@article {jian_note_2021, title = {Note on entropy dynamics in the {Brownian} {SYK} model}, journal = {J. High Energy Phys.}, number = {3}, year = {2021}, note = {Place: ONE NEW YORK PLAZA, SUITE 4600, NEW YORK, NY, UNITED STATES Publisher: SPRINGER Type: Article}, month = {mar}, abstract = {We study the time evolution of Renyi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The Renyi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of Renyi entropy, respectively.}, keywords = {AdS-CFT Correspondence, Black Holes, Nonperturbative Effects, Random Systems}, issn = {1029-8479}, doi = {10.1007/JHEP03(2021)042}, author = {Jian, Shao-Kai and Swingle, Brian} } @article {winer_exponential_2020, title = {Exponential {Ramp} in the {Quadratic} {Sachdev}-{Ye}-{Kitaev} {Model}}, journal = {Phys. Rev. Lett.}, volume = {125}, number = {25}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {dec}, abstract = {

A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.250602}, author = {Winer, Michael and Jian, Shao-Kai and Swingle, Brian} } @article {jian_landau_2020, title = {Landau poles in condensed matter systems}, journal = {Phys. Rev. Res.}, volume = {2}, number = {2}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {jun}, abstract = {The existence or not of Landau poles is one of the oldest open questions in nonasymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the phi(4) theory. We find that the irrelevant but symmetry-allowed couplings, such as the phi(6) potential, can significantly change the fate of the Landau pole in the emergent phi(4) theory. We obtain the coupled beta functions of a phi(4) + phi(6) potential at both small and large orders. Already from the one-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a phi(6) term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in a very different system: Dirac fermions in 2 + 1 dimensions with long-range Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to two loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a pure bosonic phi(4) theory, and consequently graphene is free from Landau poles if the pure (4) theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.}, doi = {10.1103/PhysRevResearch.2.023310}, author = {Jian, Shao-Kai and Barnes, Edwin and Das Sarma, Sankar} }