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arXiv:2206.14900 · Journal of High Energy Physics

Phases of $$ \mathcal{N} $$ = 2 Sachdev-Ye-Kitaev models

Matthew Heydeman, Gustavo J. Turiaci, Wen Kui Zhao

Published Jan 18, 2023• 22 citations
arXivHTMLPDF

Abstract

Abstract We study $$ \mathcal{N} $$ N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new $$ \mathcal{N} $$ N = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.

DOI
10.1007/jhep01(2023)098

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Phases of N \mathcal{N} N = 2 Sachdev-Ye-Kitaev models
Abstract We study N\mathcal{N}N N = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new N\mathcal{N}N N = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.
We study a class of Sachdev, Ye, and Kitaev (SYK) models with N = 2 supersymmetry, described by N fermions in chiral Fermi multiplets, as well as α N first-order bosons in chiral multiplets. The interactions are characterized by two integers ( p , q ) . We focus on the large N and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use I -extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large p and large p , q limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.
Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.
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.
The Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of NNN Majorana fermions which displays a number of appealing features---solvability in the strong coupling regime, near-conformal invariance and maximal chaos---which make it a suitable model for black holes in the context of the AdS/CFT\mathrm{AdS}/\mathrm{CFT}AdS/CFT holography. In this paper, we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the large-NNN expansion preserves the conformal invariance of the two-point function in the strong-coupling regime, up to the contribution of the pseudo-Goldstone bosons due to the explicit breaking of the symmetry which are already seen in the leading-order four-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models.
We study the thermodynamic properties of a two-site coupled complex qqq-body Sachdev-Ye-Kitaev (SYK) model in the large-NNN limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped, and for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is a good indicator to study the phase diagram of the model; it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with $SL(2,R)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry with an additional potential and an extra degree of freedom related to the charge. In the large NNN and low temperature limit, results from this low energy action are consistent with those from the solution of the SD equations. Likewise, a large-qqq analytical calculation of thermodynamic properties confirms the existence of the wormhole phase. Our findings are a preliminary step toward the characterization of traversable wormholes by its field theory dual, a charged strongly interacting fermionic system, that is easier to model experimentally.
We investigate the charged q/2q/2q/2-body interacting Sachdev-Ye-Kitaev (SYK) model in the grand-canonical ensemble. By treating qqq as a large parameter, we are able to analytically study its phase diagram. By varying the chemical potential or temperature, we find that the system undergoes a phase transition between low and high entropies in the maximally chaotic regime. A similar transition in entropy is seen in charged anti--de Sitter (AdS) black holes transitioning between a large and small event horizon. Approaching zero temperature, we find a first-order chaotic-to-nonchaotic quantum phase transition, where the finite extensive entropy drops to zero. This again has a gravitational analog---the Hawking-Page transition between a large black hole and thermal radiation. An analytical study of the critical phenomena associated with the continuous phase transition provides us with mean-field van der Waals critical and effective exponents. We find that all analogous power laws are shared with several charged AdS black hole phase transitions. Together, these findings indicate a connection between the charged $q\ensuremath{\rightarrow}\ensuremath{\infty}$ SYK model and black holes.