Doctoral Dissertations
Date of Award
8-2025
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Physics
Major Professor
Adrian Del Maestro
Committee Members
Steve Johnston, Elbio Dagotto, Vasileios Maroulas
Abstract
One-dimensional quantum matter, like the Wonderland that astonished Alice, breaks the paradigms of higher-dimensional physics: quasiparticles fragment, spin and charge decouple, and correlations exhibit universal power-law decay. The emergent low-energy theory of these systems is the Tomonaga–Luttinger liquid (TLL). In this thesis, we study the \emph{$n$-particle entanglement entropy}—the entropy obtained by tracing out $N-n$ particles in a system of $N$ identical fermions. This entropy is sensitive to particle statistics, interactions, and proximity to phase transitions, yet independent of external length scales or basis choice. Because it can be computed from experimentally accessible $n$-point correlation functions, it offers a powerful probe of many-body correlations and entanglement.
Combining bosonization with large-scale density matrix renormalization group (DMRG) simulations, we extend prior studies on particle entanglement. In \autoref{ch:scaling}, we propose and verify a scaling form for the Rényi $n$-particle entropy in an interacting model, identifying universal contributions and subleading corrections. In \autoref{ch:2rdm}, we obtain a closed-form expression for the equal-time four-point function in a fermionic TLL, clarifying the microscopic origins of the entropy scaling. Diagonal elements recover known density correlations, while off-diagonal terms encode particle entanglement for $n>1$.
We then examine nonequilibrium dynamics in \autoref{ch:quench}, deriving the time-dependent one-particle entropy following an interaction quench. We show that strong coupling alters the entanglement spectrum and modifies late-time decay exponents. In \autoref{ch:fluctuations}, we turn to bosonic systems and analyze particle number fluctuations in the Bose–Hubbard model. By fitting DMRG and Quantum Monte Carlo data to bosonization predictions, we extract the Luttinger parameter $K$ and resolve the long-standing location of the Berezinskii–Kosterlitz–Thouless transition. Our finite-size RG scaling reveals the critical point $(U/J)_C$ with high precision.
Together, these results deepen our understanding of entanglement scaling and dynamics in one dimension, and bridge the gap between low-energy field theory and microscopic models. Extensions include finite-temperature effects, spinful systems, and particle entanglement in bosons — promising further adventures down the one-dimensional rabbit hole.
Recommended Citation
Radhakrishnan, Harini, "Alice in 1D-Land: Fluctuations and particle entanglement in one-dimensional systems of identical particles. " PhD diss., University of Tennessee, 2025.
https://trace.tennessee.edu/utk_graddiss/12758