# Excited-State Quantum Phase Transitions in Bosonic Lattice Systems

## TL;DR

This paper investigates the occurrence of Excited State Quantum Phase Transitions (ESQPTs) in bosonic lattice systems, especially in the boson Hubbard model, highlighting their similarities to van Hove singularities and exploring their relation to ground state quantum phase transitions.

## Contribution

It provides a detailed analysis of ESQPTs in bosonic lattice models and draws analogies with van Hove singularities, offering new insights into spectral singularities above ground state phases.

## Key findings

- Identification of spectral singularities in the boson Hubbard model
- Analogy established between ESQPTs and van Hove singularities
- Insights into the relationship between ESQPTs and ground state QPTs

## Abstract

Concentrating on bosonic lattice systems, we ask whether and how Excited State Quantum Phase Transition (ESQPT) singularities occur in condensed matter systems with ground state QPTs. We study in particular the spectral singularities above the ground-state phase diagram of the boson Hubbard model. As a general prerequisite, we point out the analogy between ESQPTs and van Hove singularities (vHss).