We compare different limits of the Sachdev-Ye-Kitaev model of $\textit{N}$ complex fermion with $\textit{p}$-fermion interactions. First, we compute the fermion Green’s function and free energy in the limit of large $\textit{N}$ followed subsequently by the limit of large $\textit{p}$. Next, we examine the ‘double-scaling’ limit in which the large $\textit{N}$, $\textit{p}$ limits are taken at fixed $\textit{λ}$ = $\textit{p}$ /$\textit{N}$. Earlier results on the latter limit are resummed for small $\textit{λ}$, and shown to match our results for the first limit. We also describe the holographic match of our results to two-dimensional Jackiw-Teitelboim gravity with an additional U(1) gauge field.

United States

Elena Gubankova

Subir Sachdev

Grigory Tarnopolsky

Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry

In this work we study the quark-meson model within a real-time formulation of the functional renormalization group (FRG) on the Schwinger-Keldysh contour. First, we discuss in detail the symmetry of thermal equilibrium for the fermionic sector of the Keldysh action. We take into account dissipation for the bosonic degrees of freedom in the spirit of the Caldeira-Leggett model by coupling the system to an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> invariant external heat bath. We study the effect of dissipation on static equilibrium properties, most prominently on the FRG flow of the effective potential and thus on the resulting phase diagram. We find that, unlike in classical systems, through the contributions from nonzero Matsubara modes the dissipative dynamics can in general have an effect on static observables. We investigate these effects within two phenomenological models for the temperature dependence of the pion damping to verify that they are quantitatively small. To estimate their largest possible influence, we consider limits where the damping constants approach infinity.

Germany

Johannes V. Roth

Yunxin Ye

Sören Schlichting

Lorenz von Smekal

Effects of dissipation on phase diagram and bosonic excitations in the quark-meson model

This paper presents a systematic study of hyperon non-leptonic two-body decays induced by light quark transitions, particularly the $ s \rightarrow u\bar{u}d $ process, within the framework of $\textit{SU}$(3) flavor symmetry. The effective weak Hamiltonian is decomposed into irreducible $\textit{SU}$(3) representations, including the 27-plet and octet components, and applied to analyze decays of octet and decuplet baryons and charmed baryons. Both the irreducible representation amplitude (IRA) approach and the topological diagrammatic analysis (TDA) are employed to construct decay amplitudes and constrain the parameter space. $\textit{SU}$(3) symmetry-breaking effects arising from the strange quark mass are incorporated systematically. A global fit to current experimental data allows us to extract form factors and predict branching ratios and asymmetry parameters for several decay channels. Our results demonstrate the predictive power of $\textit{SU}$(3) flavor symmetry while highlighting significant symmetry-breaking effects, especially in amplitudes related to the 27-plet. Notably, the $ \Sigma^+ \rightarrow p\pi^0 $ decay channel exhibits a deviation exceeding $ 1\sigma $ from experimental measurements, suggesting the possible presence of new decay mechanisms or contributions beyond the Standard Model. Besides, we also evaluate the size of symmetry breaking. However, the large uncertainty of the experimental data makes it difficult to precisely determine the value of symmetry breaking. We strongly recommend that future experimental efforts aim to reduce the measurement uncertainties, especially for the processes $ \Lambda^0\to p\pi^- $ and $ \Lambda^0\to n\pi^0 $ , which have larger experimental errors compared to other data and play an important role in determining the symmetry breaking parameter. This study provides a systematic framework for future tests of the Standard Model and the search for new physics in hyperon decays.

China

Xin Wu

Qi Chen

Ye Xing

Zhi-Peng Xing

Ruilin Zhu

$\textit{SU}$(3) flavor symmetry analysis of hyperon non-leptonic two body decays * Ruilin Zhu is supported by NSFC (12322503, 12075124) and the Natural Science Foundation of Jiangsu (BK20211267). Zhi-Peng Xing is supported by NSFC (12375088, 12335003, 12405113). Ye Xing is supported by NSFC (12005294)

Inspired by recent developments in the study of the model of double scaled SYK (DSSYK), as elucidated in a recent paper, we embark on a re-evaluation of the Sachdev-Ye-Kitaev (SYK) model. Our motivation stems from the insights gained from the DSSYK model, particularly its ability to capture essential features of quantum dynamics and gravitational effects. In this work, we delve into the SYK model, uncovering precise solutions for the two-point function and self-energy that have not been previously reported. Building upon the advancements made in particle physics phenomenology, we extend the SYK model to encompass tensor field theory. Through the incorporation of a cutoff term to ensure convergence, we substantially advance our understanding of quantum many-body physics. Our investigation extends to experimental parameter estimation and the exploration of cutoff dependency in random couplings, providing invaluable insights into system dynamics. The introduction of a novel tensor field theory replaces conventional fermionic degrees of freedom with tensorial counterparts, leading to the discovery of intriguing phase transition phenomena characterized by a first-order transition. Furthermore, we elucidate a direct linear relationship between the coupling parameter and the cutoff scale. These findings not only shed light on emergent behavior across both high-energy physics and condensed matter systems but also pave the way for further theoretical and experimental exploration, inspired by the recent advancements in the SYK model.

