Exact Yrast Spectra of Cold Atoms on a Ring

TL;DR

This paper develops an analytical method to construct and analyze excited states with fixed angular momentum in finite one-dimensional bosonic systems on a ring, revealing near-degenerate energy groups and connections to conformal field theories.

Contribution

It introduces a systematic approach to derive exact yrast and excited states energies using system-size asymptotic expansion and dressed energy, linking supercurrent states to conformal field theories.

Findings

Excited states with fixed angular momentum are constructed analytically.

Energy levels form almost degenerate groups.

Low-lying spectrum matches conformal field theory predictions.

Abstract

We propose a methodology to construct excited states with a fixed angular momentum, namely, "yrast excited states" of finite-size one-dimensional bosonic systems with periodic boundary conditions. The excitation energies such as the first yrast excited energy are calculated through the system-size asymptotic expansion and expressed analytically by dressed energy. Interestingly, they are grouped into sets of almost degenerate energy levels. The low-lying excitation spectrum near the yrast state is consistent with the $ U(1)$ conformal field theories if the total angular momentum is given by an integral multiple of particle number; i.e., if the system is supercurrent.