A Generalized Coherent State Framework for Many-Body Density of States

TL;DR

This paper introduces a versatile framework using generalized coherent states to compute the many-body density of states in quantum systems, enabling analysis of phase transitions and spectral properties.

Contribution

The authors develop a general, symmetry-based method for calculating the density of states and ground state bounds in high-dimensional quantum sectors, applicable to various models.

Findings

Successfully identified quantum phase transitions in the LMG model.

Validated the framework on the transverse field Ising chain with power law interactions.

Established qualitative similarity of DOS between different spin sectors.

Abstract

We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb bounds for a quantum partition function, our method provides a general method of calculation for the DOS in high-dimensional irreducible sectors. This framework further provides rigorous bounds for the ground state energy in each sector and enables the calculation of microcanonical observables across the entire spectrum. Using the Lipkin-Meshkov-Glick (LMG) model as a test bed, we validate our framework by successfully identifying quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs) across spin sectors. Unlike existing model-specific numerical or analytical techniques, our formalism relies on general underlying symmetries, making it broadly applicable. Applying our method to the ferromagnetic transverse field Ising chain with power law interactions, we demonstrate that its highest-spin-sector DOS is qualitatively identical to that of LMG-type Hamiltonians. Our work establishes a versatile and computationally efficient bridge between algebraic structure and many-body thermodynamics.