arXiv subjects

Debarghya Chakraborty

Publications and source records attributed to Debarghya Chakraborty.

5 recordsLinked to original sources

arXiv2026

Krylov Complexity from Loschmidt Amplitude

Krylov complexity is a powerful diagnostic of quantum dynamics, with clear connections to other measures of quantum chaos and operator growth. One such measure is the Loschmidt amplitude, defined as the overlap of initially identical states evolved under two slightly different Hamiltonians. Its decay in certain systems is controlled by the classical Lyapunov exponent. Using the algebraic properties of the Krylov complexity operator, we express Krylov complexity as the derivative of a Loschmidt amplitude whose perturbation is parameterized by an angular variable $ϕ$. This formulation allows us to define a spectral propagator that encodes the entire complexity distribution, which we characterize for specific types of systems. We study the two-dimensional quantum geometry spanned by time and $ϕ$ where the original and deformed trajectories reside, demonstrating that Krylov complexity is upper-bounded by its volume. We also express the time derivative of Krylov complexity in terms of a distinct Loschmidt amplitude. Depending on the growth of the Lanczos coefficients, the perturbation term in this amplitude can be truncated. We propose that the strength of this perturbation provides a classification scheme for Krylov complexity dynamics and relate it to the $ϕ$-derivative of the spectral propagator. Using this analytical framework, we derive general relations between the time-dependence of the survival amplitude and Krylov space measures.

hep-th↗

arXiv2026

Revival Dynamics from Equilibrium States: Scars from Chords in SYK

We develop a novel framework to build quantum many-body scar states in bipartite systems characterized by perfect correlation between the Hamiltonians governing the two sides. By means of a Krylov construction, we build an interaction term which supports a tower of equally-spaced energy eigenstates. This gives rise to finite-time revivals whenever the system is initialized in a purification of a generic equilibrium state. The dynamics is universally characterized, and is largely independent of the specific details of the Hamiltonians defining the individual partitions. By considering the two-sided chord states of the double-scaled SYK model, we find an approximate realization of this framework. We analytically study the revival dynamics, finding rigid motion for wavepackets localized on the spectrum of a single SYK copy. These findings are tested numerically for systems of finite size, showing excellent agreement with the analytical predictions.

cond-mat.str-el↗

arXiv2025

Temperature dependence in Krylov space

We consider the recursion method applied to a generic 2pt function of a quantum system and show, in full generality, that the temperature dependence of the corresponding Lanczos coefficients is governed by integrable dynamics. After an appropriate change of variables, Lanczos coefficients with even and odd indices are described by two independent Toda chains, related at the level of the initial conditions. Consistency of the resulting equations can be used to show that certain scale-invariant models necessarily have a degenerate spectrum. We dub this self-consistency-based approach the ''Krylov bootstrap''. The known analytic behavior of the Toda chain at late times translates into analytic control over the 2pt function and Krylov complexity at very low temperatures. We also discuss the behavior of Lanczos coefficients when the temperature is low but not much smaller than the spectral gap, and elucidate the origin of the staggering behavior of Lanczos coefficients in this regime.

hep-th↗

arXiv2024

Entanglement Entropy in Ground States of Long-Range Fermionic Systems

We study the scaling of ground state entanglement entropy of various free fermionic models on one dimensional lattices, where the hopping and pairing terms decay as a power law. We seek to understand the scaling of entanglement entropy in generic models as the exponent of the power law $α$ is varied. We ask if there exists a common $α_{c}$ across different systems governing the transition to area law scaling found in local systems. We explore several examples numerically and argue that when applicable, the scaling of entanglement entropy in long-range models is constrained by predictions from the low-energy theory. In contrast, disordered models and models without a continuum limit show fractal scaling of entanglement approaching volume-law behavior as $α$ approaches zero. These general features are expected to persist on turning on interactions.

cond-mat.str-el↗

arXiv2022

Optimal Narain CFTs from Codes

Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities. We generalize previous constructions to include many new theories, in particular we show that all known optimal Narain theories, i.e. those maximizing the value of spectral gap, can be constructed from codes. For asymptotically large central charge $c$ we show there are code theories with the spectral gap growing linearly with $c$, with the coefficient saturating the conjectural upper bound. We therefore conjecture that optimal Narain theories for any value of $c$ can be obtained from codes.

hep-th↗