport [35][36][37][38][39][40][41][42][43][44][45][46]. These efforts culminated in the development of a hydrodynamic picture adapted to integrable systems [47,48]. However, these understandings are restricted to closed, predominantly ballistic, systems.Many quantum transport processes are diffusive rather than ballistic [49] and, to some extends, physical systems are generically in contact with external environments. It is thus crucial to extend the previous studies by developing simple models for fluctuations in open, quantum many body, locally diffusive, out of equilibrium systems. Putting aside the quantum nature of the environments leads to co...

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Section: Figmentioning

confidence: 99%

Open Quantum Symmetric Simple Exclusion Process

Bernard

Jin

2019

Phys. Rev. Lett.

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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%

“…There have been several numerical and analytical works on entanglement entropy [43,[63][64][65][66]72] in the SYK model for various different contexts. The analytical approaches have used standard replica path-integral approach for Rényi entropy.…”

Section: B Syk Model: Rényi Entropy Of a Non-fermi Liquidmentioning

confidence: 99%

“…[43] to look into ground-state entanglement between two quadratically coupled SYK dots. During the preparation of our paper, we became aware of a very recent work [66] on subsystem Rényi entropy in the thermal ensemble for the SYK model using a standard approach with the boundary conditions. Overall, their results compares well with our results on SYK model obtained using the field-theoretic method developed in this work.…”

Section: B Syk Model: Rényi Entropy Of a Non-fermi Liquidmentioning

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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Subsystem Rényi entropy of thermal ensembles for SYK-like models

Cited by 46 publications

References 62 publications

Open Quantum Symmetric Simple Exclusion Process

Open Quantum Symmetric Simple Exclusion Process

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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