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A bipartite Sachdev-Ye-Kitaev model: Conformal limit and finite size level statistics

Mikael Fremling, Masudul Haque, Lars Fritz

Published Nov 30, 2021• 0 citations
OpenAlex

Abstract

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-N in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite size spectral properties of the model. We show how the level statistics differs from the original SYK model, and infer an additional exchange symmetry in the bipartite model.

Related papers

Bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

Mikael Fremling, Masudul Haque, Lars Fritz

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-$N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.

arXiv:2111.15215•Physical review. D/Physical review. D.•Mar 28, 2022•6 citations

A generalization of Sachdev-Ye-Kitaev

David J. Gross, Vladimir Rosenhaus

The SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of fermions, each occupying N a sites and appearing with a q a order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global O(N 1) × O(N 2) × … × O(N f ) symmetry: a subgroup of the O(N) symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large q limit and the OPE, and solve q = 2 SYK at finite N.

arXiv:1610.01569•Journal of High Energy Physics•Feb 1, 2017•315 citations

A new class of SYK-like models with maximal chaos

Eric Marcus, Stefan Vandoren

Abstract We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the $$ \mathcal{N} $$ N = 1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M = N. As we take the limit M/N → ∞ both branches coincide and we obtain the same conformal dimensions as SYK. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.

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The Sachdev-Ye-Kitaev Model and Matter Without Quasiparticles

Wenbo Fu

This thesis is devoted to the study of Sachdev-Ye-Kitaev (SYK) models, which describe matter without quasiparticles. The SYK model is an exactly solvable model that is hoped to bring insights into the understanding of strongly correlated materials.\nThe main part discusses different aspects of SYK models. Chapter 2 presents numerical studies of the SYK models, shows its non-Fermi liquid nature and verifies the analytical predictions on two-point function and thermal entropies. Chapter 3 considers the thermodynamic and transport properties of the complex SYK models in higher dimensional generalizations, we show some universal relations obtained from SYK models which are consistent with holographic theories. Chapter 4 discusses a supersymmetric generalization of the SYK model. We show a different a scaling from the normal SYK model both analytically and numerically. We also discuss a different origin of the extensive zero temperature entropy in $\\mathcal{N}=2$ theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable $t$-$J$ model of electrons with an SYK-like form. We find a $\\mathbb{Z}_2$ fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.

•May 9, 2018•5 citations

A new class of SYK-like models with maximal chaos

Eric Marcus, Stefan Vandoren

We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the $\\mathcal{N}=1$ supersymmetric SYK model. It consists of $N$ real Majorana fermions and $M$ auxiliary bosons with Yukawa interactions. We consider the large $N$ and $M$ limit and keep the ratio $M/N$ fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio $M/N$. One of the branches contains the supersymmetric saddle for $M=N$. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of $M/N$.

•Jan 22, 2019•7 citations

Combinatorial aspects of the Sachdev-Ye-Kitaev model

Matteo Laudonio, Romain Pascalie, Adrian Tanasă

The Sachdev-Ye-Kitaev (SYK) model is a model of $q$ interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large $N$ expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in $N$. We then derive the form of the effective action to all orders.

arXiv:2001.11849•Jan 31, 2020•28 citations
We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-N in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite size spectral properties of the model. We show how the level statistics differs from the original SYK model, and infer an additional exchange symmetry in the bipartite model.
We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-NNN in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.
The SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of fermions, each occupying N a sites and appearing with a q a order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global O(N 1) × O(N 2) × … × O(N f ) symmetry: a subgroup of the O(N) symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large q limit and the OPE, and solve q = 2 SYK at finite N.
Abstract We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the N \mathcal{N} N N = 1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M = N. As we take the limit M/N → ∞ both branches coincide and we obtain the same conformal dimensions as SYK. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.
This thesis is devoted to the study of Sachdev-Ye-Kitaev (SYK) models, which describe matter without quasiparticles. The SYK model is an exactly solvable model that is hoped to bring insights into the understanding of strongly correlated materials.\nThe main part discusses different aspects of SYK models. Chapter 2 presents numerical studies of the SYK models, shows its non-Fermi liquid nature and verifies the analytical predictions on two-point function and thermal entropies. Chapter 3 considers the thermodynamic and transport properties of the complex SYK models in higher dimensional generalizations, we show some universal relations obtained from SYK models which are consistent with holographic theories. Chapter 4 discusses a supersymmetric generalization of the SYK model. We show a different a scaling from the normal SYK model both analytically and numerically. We also discuss a different origin of the extensive zero temperature entropy in mathcalN=2\\mathcal{N}=2mathcalN=2 theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable ttt-JJJ model of electrons with an SYK-like form. We find a mathbbZ2\\mathbb{Z}_2mathbbZ2​ fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.
We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the mathcalN=1\\mathcal{N}=1mathcalN=1 supersymmetric SYK model. It consists of NNN real Majorana fermions and MMM auxiliary bosons with Yukawa interactions. We consider the large NNN and MMM limit and keep the ratio M/NM/NM/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/NM/NM/N. One of the branches contains the supersymmetric saddle for M=NM=NM=N. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/NM/NM/N.
The Sachdev-Ye-Kitaev (SYK) model is a model of qqq interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large NNN expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in NNN. We then derive the form of the effective action to all orders.