South Africa

Davood Momeni

Unveiling novel insights in quantum dynamics through extended Sachdev-Ye-Kitaev model

We use a novel real-time formulation of the functional renormalization group (FRG) for dynamical systems with reversible mode couplings to study model H, the conjectured dynamic universality class of the quantum chromodynamics (QCD) critical point. We emphasize the structural similarities with model G, conjectured to be the dynamic universality class of the chiral phase transition in the limit of two massless quark flavors. Importantly, our formulation of the real-time FRG preserves all relevant symmetries throughout the FRG flow which, e.g., guarantees the nonrenormalization of the reversible mode couplings, as but one exact result. We derive nonperturbative RG flow equations for the kinetic coefficients of both, model G and H, in parallel, and discuss commonalities and differences in the resulting fixed-point structure and dynamic critical exponents, such as weak-scaling relations which hold in either case versus the characteristic strong scaling of model G which is absent in model H.

Universal critical dynamics near the chiral phase transition and the QCD critical point

The study of chaos and complexity in non-Hermitian quantum systems poses significant challenges due to the emergence of complex eigenvalues in their spectra. Recently, the singular value decomposition (SVD) method was proposed to address these challenges. In this work, we identify two critical shortcomings of the SVD approach when analyzing Krylov complexity and spectral statistics in non-Hermitian settings. First, we show that SVD fails to reproduce conventional eigenvalue statistics in the Hermitian limit for systems with nonpositive definite spectra, as exemplified by a variant of the Sachdev-Ye-Kitaev (SYK) model. Second, and more fundamentally, Krylov complexity and spectral statistics derived via SVD cannot distinguish chaotic from integrable non-Hermitian dynamics, leading to results that conflict with complex spacing ratio analysis. Our findings reveal that SVD is inadequate for probing quantum chaos in non-Hermitian systems, and we advocate employing more robust methods, such as the bi-Lanczos algorithm, for future research in this direction.

Matteo Baggioli

Kyoung-Bum Huh

Spain

Hyun-Sik Jeong

Xuhao Jiang

South Korea

Keun-Young Kim

Juan F. Pedraza

Singular value decomposition and its blind spot for quantum chaos in non-Hermitian Sachdev-Ye-Kitaev models

The collective dynamics around the second-order $\textit{O}$(4) chiral phase transition in QCD with two massless quark flavors can be understood by appealing to universality. We present a novel formulation of the real-time functional renormalization group (FRG) that describes the stochastic hydrodynamic equations of motion for systems in the same dynamic universality class, which corresponds to Model G in the Halperin-Hohenberg classification. Our approach preserves all relevant symmetries of such systems with reversible mode couplings, which establishes the real-time FRG as a valuable tool complementary to classical-statistical simulations. As a first application we show that our approach is consistent with dynamic scaling relations and reproduces the non-trivial value $\textit{z}$ = $\textit{d/}$2 for the dynamic critical exponent in $\textit{d}$ spatial dimensions. Moreover, we extract a novel dynamic scaling function that describes the universal momentum and temperature dependence of the diffusion coefficient of iso-(axial-)vector charge densities in the symmetric phase.

Johannes Roth

Lorenz Smekal

Dynamic critical behavior of the chiral phase transition from the real-time functional renormalization group

We study thermodynamic phase transitions between integrable and chaotic dynamics. We do so by analyzing models that interpolate between the chaotic double scaled Sachdev-Ye-Kitaev (SYK) and the integrable <math><mi>p</mi></math>-spin systems, in a limit where they are described by chord diagrams. We develop a path integral formalism by coarse graining over the diagrams, which we use to argue that the system has two distinct phases: one is continuously connected to the chaotic system, and the other to the integrable. They are separated by a line of first order transition that ends at some finite temperature.

Israel

Micha Berkooz

Nadav Brukner

Yiyang Jia

Italy

Ohad Mamroud

From Chaos to Integrability in Double Scaled Sachdev-Ye-Kitaev Model via a Chord Path Integral

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

Belgium

Sergio Aguilar-Gutierrez

Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model

The saturation of a recently proposed universal bound on the Lyapunov exponent has been conjectured to signal the existence of a gravity dual. This saturation occurs in the low-temperature limit of the dense Sachdev-Ye-Kitaev (SYK) model, <math><mi>N</mi></math> Majorana fermions with <math><mi>q</mi></math> body (<math><mi>q</mi><mo>&gt;</mo><mn>2</mn></math>) infinite-range interactions. We calculate certain out-of-time-order correlators (OTOCs) for <math><mi>N</mi><mo>≤</mo><mn>64</mn></math> fermions for a highly sparse SYK model and find no significant dependence of the Lyapunov exponent on sparsity up to near the percolation limit where the Hamiltonian breaks up into blocks. This provides strong support to the saturation of the Lyapunov exponent in the low-temperature limit of the sparse SYK. A key ingredient to reaching <math><mi>N</mi><mo>=</mo><mn>64</mn></math> is the development of a novel quantum spin model simulation library that implements highly optimized matrix-free Krylov subspace methods on graphical processing units. This leads to a significantly lower simulation time as well as vastly reduced memory usage over previous approaches, while using modest computational resources. Strong sparsity-driven statistical fluctuations require both the use of a much larger number of disorder realizations with respect to the dense limit and a careful finite size scaling analysis. The saturation of the bound in the sparse SYK points to the existence of a gravity analog that would enlarge substantially the number of field theories with this feature.

Antonio M. García-García

Chang Liu

Jacobus J. M. Verbaarschot

Sparsity-Independent Lyapunov Exponent in the Sachdev-Ye-Kitaev Model