Real-time dynamics from convex geometry

TL;DR

This paper explores how convex geometry can be used to analyze and constrain the real-time dynamics of quantum systems, overcoming traditional computational challenges like sign problems and ill-posed analytic continuation.

Contribution

It introduces a systematic approach leveraging convex geometry to study quantum real-time dynamics, extending methods used in conformal bootstrap and ground state physics.

Findings

Efficiently explores low-dimensional projections of high-dimensional convex spaces.

Provides a framework to constrain quantum real-time evolution.

Addresses challenges posed by sign problems and analytic continuation.

Abstract

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of exponential (e.g.~in volume) dimension, but low-dimensional projections can be efficiently explored by standard algorithms. Such approaches have been used to precisely constrain critical exponents of conformal field theories ("conformal bootstrap") and, more recently, to constrain the ground state physics of various quantum-mechanical systems, including lattice field theories. In this talk we discuss related approaches to systematically constraining the real-time dynamics of quantum systems, which are otherwise obstructed from study by sign problems and the ill-posed nature of analytic continuation.