Author ORCID Identifier

https://orcid.org/0009-0000-1078-5348

Date Available

8-14-2024

Year of Publication

2024

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Physics and Astronomy

Advisor

Anatoly Dymarsky

Abstract

This dissertation explores quantum information, the use of codes to describe quantum field theories, and introduces new concepts to characterize the dynamics of quantum many-body systems. The contributions of this dissertation are the following: 1) We constructed Narain Conformal Field Theories (CFTs) using additive codes, where the modular bootstrap constraints translate into algebraic conditions on the codes, extending previous approaches. This helps express key CFT data, including the torus partition function, in terms of codewords. We constructed optimal Narain CFTs for small central charges, and described CFT ensembles for asymptotically large central charge with large spectral gap. 2) We studied the scaling of entanglement entropy in the ground states of fermionic chains with couplings that decay as a power law, to understand how it depends on the decay exponent. We found that disordered and translationally invariant models show qualitatively different scaling. 3) We studied the temperature dependence of Lanczos coefficients obtained from autocorrelation functions at arbitrary temperature. We formulated the temperature dependence as an integrable dynamical system, which we analyzed to identify the universal low temperature asymptotics of Lanczos coefficients. 4) We studied the signatures of quantum chaos in the Lanczos coefficients for operators and related Krylov basis, for large but finite systems. Our analysis used the relation between coarse-grained form of Lanczos coefficients and the distribution of energy gaps. We found two distinct indicators of quantum chaos, as seen through splitting of Lanczos coefficients into two branches and saturation value of Krylov complexity.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2024.393

Funding Information

The author was partially supported by the National Science Foundation under Grants No. PHY 1818878 and PHY 2013812 in 2021 and 2023, respectively.

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