Engineering topics

Das, Sumit R.

Publications and source records attributed to Das, Sumit R..

5 records

DOE OSTI2020

Near conformal perturbation theory in SYK type models

We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

1/N expansion↗

DOE OSTI2018

Space-time in the SYK model

We consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions. This results in a dual theory with Euclidean AdS signature with additional legfactors. As a result, we speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.

2D Gravity↗

DOE OSTI2018

Three dimensional view of arbitrary q SYK models

In [15] it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional model in AdS 2 ×S 1 /Z 2 with nontrivial boundary conditions in the additional dimension. In this paper we show that a similar picture holds for generalizations of the SYK model with q-fermion interactions. The 3D realization is now given on a space whose metric is conformal to AdS 2 × S 1 /Z 2 and is subject to a non-trivial potential in addition to a delta function at the center of the interval. It is shown that a Horava-Witten compactification reproduces the exact SYK spectrum and a non-standard propagator between points which lie at the center of the interval exactly agrees with the bilocal propagator. As q → ∞, the wave function of one of the modes at the center of the interval vanish as 1/q, while the others vanish as 1/q 2 , in a way consistent with the fact that in the SYK model only one of the modes contributes to the bilocal propagator in this limit.

1/N Expansion↗

DOE OSTI2017

An exactly solvable quench protocol for integrable spin models

Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Three dimensional view of the SYK/AdS duality

We show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS 2 , and subject to a delta function potential at the center of the interval along the third direction. This, through Kaluza-Klein procedure on AdS 2 × (S 1 )/Z 2 , generates the spectrum reproducing the bi-local propagator at strong coupling. Furthermore, the leading 1/J correction calculated in this picture reproduces the known correction to the poles of the SYK propagator, providing credence to a conjecture that the bulk dual of this model can be interpreted as a three dimensional theory.

2D Gravity↗