arXiv subjects

Abhirup Bhattacharya

Publications and source records attributed to Abhirup Bhattacharya.

4 recordsLinked to original sources

arXiv2026

A semiclassical Hilbert space for random matrix theory

We study the one-sided time evolution of thermofield double (TFD) states in random matrix theory, where the Hamiltonian is taken to be a $D\times D$ random matrix drawn from a unitarily invariant emsemble of Hermitian matrices. We argue that the Krylov basis with the maximally entangled state taken as the initial vector gives a semiclassical Hilbert space description of these TFD states in random matrix theory at any $O(1)$ temperature and time in the $D\to \infty$ limit, very analogous to the ``chord Hilbert space'' construction in the double-scaled SYK (DSSYK) model. We study this semiclassical description in detail for ensembles where the spectral density in the $D\to \infty$ limit is even, compactly supported on an interval and has square root edges. With a few more conditions on the analytic structure of the spectral density, we observe that the semiclassical Hamiltonian has the same asymptotic behavior at large Krylov depth as that of DSSYK, with the corresponding parameter $\mathfrak{q}=e^{-λ}$ being related to the location of the nearest zero of the spectral density away from the spectral cut. Furthermore, in a large class of models corresponding to ultraviolet deformations of the DSSYK spectral density, i.e., where the spectrum in the UV is modified while leaving the near-edge behavior unchanged, we show that the semiclassical effective Hamiltonian in the Krylov basis reduces to the Liouville Hamiltonian of JT gravity in a low-energy, continuum limit. This suggests that our semiclassical Hilbert space should be interpreted as the bulk Hilbert space of a dual gravity description.

hep-th↗

arXiv2026

Stabilizer complexity and the Python's lunch

In this note, we study the stabilizer complexity of the reduced density matrix corresponding to one side of a partially entangled thermal (PET) state with fixed energy boundary conditions in a holographic CFT. In particular, we study Wigner negativity, an operationally meaningful magic monotone which can be interpreted as the complexity of classically simulating any quantum circuit preparation of the reduced state on the subregion. Using assumptions on the pseudorandomness of the CFT spectrum and the heavy operator insertion, we observe that the Wigner negativity of the PET state relative to the microcanonical density matrix at the given energy is given by $\exp\left[\frac{1}{8G_N}(A_{\text{out}} - A_{\text{min}})\right]$, where $A_{\text{out}}$ is the area of the outer extremal surface, while $A_{\text{min}}$ is the area of the minimal extremal surface. Thus, the stabilizer complexity of the reduced density matrix on the boundary subregion is $O(1)$ in the absence of a python's lunch, but gets exponentially enhanced in the presence of a python's lunch in the bulk geometry.

hep-th↗

arXiv2026

Covariant phase space and the semi-classical Einstein equation

The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical matter. In this note, we consider a generalization of this formalism to the semi-classical Einstein equation coupled to quantum matter. Given a family of solutions in semi-classical gravity, we define the semi-classical symplectic two-form -- a natural generalization of the classical sympelctic two-form -- as the sum of the gravitational symplectic form and the Berry curvature associated to the quantum state of matter. We show that the semi-classical symplectic two-form is independent of the Cauchy slice, and satisfies the quantum generalization of the classical Hollands-Iyer-Wald identity. For small perturbations, we also extend our discussion to gauge-invariantly defined subregions of spacetime, where the quantum contribution is replaced by the Berry curvature of certain special purifications involving the Connes cocycle. In the AdS/CFT context, the semi-classical symplectic form defined here is naturally dual to the Berry curvature in the boundary CFT.

hep-th↗

arXiv2026

Modular Witten Diagrams and Quantum Extremality

We study entanglement entropy for ball-shaped regions in excited states of holographic conformal field theories. The excited states are prepared by the Euclidean path integral in the CFT with a source turned on for some double-trace operator, with a small, $O(1)$ amplitude $λ$. On the gravity side, the double-trace operator deforms the bulk geometry as well as the entanglement structure of the state of bulk matter fields. By the quantum extremal surface formula, this leads to a deformation of the shape of the entanglement wedge, an effect which becomes manifest in the entanglement entropy at $O(λ^2 G_N)$. On the CFT side, we explicitly calculate the entanglement entropy perturbatively in the source amplitude to $O(λ^2)$, in terms of modular-flowed correlation functions of double-trace operators. We then evaluate these modular-flowed correlation functions using Witten diagrams. This calculation involves a Schwinger-Keldysh contour ordering prescription in the bulk, which we motivate using analytic continuation from Euclidean replica correlators. Focusing on a particular graviton-exchange diagram, we rewrite it in a form where it manifestly reproduces the canonical energy term present in the quantum Ryu-Takayanagi formula, including the shape deformation of the entanglement wedge due to backreaction and quantum effects.

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