Integrability Breaking Quantum Chaos

---
name: integrability-breaking-quantum-chaos
description: "Quantitative theory for integrability-to-chaos transition in quantum many-body systems via tunable integrability-breaking gates. Use when analyzing OTOC crossover from integrable to chaotic regimes, computing butterfly velocity and front broadening, studying characteristic time/length scales of chaos emergence, or modeling free fermion circuits doped with non-integrable gates."
metadata:
  arxiv_id: "2607.02506"
  published: "2026-07-02"
  authors: "Sounak Biswas, Sthitadhi Roy, Roderich Moessner"
  tags: ["quantum-chaos", "OTOC", "integrability-breaking", "butterfly-velocity", "free-fermion", "many-body"]
---

# Integrability-Breaking Quantum Chaos Theory

## Core Framework

Quantitative theory for emergence of quantum many-body chaos as integrability is broken via tunable parameter. In circuit model of free fermions 'doped' with tunable density of integrability-breaking gates, microscopic mechanisms underpin crossover from early-time integrable behavior to late-time chaos.

### Key Methodology

**Pattern 1: Integrability-Breaking Gate Doping**
- Start with free fermion circuit (integrable baseline)
- Add tunable density of integrability-breaking gates as local hotspots
- Each gate locally amplifies OTOCs in spacetime neighborhood
- Accumulation of hotspots → fully-developed chaos

**Pattern 2: OTOC Crossover Analysis**
- Identify explicit characteristic time and length scales governing integrable→chaotic crossover
- Extract butterfly velocity from OTOC front propagation
- Measure front broadening as function of integrability-breaking parameter
- OTOC growth rate ∝ density of integrability-breaking gates

**Pattern 3: Scale Identification**
- **Crossover time**: when accumulated hotspots percolate through system
- **Butterfly velocity**: speed of information front propagation
- **Front broadening**: dispersion of OTOC wavefront

## Activation Keywords
- integrability breaking quantum chaos
- OTOC crossover free fermion
- butterfly velocity quantum circuit
- quantum chaos characteristic scales
- tunable integrability breaking
- quantum many-body chaos transition
- 量子多体混沌可积性破缺